diff --git a/.github/workflows/continued-kappa-research.yml b/.github/workflows/continued-kappa-research.yml new file mode 100644 index 0000000000..bcc90e948b --- /dev/null +++ b/.github/workflows/continued-kappa-research.yml @@ -0,0 +1,22 @@ +name: Verify shared entrance gauge construction +on: + pull_request: + paths: + - 'research/coordinated-crossover-pr200/**' + - '.github/workflows/continued-kappa-research.yml' + workflow_dispatch: +permissions: + contents: read +jobs: + immutable-offline: + runs-on: ubuntu-24.04 + timeout-minutes: 45 + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 + with: + python-version: '3.14' + - run: python3 -B research/coordinated-crossover-pr200/verify.py + - run: git diff --exit-code diff --git a/.github/workflows/verify.yml b/.github/workflows/verify.yml index bc1741b08f..e36fcba356 100644 --- a/.github/workflows/verify.yml +++ b/.github/workflows/verify.yml @@ -83,3 +83,19 @@ jobs: run: lake exe cache get - name: Check formal package and theorem axiom dependencies run: make formal-${{ matrix.package }}-verify + + plateau-certificate: + if: github.event_name == 'workflow_dispatch' + runs-on: ubuntu-24.04 + timeout-minutes: 45 + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 + with: + python-version: '3.14' + - name: Rebuild the committed PR210 plateau search and replay its full certificate + run: python3 -B research/coordinated-crossover-pr200/verify.py --temp-root /tmp + - name: Require reproducible certificate artifacts + run: git diff --exit-code diff --git a/research/balanced-nullity-banks-163/AUDIT-TARGETS.json b/research/balanced-nullity-banks-163/AUDIT-TARGETS.json new file mode 100644 index 0000000000..31acd84088 --- /dev/null +++ b/research/balanced-nullity-banks-163/AUDIT-TARGETS.json @@ -0,0 +1,54 @@ +[ + "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_apply", + "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_zero", + "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_comp_disjoint", + "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_involutive", + "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_id", + "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_commute", + "Mathproof.BeyondNLogN.TakeoverBit.bankSwap_eq_sum", + "Mathproof.BeyondNLogN.TakeoverBit.bankSwap_full", + "Mathproof.BeyondNLogN.TakeoverBit.weighted_apply", + "Mathproof.BeyondNLogN.TakeoverBit.weighted_comp", + "Mathproof.BeyondNLogN.TakeoverBit.weighted_id", + "Mathproof.BeyondNLogN.TakeoverBit.weightedBank_eq", + "Mathproof.BeyondNLogN.TakeoverBit.weightedBank_full", + "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_apply", + "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_idempotent", + "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_disjoint", + "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_sum", + "Mathproof.BeyondNLogN.TakeoverBit.coordinateBank_full", + "Mathproof.BeyondNLogN.TakeoverBit.bankAddress_bijective", + "Mathproof.BeyondNLogN.TakeoverBit.bankAddress_roles_injective", + "Mathproof.BeyondNLogN.TakeoverBit.P12.selected_block_capacity", + "Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_block_capacity", + "Mathproof.BeyondNLogN.TakeoverBit.P12.selected_bank_full", + "Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_bank_full", + "Mathproof.BeyondNLogN.TakeoverBit.P12.inherited_rank_mass", + "Mathproof.BeyondNLogN.TakeoverBit.P12.removed_exterior_count", + "Mathproof.BeyondNLogN.TakeoverBit.P12.packed_rank_mass", + "Mathproof.BeyondNLogN.TakeoverBit.P12.packed_max_rank", + "Mathproof.BeyondNLogN.TakeoverBit.P12.normalized_volume", + "Mathproof.BeyondNLogN.TakeoverBit.P12.packed_deficit", + "Mathproof.BeyondNLogN.TakeoverBit.P12.actual_role_counts", + "Mathproof.BeyondNLogN.TakeoverBit.P12.selected_weighted_bank_full", + "Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_weighted_bank_full", + "Mathproof.BeyondNLogN.TakeoverBit.Contents.run_eq_address", + "Mathproof.BeyondNLogN.TakeoverBit.Contents.run_full", + "Mathproof.BeyondNLogN.TakeoverBit.Contents.p12_selected_contents", + "Mathproof.BeyondNLogN.TakeoverBit.Contents.p12_undeferred_contents", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.inherited_rank_mass", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.removed_exterior_count", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_rank_mass", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_max_rank", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.normalized_volume", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_deficit", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.actual_role_counts", + "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.actual_bank_and_inventory_certificate", + "Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.literal_charge_lt", + "Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.finite_row_reserve", + "Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.row_reserve_value", + "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.core_slacks_positive", + "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.all_47_slacks_positive", + "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.strengthened_public_margin", + "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.all_47_concrete_guards" +] diff --git a/research/balanced-nullity-banks-163/BankAndBalanced.lean b/research/balanced-nullity-banks-163/BankAndBalanced.lean new file mode 100644 index 0000000000..b681bd7acf --- /dev/null +++ b/research/balanced-nullity-banks-163/BankAndBalanced.lean @@ -0,0 +1,625 @@ +/- Publication snapshot: actual bank endpoints and conditional finite arithmetic only. -/ +import Mathlib.LinearAlgebra.Prod +import Mathlib.Tactic.Abel +import Mathlib.Algebra.BigOperators.Group.List.Defs +import Mathlib.Data.List.Pairwise +import Mathlib.Data.List.FinRange +import Mathlib.Data.Fintype.Card +import Mathlib.Data.Nat.Basic +import Mathlib.Tactic.NormNum +import Mathlib.Tactic.FinCases +import Mathlib.Tactic.GCongr +import Mathlib.Tactic.Linarith +import Mathlib.Tactic.Positivity +import Mathlib.Data.Real.Basic +import Mathlib.Tactic.NormNum + + +/-! Exact partial bit address interchanges for split-projector bank packing. +No supplier, routing, recurrence, precision, or tape theorem is assumed here. -/ +namespace Mathproof.BeyondNLogN.TakeoverBit + +variable {R V : Type*} [CommRing R] [AddCommGroup V] [Module R V] + +/-- Exchange the P-address component between two arbitrary incoming banks. -/ +def partialSwap (P : V →ₗ[R] V) : (V × V) →ₗ[R] (V × V) where + toFun z := (z.1 - P z.1 + P z.2, z.2 - P z.2 + P z.1) + map_add' a b := by + apply Prod.ext <;> simp only [Prod.fst_add, Prod.snd_add, map_add] <;> abel + map_smul' r z := by + apply Prod.ext <;> simp only [Prod.smul_fst, Prod.smul_snd, map_smul, + RingHom.id_apply, smul_add, smul_sub] + +@[simp] theorem partialSwap_apply (P : V →ₗ[R] V) (z : V × V) : + partialSwap P z = (z.1 - P z.1 + P z.2, z.2 - P z.2 + P z.1) := rfl + +@[simp] theorem partialSwap_zero : partialSwap (0 : V →ₗ[R] V) = LinearMap.id := by + apply LinearMap.ext + intro z + simp + +/-- Every disjoint projector pair composes by adding its exchanged components. +The incoming pair is arbitrary, so correlated dirty contents are included. -/ +theorem partialSwap_comp_disjoint (P Q : V →ₗ[R] V) + (hPQ : P.comp Q = 0) (hQP : Q.comp P = 0) : + (partialSwap P).comp (partialSwap Q) = partialSwap (P + Q) := by + have hpq (z : V) : P (Q z) = 0 := by + simpa using LinearMap.congr_fun hPQ z + have hqp (z : V) : Q (P z) = 0 := by + simpa using LinearMap.congr_fun hQP z + apply LinearMap.ext + intro z + rcases z with ⟨x,y⟩ + apply Prod.ext <;> + simp only [LinearMap.comp_apply, partialSwap_apply, map_add, map_sub, + LinearMap.add_apply, hpq] <;> abel + +/-- A completed split-projector core is its own exact inverse. -/ +theorem partialSwap_involutive (P : V →ₗ[R] V) (hP : P.comp P = P) : + Function.Involutive (partialSwap P) := by + have hpp (z : V) : P (P z) = P z := by + simpa using LinearMap.congr_fun hP z + intro z + rcases z with ⟨x,y⟩ + apply Prod.ext <;> simp only [partialSwap_apply, map_add, map_sub, hpp] <;> abel + +@[simp] theorem partialSwap_id (z : V × V) : + partialSwap (LinearMap.id : V →ₗ[R] V) z = (z.2,z.1) := by + simp + +/-- Split-projector factors commute at the actual address-map level. -/ +theorem partialSwap_commute (P Q : V →ₗ[R] V) + (hPQ : P.comp Q = 0) (hQP : Q.comp P = 0) : + (partialSwap P).comp (partialSwap Q) = + (partialSwap Q).comp (partialSwap P) := by + rw [partialSwap_comp_disjoint P Q hPQ hQP, + partialSwap_comp_disjoint Q P hQP hPQ, add_comm] + + + + +/-- Execute completed cores in any explicit chronological bank schedule. -/ +def bankSwap : List (V →ₗ[R] V) → ((V × V) →ₗ[R] (V × V)) + | [] => LinearMap.id + | P :: Ps => (partialSwap P).comp (bankSwap Ps) + +private theorem comp_sum_zero (P : V →ₗ[R] V) (Ps : List (V →ₗ[R] V)) + (h : ∀ Q ∈ Ps, P.comp Q = 0) : P.comp Ps.sum = 0 := by + induction Ps with + | nil => simp + | cons Q Ps ih => + have hQ := h Q (by simp) + have ht : ∀ A ∈ Ps, P.comp A = 0 := fun A hA => h A (by simp [hA]) + simp only [List.sum_cons, LinearMap.comp_add, hQ, ih ht, zero_add] + +private theorem sum_comp_zero (P : V →ₗ[R] V) (Ps : List (V →ₗ[R] V)) + (h : ∀ Q ∈ Ps, Q.comp P = 0) : Ps.sum.comp P = 0 := by + induction Ps with + | nil => simp + | cons Q Ps ih => + have hQ := h Q (by simp) + have ht : ∀ A ∈ Ps, A.comp P = 0 := fun A hA => h A (by simp [hA]) + simp only [List.sum_cons, LinearMap.add_comp, hQ, ih ht, zero_add] + +/-- A whole shared bank executes exactly the swap on the sum of its disjoint +address blocks. The statement is on every input, not only clean scratch. -/ +theorem bankSwap_eq_sum (Ps : List (V →ₗ[R] V)) + (h : Ps.Pairwise (fun P Q => P.comp Q = 0 ∧ Q.comp P = 0)) : + bankSwap Ps = partialSwap Ps.sum := by + induction Ps with + | nil => simp [bankSwap] + | cons P Ps ih => + rcases List.pairwise_cons.mp h with ⟨hp, ht⟩ + rw [bankSwap, ih ht, List.sum_cons] + exact partialSwap_comp_disjoint P Ps.sum + (comp_sum_zero P Ps (fun Q hQ => (hp Q hQ).1)) + (sum_comp_zero P Ps (fun Q hQ => (hp Q hQ).2)) + +/-- A complete split partition needs no exterior auxiliary child. -/ +theorem bankSwap_full (Ps : List (V →ₗ[R] V)) + (h : Ps.Pairwise (fun P Q => P.comp Q = 0 ∧ Q.comp P = 0)) + (hsum : Ps.sum = LinearMap.id) (z : V × V) : + bankSwap Ps z = (z.2,z.1) := by + rw [bankSwap_eq_sum Ps h, hsum] + exact partialSwap_id z + +/-- One common ancestor-dependent weighted chart, retained for the whole bank. -/ +def weighted (A : (V × V) ≃ₗ[R] (V × V)) + (T : (V × V) →ₗ[R] (V × V)) : (V × V) →ₗ[R] (V × V) := + A.toLinearMap.comp (T.comp A.symm.toLinearMap) + +@[simp] theorem weighted_apply (A : (V × V) ≃ₗ[R] (V × V)) + (T : (V × V) →ₗ[R] (V × V)) (z : V × V) : + weighted A T z = A (T (A.symm z)) := rfl + +/-- Chart conjugations telescope exactly, with no restriction on dirty data. -/ +theorem weighted_comp (A : (V × V) ≃ₗ[R] (V × V)) + (T U : (V × V) →ₗ[R] (V × V)) : + (weighted A T).comp (weighted A U) = weighted A (T.comp U) := by + apply LinearMap.ext + intro z + simp + +@[simp] theorem weighted_id (A : (V × V) ≃ₗ[R] (V × V)) : + weighted A (LinearMap.id : (V × V) →ₗ[R] (V × V)) = LinearMap.id := by + apply LinearMap.ext + intro z + simp + +def weightedBank (A : (V × V) ≃ₗ[R] (V × V)) : + List (V →ₗ[R] V) → ((V × V) →ₗ[R] (V × V)) + | [] => LinearMap.id + | P :: Ps => (weighted A (partialSwap P)).comp (weightedBank A Ps) + +/-- Every paid weighted core is retained in its chronological product. -/ +theorem weightedBank_eq (A : (V × V) ≃ₗ[R] (V × V)) + (Ps : List (V →ₗ[R] V)) : weightedBank A Ps = weighted A (bankSwap Ps) := by + induction Ps with + | nil => simp [weightedBank, bankSwap] + | cons P Ps ih => + rw [weightedBank, ih, weighted_comp, bankSwap] + +/-- Heterogeneous completed-core packing has the exact full weighted endpoint. -/ +theorem weightedBank_full (A : (V × V) ≃ₗ[R] (V × V)) + (Ps : List (V →ₗ[R] V)) + (h : Ps.Pairwise (fun P Q => P.comp Q = 0 ∧ Q.comp P = 0)) + (hsum : Ps.sum = LinearMap.id) (z : V × V) : + weightedBank A Ps z = A ((A.symm z).2,(A.symm z).1) := by + rw [weightedBank_eq, weighted_apply, bankSwap_full Ps h hsum] + + + +section CoordinateBanks +variable {ι κ : Type*} [DecidableEq ι] + +/-- Explicit split address blocks from an actual coordinate-owner ledger. -/ +def coordinateProjector (owner : κ → ι) (s : ι) : + (κ → R) →ₗ[R] (κ → R) where + toFun v k := if owner k = s then v k else 0 + map_add' v w := by + funext k + by_cases h : owner k = s <;> simp [h] + map_smul' r v := by + funext k + by_cases h : owner k = s <;> simp [h] + +@[simp] theorem coordinateProjector_apply (owner : κ → ι) (s : ι) + (v : κ → R) (k : κ) : + coordinateProjector (R := R) owner s v k = if owner k = s then v k else 0 := rfl + +theorem coordinateProjector_idempotent (owner : κ → ι) (s : ι) : + (coordinateProjector (R := R) owner s).comp (coordinateProjector (R := R) owner s) = + coordinateProjector (R := R) owner s := by + apply LinearMap.ext + intro v + funext k + by_cases h : owner k = s <;> simp [h] + +theorem coordinateProjector_disjoint (owner : κ → ι) (s t : ι) (hst : s ≠ t) : + (coordinateProjector (R := R) owner s).comp (coordinateProjector (R := R) owner t) = 0 := by + apply LinearMap.ext + intro v + funext k + by_cases h : owner k = s + · have ht : owner k ≠ t := by simpa [h] using hst + simp [h,hst] + · simp [h] + +private theorem coordinateProjector_sum_apply (owner : κ → ι) + (roles : List ι) (hroles : roles.Nodup) (v : κ → R) (k : κ) : + (roles.map (coordinateProjector (R := R) owner)).sum v k = + if owner k ∈ roles then v k else 0 := by + induction roles with + | nil => simp + | cons s roles ih => + rcases List.nodup_cons.mp hroles with ⟨hs, ht⟩ + simp only [List.map_cons, List.sum_cons, LinearMap.add_apply, Pi.add_apply, + coordinateProjector_apply, ih ht, List.mem_cons] + by_cases he : owner k = s + · have hn : owner k ∉ roles := by simpa [he] using hs + simp [he,hs] + · simp [he] + +/-- A disjoint exhaustive coordinate ledger gives an actual identity projector. -/ +theorem coordinateProjector_sum (owner : κ → ι) (roles : List ι) + (hroles : roles.Nodup) (hcover : ∀ k, owner k ∈ roles) : + (roles.map (coordinateProjector (R := R) owner)).sum = LinearMap.id := by + apply LinearMap.ext + intro v + funext k + rw [coordinateProjector_sum_apply owner roles hroles v k] + simp [hcover k] + +/-- The concrete coordinate-owner construction supplies every projector premise +of the heterogeneous bank endpoint, including arbitrary incoming correlations. -/ +theorem coordinateBank_full (owner : κ → ι) (roles : List ι) + (hroles : roles.Nodup) (hcover : ∀ k, owner k ∈ roles) + (z : (κ → R) × (κ → R)) : + bankSwap (roles.map (coordinateProjector (R := R) owner)) z = (z.2,z.1) := by + apply bankSwap_full + · rw [List.pairwise_map] + exact (List.nodup_iff_pairwise_ne.mp hroles).imp (fun hst => + ⟨coordinateProjector_disjoint owner _ _ hst, + coordinateProjector_disjoint owner _ _ (Ne.symm hst)⟩) + · exact coordinateProjector_sum owner roles hroles hcover + +end CoordinateBanks + +section Routing +variable {G S : Type*} [Group G] + +/-- Actual bank address for invocation g and fixed role embedding H_s. -/ +def bankAddress (H : S → G) (g : G) (s : S) : G := g * (H s)⁻¹ + +/-- Every role visits every physical bank once; no favorable subset is selected. -/ +theorem bankAddress_bijective (H : S → G) (s : S) : + Function.Bijective (fun g => bankAddress H g s) := by + constructor + · intro g g' h + exact mul_right_cancel h + · intro b + refine ⟨b * H s, ?_⟩ + simp [bankAddress, mul_assoc] + +/-- Distinct role embeddings rule out within-invocation physical aliasing. -/ +theorem bankAddress_roles_injective (H : S → G) (hH : Function.Injective H) + (g : G) : Function.Injective (bankAddress H g) := by + intro s t h + apply hH + have hi : (H s)⁻¹ = (H t)⁻¹ := mul_left_cancel h + exact inv_injective hi + +end Routing +end Mathproof.BeyondNLogN.TakeoverBit + + + + + +/-! Concrete PR155 p12 bit orbit-bank construction and complete paid ledger. +The inherited all-input local word, stage cover and routing contracts remain +explicit upstream dependencies; this file proves the new address endpoints, +coordinate capacities and exact inventory, not an all-size running-time claim. -/ +namespace Mathproof.BeyondNLogN.TakeoverBit.P12 +open Mathproof.BeyondNLogN.TakeoverBit + +variable {R : Type*} [CommRing R] + +/-- The 18 actual disjoint four-coordinate blocks for retained-gauge cores. -/ +def selectedOwner (j : Fin 72) : Fin 18 := ⟨j.val / 4, by omega⟩ + +/-- The three actual disjoint 24-coordinate blocks for undeferred cores. -/ +def undeferredOwner (j : Fin 72) : Fin 3 := ⟨j.val / 24, by omega⟩ + +theorem selected_block_capacity (s : Fin 18) : + (Finset.univ.filter (fun j : Fin 72 => selectedOwner j = s)).card = 4 := by + fin_cases s <;> decide + +theorem undeferred_block_capacity (s : Fin 3) : + (Finset.univ.filter (fun j : Fin 72 => undeferredOwner j = s)).card = 24 := by + fin_cases s <;> decide + +/-- Eighteen completed selected cores cover the entire address module. -/ +theorem selected_bank_full (z : (Fin 72 → R) × (Fin 72 → R)) : + bankSwap ((List.finRange 18).map (coordinateProjector (R := R) selectedOwner)) z = + (z.2,z.1) := by + exact coordinateBank_full selectedOwner (List.finRange 18) + (List.nodup_finRange 18) (fun k => by simp) z + +/-- Three completed undeferred cores also cover the entire address module. -/ +theorem undeferred_bank_full (z : (Fin 72 → R) × (Fin 72 → R)) : + bankSwap ((List.finRange 3).map (coordinateProjector (R := R) undeferredOwner)) z = + (z.2,z.1) := by + exact coordinateBank_full undeferredOwner (List.finRange 3) + (List.nodup_finRange 3) (fun k => by simp) z + +/-- Every child in the immutable freshly replayed p12 profile, including rank60. -/ +def inheritedHistogram : List (Nat × Nat) := + [(1,120468),(2,68080),(3,28824),(4,7200),(5,11952),(6,3312), + (7,6120),(8,4464),(9,1440),(10,2016),(11,2664),(12,3528), + (13,1944),(14,2736),(15,1152),(16,4104),(17,6192),(18,5832), + (19,4536),(20,7260),(21,8580),(22,15912),(60,5720)] + +/-- The actual coordinate-full orbit banks remove precisely auxiliary exteriors; +all internal, source, target, center and data exterior entries remain charged. -/ +def packedHistogram : List (Nat × Nat) := + inheritedHistogram.filter (fun p => p.1 != 60) + +def rankMass (H : List (Nat × Nat)) : Nat := + (H.map (fun p => p.1*p.2)).sum + +theorem inherited_rank_mass : rankMass inheritedHistogram = 2096432 := by decide + +theorem removed_exterior_count : + (inheritedHistogram.filter (fun p => p.1 == 60)).map Prod.snd = [5720] := by decide + +theorem packed_rank_mass : rankMass packedHistogram = 1753232 := by decide + +theorem packed_max_rank : ∀ p ∈ packedHistogram, p.1 ≤ 22 := by decide + +/-- Three private stage banks for every full orbit, including fractional stock. -/ +def normalizedVolume : ℚ := 2*1760 + 3*((5720:ℚ)/18 + (19904:ℚ)/3) + +theorem normalized_volume : normalizedVolume = 73132/3 := by + norm_num [normalizedVolume] + +theorem packed_deficit : (72:ℚ)*normalizedVolume - rankMass packedHistogram = 1936 := by + rw [packed_rank_mass, normalized_volume] + norm_num + +theorem actual_role_counts : + 5720 + 19904 = (25624:Nat) ∧ 18*4 = (72:Nat) ∧ 3*24 = (72:Nat) := by decide + + + + +/-- The actual common weighted chart retains the selected-bank full endpoint. -/ +theorem selected_weighted_bank_full + (A : ((Fin 72 → R) × (Fin 72 → R)) ≃ₗ[R] ((Fin 72 → R) × (Fin 72 → R))) + (z : (Fin 72 → R) × (Fin 72 → R)) : + weightedBank A ((List.finRange 18).map (coordinateProjector (R := R) selectedOwner)) z = + A ((A.symm z).2,(A.symm z).1) := by + rw [weightedBank_eq, weighted_apply, selected_bank_full] + +/-- The same exact weighted endpoint holds for every undeferred bank. -/ +theorem undeferred_weighted_bank_full + (A : ((Fin 72 → R) × (Fin 72 → R)) ≃ₗ[R] ((Fin 72 → R) × (Fin 72 → R))) + (z : (Fin 72 → R) × (Fin 72 → R)) : + weightedBank A ((List.finRange 3).map (coordinateProjector (R := R) undeferredOwner)) z = + A ((A.symm z).2,(A.symm z).1) := by + rw [weightedBank_eq, weighted_apply, undeferred_bank_full] + +end Mathproof.BeyondNLogN.TakeoverBit.P12 + + + +/-! Lift the checked address maps to actual arbitrary register contents. +No clean-scratch or independence assumption occurs in these statements. -/ +namespace Mathproof.BeyondNLogN.TakeoverBit.Contents +open Mathproof.BeyondNLogN.TakeoverBit + +variable {R V B : Type*} [CommRing R] [AddCommGroup V] [Module R V] + +/-- Chronological execution on the complete contents of a physical bank. -/ +def run : List (V →ₗ[R] V) → ((V × V) → B) → ((V × V) → B) + | [], contents => contents + | P :: Ps, contents => run Ps (fun z => contents (partialSwap P z)) + +theorem run_eq_address (Ps : List (V →ₗ[R] V)) (contents : (V × V) → B) + (z : V × V) : run Ps contents z = contents (bankSwap Ps z) := by + induction Ps generalizing contents with + | nil => rfl + | cons P Ps ih => + simp only [run, ih, bankSwap, LinearMap.comp_apply] + +/-- A complete split partition executes the full transform on every dirty table. -/ +theorem run_full (Ps : List (V →ₗ[R] V)) + (h : Ps.Pairwise (fun P Q => P.comp Q = 0 ∧ Q.comp P = 0)) + (hsum : Ps.sum = LinearMap.id) (contents : (V × V) → B) (z : V × V) : + run Ps contents z = contents (z.2,z.1) := by + rw [run_eq_address, bankSwap_full Ps h hsum] + +/-- The actual p12 selected orbit bank works for arbitrary full bank contents. -/ +theorem p12_selected_contents + (contents : ((Fin 72 → R) × (Fin 72 → R)) → B) + (z : (Fin 72 → R) × (Fin 72 → R)) : + run ((List.finRange 18).map (coordinateProjector (R := R) P12.selectedOwner)) contents z = + contents (z.2,z.1) := by + rw [run_eq_address, P12.selected_bank_full] + +/-- The actual p12 undeferred orbit bank has the same unconditional endpoint. -/ +theorem p12_undeferred_contents + (contents : ((Fin 72 → R) × (Fin 72 → R)) → B) + (z : (Fin 72 → R) × (Fin 72 → R)) : + run ((List.finRange 3).map (coordinateProjector (R := R) P12.undeferredOwner)) contents z = + contents (z.2,z.1) := by + rw [run_eq_address, P12.undeferred_bank_full] + +end Mathproof.BeyondNLogN.TakeoverBit.Contents + + + +/-! Immutable PR161 p12 bank specialization. The actual coordinate-owner, +weighted-chart and dirty-content endpoints are reused from the independently +checked P12 construction; only the new frozen supplier inventory is specialized. +The retained all-input local word, charts, stage cover, routing, fallback and +sharp all-size framework are upstream contracts, not proved by this ledger. -/ +namespace Mathproof.BeyondNLogN.TakeoverBit.PR161P12 +open Mathproof.BeyondNLogN.TakeoverBit + +/-- Complete child inventory from immutable PR161 head +`d14e29157bc905be1ced0776dd893d0714013f3a`, profile_p12.json. -/ +def inheritedHistogram : List (Nat × Nat) := + [(1,120972),(2,73336),(3,29832),(4,8208),(5,12096),(6,4392), + (7,4824),(8,2736),(9,648),(10,2160),(11,2016),(12,4464), + (13,1080),(14,2232),(15,216),(16,2808),(17,2736),(18,3888), + (19,3672),(20,7260),(21,8580),(22,15912),(60,5720)] + +/-- Eighteen actual four-coordinate selected cores cover Fin72, so their +auxiliary rank60 exterior is removed; all other children remain charged. -/ +def packedHistogram : List (Nat × Nat) := + inheritedHistogram.filter (fun p => p.1 != 60) + +/-- Three stage banks, with selected roles grouped eighteen at a time and +undeferred roles grouped three at a time. -/ +def normalizedVolume : ℚ := 2*1760 + 3*((5720:ℚ)/18 + (17648:ℚ)/3) + +theorem inherited_rank_mass : P12.rankMass inheritedHistogram = 1934000 := by decide + +theorem removed_exterior_count : + (inheritedHistogram.filter (fun p => p.1 == 60)).map Prod.snd = [5720] := by decide + +theorem packed_rank_mass : P12.rankMass packedHistogram = 1590800 := by decide + +theorem packed_max_rank : ∀ p ∈ packedHistogram, p.1 ≤ 22 := by decide + +theorem normalized_volume : normalizedVolume = 66364/3 := by + norm_num [normalizedVolume] + +theorem packed_deficit : + (72:ℚ)*normalizedVolume - P12.rankMass packedHistogram = 1936 := by + rw [packed_rank_mass, normalized_volume] + norm_num + +theorem actual_role_counts : + 5720 + 17648 = (23368:Nat) ∧ 18*4 = (72:Nat) ∧ 3*24 = (72:Nat) := by decide + +/-- New source binding assembled with actual reused coordinate projectors; +no new abstract packing gadget or independence of register contents is assumed. -/ +theorem actual_bank_and_inventory_certificate + {R : Type*} [CommRing R] (z : (Fin 72 → R) × (Fin 72 → R)) : + (∀ s : Fin 18, (Finset.univ.filter + (fun j : Fin 72 => P12.selectedOwner j = s)).card = 4) ∧ + (∀ s : Fin 3, (Finset.univ.filter + (fun j : Fin 72 => P12.undeferredOwner j = s)).card = 24) ∧ + bankSwap ((List.finRange 18).map + (coordinateProjector (R := R) P12.selectedOwner)) z = (z.2,z.1) ∧ + bankSwap ((List.finRange 3).map + (coordinateProjector (R := R) P12.undeferredOwner)) z = (z.2,z.1) ∧ + normalizedVolume = 66364/3 ∧ + P12.rankMass packedHistogram = 1590800 ∧ + (72:ℚ)*normalizedVolume - P12.rankMass packedHistogram = 1936 := by + exact ⟨P12.selected_block_capacity, P12.undeferred_block_capacity, + P12.selected_bank_full z, P12.undeferred_bank_full z, + normalized_volume, packed_rank_mass, packed_deficit⟩ + +end Mathproof.BeyondNLogN.TakeoverBit.PR161P12 + + + +/-! The finite literal guard is discharged by an elementary universal charge +bound. No positive-guard oracle is used. The condition s ≤ mW is the ordinary +rank-mass bound of a finite supplier, not an unknown algorithm interface. -/ +namespace Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008 + +theorem literal_charge_lt (W m G s : ℝ) + (hW : 0 ≤ W) (hm : 0 ≤ m) (hG : 0 ≤ G) (hs : s ≤ m*W) : + 2*G*W*W+8*s+4*W+4+32*m < 64*(W+m+G+1)^3 := by + let X := W+m+G+1 + have hX : 1 ≤ X := by dsimp [X]; linarith + have hX0 : 0 ≤ X := by linarith + have hWX : W ≤ X := by dsimp [X]; linarith + have hmX : m ≤ X := by dsimp [X]; linarith + have hGX : G ≤ X := by dsimp [X]; linarith + have hcube : 0 < X^3 := by positivity + have hquad : X ≤ X^2 := by nlinarith + have hquad_cube : X^2 ≤ X^3 := by + have hp := mul_nonneg (show 0 ≤ X-1 by linarith) (sq_nonneg X) + nlinarith + have hfirst : 2*G*W*W ≤ 2*X*X*X := by gcongr + have hsecond : m*W ≤ X*X := by gcongr + have hlarge : 2*G*W*W+8*s+4*W+4+32*m ≤ 50*X^3 := by + nlinarith + dsimp [X] at hlarge hcube + linarith + +theorem finite_row_reserve : (0 : ℝ) < 70000-(51*12320/25) := by norm_num + +theorem row_reserve_value : (70000-(51*12320/25) : ℝ) = 224336/5 := by norm_num + + +end Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008 + + + +/- Source-bound arithmetic for PR163 paid balanced transfer and our new nullity-bank refinement. + This is not a formalization of all-size integer multiplication. -/ +namespace Mathproof.BeyondNLogN.TakeoverBalanced16320261009 +noncomputable def a : ℝ := (297370240363722999999999702129759636277/500000000000000000000000000000000000000000) +noncomputable def b : ℝ := (297370240363723/500000000000000000) +noncomputable def eta : ℝ := (1/1000000000000000000000000) +noncomputable def beta : ℝ := (1/1000000000000000000000000) +noncomputable def kappa : ℝ := (118877394946471/200000000000000000) +noncomputable def tau : ℝ := 1-a +noncomputable def sigma : ℝ := 1-b +noncomputable def q : ℝ := a*(1-2*eta) +noncomputable def c : ℝ := q+eta/4 +noncomputable def eps : ℝ := (1-eta)/(1+q) +noncomputable def lp : ℝ := 1-q +noncomputable def lam : ℝ := (tau+lp)/2 +noncomputable def g : ℝ := eps*q +noncomputable def r : ℝ := (g+1-eps)/2 +noncomputable def delta : ℝ := eta/8 +noncomputable def internal : ℝ := tau+(1-beta)*max (sigma-tau) 0 +noncomputable def leaf : ℝ := sigma+beta*(1-sigma) +noncomputable def coreSlacks : List ℝ := [ + (a) /- bit_positive -/, + (b-a) /- complex_above_bit -/, + (1/32-b) /- complex_below_one_over32 -/, + (beta) /- beta_positive -/, + (1-beta) /- beta_below_one -/, + ((1-beta)*b-a) /- leaf_saving_above_bit -/, + (q) /- q_positive -/, + (1-internal-q) /- q_below_internal -/, + (1-leaf-q) /- q_below_leaf -/, + (c) /- c_positive -/, + (1-c) /- c_below_one -/, + (c-q) /- q_below_reservations -/, + (lam-tau) /- lambda_above_tau -/, + (lam-sigma) /- lambda_above_sigma -/, + (lam-internal) /- lambda_above_internal -/, + (lp-lam) /- lambda_prime_above_lambda -/, + (lp-leaf) /- compact_leaf -/, + (lp-(1-c)) /- compact_reservations -/, + (q) /- lambda_prime_below_one -/, + (eps) /- epsilon_positive -/, + (1-eps) /- epsilon_below_one -/, + (1-eps) /- guard_width -/, + (1-eps*(1+c)) /- K_geometry -/, + (eps*c) /- K_dominates_log -/, + (1-eps) /- record_suffix -/, + (1-eps-delta) /- phase_local -/, + (r-delta) /- phase_boundary -/, + (1-eps-r) /- gamma_sublinear -/, + (eps-(1-r)/2) /- cell_above_band -/, + (1-eps) /- prime_interval_packing -/, + (r) /- alpha_positive -/, + (1-r) /- alpha_below_one -/, + (1/4-r) /- alpha_below_one_fourth -/, + (delta) /- delta_positive -/, + (1/8-delta) /- delta_below_one_eighth -/, + (eps-a) /- short_record_fallback -/, + (1-eps-g) /- small_field_exposure -/, + (8-eps+r-delta-g) /- artificial_boundary -/, + ((1-eps)-kappa) /- paid_balanced_prefix_above_kappa -/, + ((a)-kappa) /- coordinate_movement_above_kappa -/, + ((g)-kappa) /- compact_phase_layer_above_kappa -/, + ((a)-kappa) /- bulk_exposure_above_kappa -/, + ((min (1-eps-delta) (r-delta))-kappa) /- Gaussian_arithmetic_above_kappa -/, + ((1-eps-delta)-kappa) /- scalar_work_above_kappa -/, + ((eps)-kappa) /- dimension_above_kappa -/ +] +theorem core_slacks_positive : ∀ x ∈ coreSlacks, 0 < x := by + norm_num [coreSlacks, a, b, eta, beta, kappa, tau, sigma, q, c, eps, lp, lam, g, r, delta, internal, leaf] + +theorem all_47_slacks_positive (literal row : ℝ) + (hl : 0 < literal) (hr : 0 < row) : + ∀ x ∈ coreSlacks ++ [literal, row], 0 < x := by + intro x hx + rcases List.mem_append.mp hx with h | h + · exact core_slacks_positive x h + · simp only [List.mem_cons, List.not_mem_nil, or_false] at h + rcases h with h | h + · simpa [h] using hl + · simpa [h] using hr + +theorem strengthened_public_margin : + (148492550769873/250000000000000000 : ℝ) < kappa ∧ kappa < g := by + norm_num [kappa, g, eps, c, q, a, eta] + +/-- Complete arithmetic composition of our certified bit bank with the +pinned PR163 paid balanced transfer physical complex supplier. All finite guards are proved, subject +only to explicit nonnegative counts and their standard rank-mass bound. +This theorem does not claim the retained analytic/tape interfaces. -/ +theorem all_47_concrete_guards (W m G s : ℝ) + (hW : 0 ≤ W) (hm : 0 ≤ m) (hG : 0 ≤ G) (hs : s ≤ m*W) : + ∀ x ∈ coreSlacks ++ + [64*(W+m+G+1)^3-(2*G*W*W+8*s+4*W+4+32*m), + 70000-(51*12320/25)], 0 < x := by + apply all_47_slacks_positive + · exact sub_pos.mpr + (Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.literal_charge_lt + W m G s hW hm hG hs) + · exact Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.finite_row_reserve + +end Mathproof.BeyondNLogN.TakeoverBalanced16320261009 diff --git a/research/balanced-nullity-banks-163/LICENSE b/research/balanced-nullity-banks-163/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/balanced-nullity-banks-163/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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No personal author name has been added by this package. +Upstream framework: OpenAI integer multiplication manuscript; Douglas Colkitt/CrocSwap. +PR161 annealed modules, paired word and signed merging: eumemic, with Anthropic Claude assistance. +Paired-cube decoder, shared ledger and pricing: icekylinx/William Porter. +Full lineage remains in the pinned PR161 NOTICE and SOURCES.json. +PR163 fused supplier and adapter: chafreaky; paid layout lineage PR23/29 (Zhihao Chen), RaD, +PR34 (James Chang), PR100/103 (Rohan Arun), and retained PR141 arithmetic body. +Bit local words and completed-core sharing retain their PR161 attribution, including +an664 PR128, eumemic PR117, and Zhihao Chen/Swapnil Jain PR97. +This contribution claims the displayed nullity-bank refinement and composition only, +not authorship of upstream suppliers, balanced layout, or the all-size framework. +Apache-2.0. Consult the pinned upstream notices for full attribution. diff --git a/research/balanced-nullity-banks-163/PROOF-ORIGINS.json b/research/balanced-nullity-banks-163/PROOF-ORIGINS.json new file mode 100644 index 0000000000..884821366c --- /dev/null +++ b/research/balanced-nullity-banks-163/PROOF-ORIGINS.json @@ -0,0 +1,32 @@ +[ + { + "filename": "TakeoverBit20261008.lean", + "sha256": "7f5d05001824fd59c4070be55786151777a03972499092b2222c5b673f8bbe0a", + "change": "proof bodies unchanged; imports removed and hoisted" + }, + { + "filename": "TakeoverBit20261008P12.lean", + "sha256": "52ae9bca980c634fcc206f94832a5b72ace2a47609e1d57c663424347d2944c4", + "change": "proof bodies unchanged; imports removed and hoisted" + }, + { + "filename": "TakeoverBit20261008Contents.lean", + "sha256": "8b9e75c1ab67d210e9a6385577c9ca965ccc42c930f5279e2ab2e23e96cc2664", + "change": "proof bodies unchanged; imports removed and hoisted" + }, + { + "filename": "TakeoverBit16120261008P12.lean", + "sha256": "2ea23c607c23a2590660f588b18eb9f3525d58f9ac6b9461a30331002ed18aae", + "change": "proof bodies unchanged; imports removed and hoisted" + }, + { + "filename": "TakeoverLiteralGuard20261008.lean", + "sha256": "8fe9acaccb68ff70eb43d308f0a8b34f38119779ba3514a35078d3a4348d47c6", + "change": "imports removed and hoisted; obsolete original-layout assembly wrapper omitted from literal guard" + }, + { + "filename": "TakeoverBalanced16320261009.lean", + "sha256": "ce2087d53c07e07324556e06e4a4b940905db137b4c723291a77bb2aae511fd7", + "change": "proof bodies unchanged; imports removed and hoisted" + } +] diff --git a/research/balanced-nullity-banks-163/PROOF.md b/research/balanced-nullity-banks-163/PROOF.md new file mode 100644 index 0000000000..f83a8192e0 --- /dev/null +++ b/research/balanced-nullity-banks-163/PROOF.md @@ -0,0 +1,64 @@ +# PR163 paid-balanced review and actual combination with our bit engine + +Pinned source: chafreaky/integer-mult-bounds e1813796ef5c3ca38c5dd7b9e8d81b3908ff5997, research/paired-cube-balanced-161. Full finite package replay is owned by the physical/PUBLIC lane. This lane read PROOF.md, the full reference ORIGINAL-PROOF.md, balanced_shared.py, shared_bridge.py, certificate.py, complex/prove.py and the fused verifier's exact signed decoder/frame checks. + +## New certified arithmetic point + +Use the pinned PR163 fused complex supplier b=297370240363723/(5*10^17) and our previously checked PR161 p12 completed-core nullity-sharing uniform-bit supplier. The latter's exact constants are + + coarse = 302618322217 / 500000000000000, + atom = 302446903 / 500000000000, + old = 384599 / 10^10, + A = (1-atom)*coarse + atom*old + = 151223451172976757106049 / 250000000000000000000000000. + +The paid atom inequalities A0 is RETAINED. This is not permission to delete the old prefix bill without providing the positional router. The existing completed ordinary supplier must expose the arbitrary-width interchange/complete-spectator/restored-row contract; the exact complex supplier must expose the completed tensor contract. Those are the explicit all-size interfaces assumed by this conditional combination. + +With c=q+eta/4, r=(g+1-epsilon)/2 and delta=eta/8, exact arithmetic gives + + 1-epsilon-g=eta, + 1-epsilon-r=eta/2, + 1-epsilon*(1+c)=eta-epsilon*eta/4 >0. + +The internal complex exponent and stopping-leaf exponent stay unchanged. Since a<(1-beta)*b, the leaf-ordering gap is strict. The tiny positive backoffs establish eventual asymptotic inequalities, not a usable practical input threshold. + +## Full fixed-tape / scalar / row bills retained + +The public fused word has scalar_R=15681, physical_R=13041, reuse_pairs=2640, c=19385, q=3157, matched=6861, M_operations=33746. The normalized complex inventory has m66,W15681,rank1033626,deficit1320,maxchild20. Compared with161, the rank mass is unchanged but the complete child histogram changes; that is why its strict complex moment improves. The scalar word and compensation counts are not replaced by the smaller physical role stock. + +Our replay recomputes the full |O(66,2)| group factor, complete local literal scalar bound, logical bill, finite router guard, E, B=s+E and C0=32*66*B^2. Its local scalar bill matches the exact source-bound physical scalar_bound field. The full group factor cancels only in normalized moments, never in scalar work, routing or row stock. + +The row validator retains both conservative external reserves9909 and252, the full complex wire-bit count2159, row coefficient12320, polynomial degree70000 and positive degree gap224336/5. Internally borrowed/restored q-adic rows are not reinterpreted as free external stock. The odd divisor remains3, scalar denominators divide6, children retain incoming odd exponents and no child boundary rounding is introduced. + +Replacing PR163's bit frame refinement by our already checked bit supplier does not change the complex finite bridge, complex scalar bill or physical word. It changes only the validated bit_uniform coarse/atom/ordinary fields. The strengthened bit construction and compatible weighted local-ring implementation are separate source-bound inputs; this arithmetic replay does not assert them from a numeric exponent. + +## Exact complex fused-broadcast phases + +The fused source combines signed channels feeding the SAME target before readout. For a singleton target T=(I,b0,b1,b2), the three last contributions are + + P/2 + (2*b0-1)Q/2 + (2*b1-1)R/2. + +Repeated application of our independently verified TakeoverMerge16120261008.decoder_merge gives exactly + + (P+(2*b0-1)Q+(2*b1-1)R)/2. + +This equality holds in every actual complex module. An actual common complex-linear frame transports it exactly by decoder_merge_common_frame; no scalar phase is discarded or inferred merely from a binary symplectic label. Signed additions are undone in literal reverse order. Conservative original-source supports are unioned and never shrunk by cancellation. The face2, edge02 and edge12 source-cube intersection classes are disjoint, so iterative disjoint_merge_support proves exact support preservation. The actual fused verifier checks every signed source/target coefficient, value span, common cap and chronological chain. + +The original22 complex/P18 certificates and11 merge certificates remain unchanged and reusable. P18 fourth-root Fourier/Gauss identities certify phase energy under their displayed hypotheses; they do not supply the fused histogram, paid positional router or new exponent by themselves. + +## Explicit conditional boundary + +The exact finite arithmetic point is established. General Clifford lifts and actual phase reconciliation, common generic bases, uniform weighted local-ring compilation, arbitrary-width routing, complete row/spectator restoration, positional layout applicability, prime supply, precision/recovery, uniform setup and analytic fixed-tape transfer remain inherited all-size proof contracts. No unconditional multiplication theorem, fully closed Lean multiplier root, or general optimality result is claimed here. The next-grid failure concerns only this fixed supported margin. diff --git a/research/balanced-nullity-banks-163/README.md b/research/balanced-nullity-banks-163/README.md new file mode 100644 index 0000000000..ee29fa8a62 --- /dev/null +++ b/research/balanced-nullity-banks-163/README.md @@ -0,0 +1,78 @@ +# Conditional paid-balanced transfer with nullity banks + +Under the explicitly retained all-size contracts, this composition supports +`T(n) = O(n (log n)^(1-kappa))` with + + kappa = 118877394946471 / 200000000000000000 + = 0.000594386974732355. + +This is about 0.0702% above pinned PR163's 0.000593970203079492. +It combines PR163's fused complex supplier and paid balanced positional transfer +with the PR161 completed-core nullity-bank bit refinement. Gains are not added. +The resulting supported saving is complex-limited. + +## What changes + +For PR161's bit word, eighteen explicit four-coordinate blocks and three explicit +24-coordinate blocks each partition Fin72. Applying completed-core bank sharing +removes exactly 5720 rank60 exterior children while retaining all other children. +The normalized volume is 66364/3, rank mass 1590800, deficit 1936, maximum child22. +The paid bit moment and positive atom toll yield ordinary saving +151223451172976757106049 / 250000000000000000000000000, +which clears the PR163 complex supplier. The full scalar, router, group and row +bills are retained; all47 strict constraints and seven margins pass. + +## Reproduce exact arithmetic (Python3.11+, standard library; assertions enabled) + +Obtain two separate source snapshots at these immutable commits: + +- PR161: https://github.com/eumemic/integer-mult-bounds , commit + d14e29157bc905be1ced0776dd893d0714013f3a. +- PR163: https://github.com/chafreaky/integer-mult-bounds , commit + e1813796ef5c3ca38c5dd7b9e8d81b3908ff5997. + +The verifier requires Git checkouts pinned to those exact commits, with unchanged +tracked sources. A reviewer can acquire them using Git; the submitter can upload +this folder using GitHub's website without using Git locally. + + python3 -B research/balanced-nullity-banks-163/verify.py --pr161 /path/to/pr161 --pr163 /path/to/pr163 + +The verifier does not download or modify sources. It reconstructs the packed +ledger, proves the finite coordinate partitions by enumeration, recomputes the +bit moment using two interval implementations, checks its adjacent-grid control, +recomputes the PR163 complex moment, and replays the unchanged paid-balanced +assembly and full finite bill against expected.json. It rejects the next final +10^-18 grid point at these fixed certificates and parameters. This is not a claim +of global optimality. The verifier checks arithmetic; it does not substitute for +upstream physical-word verification. + +## Lean scope + +BankAndBalanced.lean is a single-file Mathlib-importing snapshot of existing +proof bodies: actual split-projector address interchanges, explicit partitions, +weighted endpoints, arbitrary dirty-content semantics, PR161 packed inventory, +and the47 finite arithmetic guards. See PROOF-ORIGINS.json for provenance. +It does not assert an all-size multiplication theorem. The bit inventory theorem +is proved alongside actual bank endpoints; connecting them to the full physical +multiplier still uses the contracts below, not merely the histogram arithmetic. +The Lean version is4.33.0. The compatible Mathlib commit is +`db584cd6d46c92f209a44c0f1c829460d327499d`. VERIFICATION.json records the +independent source replay and axiom audit. In that Mathlib environment, run +`lake env lean research/balanced-nullity-banks-163/BankAndBalanced.lean`. +The52 audited theorem names are listed in AUDIT-TARGETS.json. + +## Dependency and publication scope + +This is an additive research package. It depends on the unmerged PR161/PR163 +snapshots above and changes no existing source. A PR to CrocSwap/main should +explicitly state those dependencies; it does not silently import their entire +diffs or claim they are already merged. + +The completed all-input word, split-frame charts, invocation/stage cover, +weighted local-ring implementation, arbitrary-width complete-spectator routing, +borrowed-row restoration, paid layout applicability, precision/recovery, +prime supply, uniform setup and sharp fixed-tape analytic transfer remain +inherited all-size contracts. PROOF.md states these boundaries. This is a +conditional finite witness, not a fully formalized unconditional multiplier. + +See NOTICE and LICENSE for attribution. diff --git a/research/balanced-nullity-banks-163/VERIFICATION.json b/research/balanced-nullity-banks-163/VERIFICATION.json new file mode 100644 index 0000000000..26b13611da --- /dev/null +++ b/research/balanced-nullity-banks-163/VERIFICATION.json @@ -0,0 +1,400 @@ +{ + "status": "PASS", + "source_sha256": "8f32bce76e47da3c6165ea94f179ddf351ed50271996ab179505f588333b5867", + "kernel_replay_exit_code": 0, + "theorem_count": 52, + "axiom_records": [ + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_apply", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_zero", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_comp_disjoint", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_involutive", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_id", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.partialSwap_commute", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.bankSwap_eq_sum", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.bankSwap_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.weighted_apply", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.weighted_comp", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.weighted_id", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.weightedBank_eq", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.weightedBank_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_apply", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_idempotent", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_disjoint", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_sum", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.coordinateBank_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.bankAddress_bijective", + "axioms": [ + "propext" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.bankAddress_roles_injective", + "axioms": [ + "propext" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.selected_block_capacity", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_block_capacity", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.selected_bank_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_bank_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.inherited_rank_mass", + "axioms": [ + "propext" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.removed_exterior_count", + "axioms": [] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.packed_rank_mass", + "axioms": [ + "propext" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.packed_max_rank", + "axioms": [] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.normalized_volume", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.packed_deficit", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.actual_role_counts", + "axioms": [] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.selected_weighted_bank_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_weighted_bank_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.Contents.run_eq_address", + "axioms": [ + "propext", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.Contents.run_full", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.Contents.p12_selected_contents", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.Contents.p12_undeferred_contents", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.inherited_rank_mass", + "axioms": [ + "propext" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.removed_exterior_count", + "axioms": [] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_rank_mass", + "axioms": [ + "propext" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_max_rank", + "axioms": [] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.normalized_volume", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_deficit", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.actual_role_counts", + "axioms": [] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBit.PR161P12.actual_bank_and_inventory_certificate", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.literal_charge_lt", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.finite_row_reserve", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.row_reserve_value", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.core_slacks_positive", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.all_47_slacks_positive", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.strengthened_public_margin", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + { + "theorem": "Mathproof.BeyondNLogN.TakeoverBalanced16320261009.all_47_concrete_guards", + "axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + } + ], + "allowed_axioms": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "forbidden_axiom_count": 0, + "sorry_count": 0, + "imports": "Mathlib only", + "lean_version": "4.33.0", + "mathlib_commit": "db584cd6d46c92f209a44c0f1c829460d327499d", + "independent_replay_sha256": "4a843d015dd3fa5daa696fcea6beca654a52ef0773720e979928cdfaa605c512", + "log_sha256": "d4b24c5a28ebe4db51f41fba151500fa4c0ce4a739069e0cc1fc180b8d2117e4", + "portable_arithmetic_replay": { + "status": "PASS", + "kappa": "118877394946471/200000000000000000", + "decimal": "0.000594386974732355", + "strict_constraints": 47, + "margins": 7, + "bit_mass": 1590800, + "bit_volume": "66364/3", + "scope": "Exact conditional finite arithmetic plus ledger and coordinate partitions; full physical realization and all-size inherited contracts are separate." + }, + "arithmetic_log_sha256": "393570c538268eb8ef36dd89a007861a7c4e6a6c7782f5fdd0c060e99bc37df0", + "scope": "Actual universal bank/address/content endpoints, explicit inventory and finite balanced arithmetic. Does not certify all-size multiplication or discharge retained implementation/analytic contracts." +} diff --git a/research/balanced-nullity-banks-163/arithmetic-replay.log b/research/balanced-nullity-banks-163/arithmetic-replay.log new file mode 100644 index 0000000000..f543fe4f7a --- /dev/null +++ b/research/balanced-nullity-banks-163/arithmetic-replay.log @@ -0,0 +1,10 @@ +{ + "status": "PASS", + "kappa": "118877394946471/200000000000000000", + "decimal": "0.000594386974732355", + "strict_constraints": 47, + "margins": 7, + "bit_mass": 1590800, + "bit_volume": "66364/3", + "scope": "Exact conditional finite arithmetic plus ledger and coordinate partitions; full physical realization and all-size inherited contracts are separate." +} diff --git a/research/balanced-nullity-banks-163/expected.json b/research/balanced-nullity-banks-163/expected.json new file mode 100644 index 0000000000..ac35a985d5 --- /dev/null +++ b/research/balanced-nullity-banks-163/expected.json @@ -0,0 +1,203 @@ +{ + "public163_pin": "e1813796ef5c3ca38c5dd7b9e8d81b3908ff5997", + "public161_pin": "d14e29157bc905be1ced0776dd893d0714013f3a", + "public163_kappa": "148492550769873/250000000000000000", + "combo": { + "kappa": "118877394946471/200000000000000000", + "a": "297370240363722999999999702129759636277/500000000000000000000000000000000000000000", + "actual_bit_saving": "151223451172976757106049/250000000000000000000000000", + "complex_saving": "297370240363723/500000000000000000", + "beta": "1/1000000000000000000000000", + "eta": "1/1000000000000000000000000", + "weakening": "1/1000000000000000000000000000000", + "layout": "balanced", + "minimum_margin": "148684971496890003109996295013224259329740670260073915526993780506219493482636277/250148434971746889753110246443448196006219493780506517363723000000000000000000000000", + "assembly": { + "parameters": { + "a_bit": "297370240363722999999999702129759636277/500000000000000000000000000000000000000000", + "a_complex": 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24538834031585449512199149502366135413377258946440509856083528123121059335401955514320480957564185672229119448937271930119361679964782615957975788782007122310665463611105043819149575171648581869512415932848404879475563077926893696915874972729178579030689490668100642223159298676794638834637769493270623542715214278483698945002837431718306320338089525754948082676027143516482673980763268533015571812390028016143269541922653215821248572254537569319599079636280474275974272591743284204460338979146738315631239616302437893839484096107845471420238852212608919878331281550165252572542085621282410171009124350271128524308976746559614642931056253182083824619514196403638697766799233378480090406559380503869085784016511236993746299185394643498603455059152903988994264140996024589989449615591383592560369071442797878321663228265218535080411039140534426742039450868923148459020116762535807197782998961259849289643783750407580068368171100470560267886215600087499510547615954285293058313279135271747939651454300974656089210594367593804069703217899876717792424301593718896559103240797902982441711709514495850007615211000106974814444075505513114329937956195014769567529120919617079086179430892011697784182600957104902956419272366100034702278069765658184412633381788855814843885869354405073027900639103257931434838341748334172616730848410246401187503977066924528956905337031540067527276922898474596648054133370593174195220136158445077932685052124330563219011435784827487776029375948155281083784482028778542940973919349247068721504226432123263594143740475290755552746741338318099774442040014896425844362897907009867379208471760630208402512166694785467690554276444628244063665503392016871410167511182908867908841608889901752078910133542107142801398921539741664485747365862338982167142767499525261057751205032291125313185921194403859666601624737622515355820755037306349299855488858092095239170813813128921948652571897789232546523005585495321578617625789938080710364412132869890325966492994749646938332628656362786185995418218753540089576447792809256253060775774870578076358708867412130514593843760322310802115930804853822575810115357876408787801159495657487655290447763710799820443400276982608827980438377053612400780430419206346887046789305398129803931882103212870764976006007374922953761012779281227667998747798570013378113830715078667992603739739461157116138742926803286542728343101825636486293899017760864155587176535317530493328106761783966448165157170423027398345287539351833529301439631138125489948092198861225361887951743853530667683338042559525199166095299509152503264792753545823469748858682523357320270371678103798564688994632120877787967371127194676790380994872604744587768612039264310495537985017177868816327410212668087850844426676118970453748257407911813044730977151919279720208163482722032864853160626106865363476223349451625562830740477670685839050870883460126489700864654656298394636018737378734642582502650282516658915936540465236330734070248778707099697173637643227778140656279575095416020805378163925015866219631889274997818944359964183621451861693653938769242215524753035314803156196342698466863735671075685753557850268126202163159799856023742825819752089083302195949527782959680377831050307425743901421521856583235945411057059412508171480515202043376305305063466530711736123824486322726942173255635763166532677710337790951210134772831584815603058219632867146236550181301905425960269191027342711181745370751175400841128320763982844087911532066248100949507073307638405373571669698058586747594545145163241184578568047598795369536329369831122582632715603993943574182642595038412873826355660942074061760073868390089451666881857818498281368597371750143526456919807286388940243125691735185378827832474863837008702559936138871367143214946342859076219632843446528920187575326274542088626125421834859892842445988978922876236810538304155654681307163727944058470319148886447711463727233483416321805293589738518971381364836691025684006969032779767563804126699682685851481904785659972055597464453233637634191542314784046347911350422375086693590255690682994730039407960531892578482374399033156349102830823039525696452217993830601466329008398272783171515126807210008949464650795801091302627669222005672358759841728918062118357707958646828801959616701972655954736330956006277164306554661330251514693710931529141236862350760980446930098095228103410056067231618129256839137082908195515846490078724224606135933850183536110915262029594678720458927866341592139086229393280285559646882629310115760657625429989507506518372584864019503816814011523814187560860966328193212150830984921316963690654896276279022924798542446779833881259899603667628881867666802003905326938522423723600660455451662674103969704924845271171387070832027035528414831623474822314535113497197982064203551092664067621223025179368505297311993381153750719954292198588609986855923053949982077256505439642442333599426018831175668232830059013883607234689470037517244922194231082505656192052854818948001968271597720051026555744472793959633456657850984165064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+ "fixed_odd_divisor": 3, + "exact_grid": "One dyadic grid times 3^(-K), K=G*(D_complex+1); completed children preserve the incoming odd exponent." + }, + "rows": { + "coefficient": 12320, + "complex_coefficient": 2159, + "degree": 70000, + "suffix_slope": 280000, + "degree_gap": "224336/5" + } + } + } +} diff --git a/research/balanced-nullity-banks-163/lean-audit.log b/research/balanced-nullity-banks-163/lean-audit.log new file mode 100644 index 0000000000..5943da67d0 --- /dev/null +++ b/research/balanced-nullity-banks-163/lean-audit.log @@ -0,0 +1,82 @@ +'Mathproof.BeyondNLogN.TakeoverBit.partialSwap_apply' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.partialSwap_zero' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.partialSwap_comp_disjoint' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.partialSwap_involutive' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.partialSwap_id' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.partialSwap_commute' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.bankSwap_eq_sum' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.bankSwap_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.weighted_apply' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.weighted_comp' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.weighted_id' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.weightedBank_eq' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.weightedBank_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_apply' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_idempotent' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_disjoint' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.coordinateProjector_sum' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.coordinateBank_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.bankAddress_bijective' depends on axioms: [propext] +'Mathproof.BeyondNLogN.TakeoverBit.bankAddress_roles_injective' depends on axioms: [propext] +'Mathproof.BeyondNLogN.TakeoverBit.P12.selected_block_capacity' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_block_capacity' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.P12.selected_bank_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_bank_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.P12.inherited_rank_mass' depends on axioms: [propext] +'Mathproof.BeyondNLogN.TakeoverBit.P12.removed_exterior_count' does not depend on any axioms +'Mathproof.BeyondNLogN.TakeoverBit.P12.packed_rank_mass' depends on axioms: [propext] +'Mathproof.BeyondNLogN.TakeoverBit.P12.packed_max_rank' does not depend on any axioms +'Mathproof.BeyondNLogN.TakeoverBit.P12.normalized_volume' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.P12.packed_deficit' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.P12.actual_role_counts' does not depend on any axioms +'Mathproof.BeyondNLogN.TakeoverBit.P12.selected_weighted_bank_full' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.P12.undeferred_weighted_bank_full' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.Contents.run_eq_address' depends on axioms: [propext, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.Contents.run_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.Contents.p12_selected_contents' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.Contents.p12_undeferred_contents' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.inherited_rank_mass' depends on axioms: [propext] +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.removed_exterior_count' does not depend on any axioms +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_rank_mass' depends on axioms: [propext] +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_max_rank' does not depend on any axioms +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.normalized_volume' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.packed_deficit' depends on axioms: [propext, Classical.choice, Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.actual_role_counts' does not depend on any axioms +'Mathproof.BeyondNLogN.TakeoverBit.PR161P12.actual_bank_and_inventory_certificate' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.literal_charge_lt' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.finite_row_reserve' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverLiteralGuard20261008.row_reserve_value' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBalanced16320261009.core_slacks_positive' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBalanced16320261009.all_47_slacks_positive' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBalanced16320261009.strengthened_public_margin' depends on axioms: [propext, + Classical.choice, + Quot.sound] +'Mathproof.BeyondNLogN.TakeoverBalanced16320261009.all_47_concrete_guards' depends on axioms: [propext, + Classical.choice, + Quot.sound] diff --git a/research/balanced-nullity-banks-163/verify.py b/research/balanced-nullity-banks-163/verify.py new file mode 100644 index 0000000000..6a117777c9 --- /dev/null +++ b/research/balanced-nullity-banks-163/verify.py @@ -0,0 +1,96 @@ +#!/usr/bin/env python3 +"""Read-only exact arithmetic replay. Full physical supplier checks are separate. +Requires two immutable upstream checkouts; no downloads or source edits. +""" +from pathlib import Path +from fractions import Fraction as Q +from math import lcm +import argparse,hashlib,json,subprocess,sys +sys.dont_write_bytecode=True +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0) +HERE=Path(__file__).resolve().parent + +def need(ok,msg): + if not ok:raise ValueError(msg) + +def checkout(path,pin): + path=path.resolve() + def git(*args): + p=subprocess.run(['git','-C',str(path),*args],capture_output=True,text=True) + need(p.returncode==0,'Git failed: '+p.stderr);return p.stdout.strip() + need(git('rev-parse','HEAD')==pin,'Incorrect pinned checkout: '+str(path)) + need(not git('status','--porcelain','--untracked-files=no'),'Tracked source changes in '+str(path)) + return path + +def main(): + need(not sys.flags.optimize,'Assertions must be enabled; do not use -O') + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--pr161',type=Path,required=True) + ap.add_argument('--pr163',type=Path,required=True) + args=ap.parse_args() + expected=json.loads((HERE/'expected.json').read_text()) + r161=checkout(args.pr161,expected['public161_pin']) + r163=checkout(args.pr163,expected['public163_pin']) + sys.path.insert(0,str(r161/'scripts')) + import paired_cube_network as p + from audit_community_candidate import moment + ar=r163/'research/paired-cube-balanced-161/arithmetic' + sys.path.insert(0,str(ar)) + import certificate as c + from interval_moment import saving_grid + n=json.loads((r161/'certificates/paired-cube-network.json').read_text()) + raw=json.loads((r161/'research/paired-cube-bit/out/profile_p12.json').read_text()) + inherited={int(k):int(v) for k,v in raw['child_histogram'].items()} + original=n['bit']['counts'] + need(inherited=={int(k):int(v) for k,v in original['child_multiplicities'].items()},'Bit sources disagree') + need((raw['m'],raw['h'],raw['v'],raw['R'],raw['selected_roles'])==(72,24,1760,23368,5720),'Wrong immutable word') + need(raw['selected_rank_histogram']=={'20':5720},'Wrong selected ranks') + need(sum(k*v for k,v in inherited.items())==1934000,'Inherited rank mass') + packed=dict(inherited);need(packed.pop(60)==5720,'Exterior child inventory') + W=2*1760+3*(Q(5720,18)+Q(17648,3)) + rank=sum(k*v for k,v in packed.items()) + need((W,rank,72*W-rank,max(packed))==(Q(66364,3),1590800,1936,22),'Packed ledger') + # Actual disjoint coordinate blocks, not nullity divisibility alone. + need(all(sum(j//4==i for j in range(72))==4 for i in range(18)),'Selected blocks') + need(all(sum(j//24==i for j in range(72))==24 for i in range(3)),'Undeferred blocks') + profile=dict(original,W_per_vertex=W,rank_per_vertex=rank,deficit_per_vertex=1936, + child_multiplicities={r:Q(v) for r,v in packed.items()},edge_count=sum(packed.values()),maxchild=22) + coarse=Q(302618322217,500000000000000) + atom=Q(302446903,500000000000) + old=Q(384599,10**10) + effective=(1-atom)*coarse+atom*old + need(0 Historical predecessor proof. The current16-gauge construction, including mixed4/5/6/24 residual banks, is specified and replayed by JOINT-GAUGES.md and joint/. + +Historical predecessor note. The current joint-gauge extension is specified in JOINT-GAUGES.md and PROOF.md; current execution starts at verify.py. + +# Frame refinement, concrete charts and completed banks + +2026-10-09. This supersedes the234-frame candidate for packaging. It is a sufficient finite construction under the unchanged all-size interfaces, not an unconditional multiplication theorem. + +## Admitted bit word and paid inventory + +The new word uses immutable PR200 at a1175449f34d39ff933d9d8ab23ced1f32b290ec, with 6,416 listed operation-frame bases (274 subspaces changed beyond PR211). All source/gauge/root endpoints,1760 compensated aliases, source/target chronology and34 terminal sinks are retained. The frame lane executed the complete F2 and defining-integer dirty-column replay. The geometry lane independently reconstructed every actual modified frame and full paid ledger, audited its terminal−102 rank3/−102 rank21 histogram substitution, and recomputed all distinct used-basis Bareiss prime witnesses from their actual bases. Everyprime q>2^80 remains eligible. + +The entrance classes remain exactly2200 rank20 genuine physical starts; rank21 recipient gauges remain internal splices. Sources, centre-touched roles and deleted terminals are forbidden as entrance gauges, with explicit rejected controls. Remove only2200 per-vertex rank60 exterior children after the complete bank endpoint proof. Every source, target, internal, centre, compensation and fallback child stays charged. + +The resulting full normalized profile is m72, W56402/3, rank1351712, deficit1936, largest child22. Integer moment normalization multiplies stock, every child count and deficit by three. Nine physical replicas supply1100 selected18×4 banks and44742 undeferred3×24 banks per stage, with31680 data registers: literal stock169206. All462078 role-copy assignments across three stages are checked exactly once. + +Two independent rational enclosures, including the full10^-16 bad-class32*72²-per-edge fallback, certify + +`coarse = 136731504666219/200000000000000000`, + +`ordinary = 546573370825043616599485038841961823/800000000000000000000000000000000000000`, + +`ordinary ≈ 0.0006832167135313045`. + +Adjacent coarse and preceding atom-grid controls fail for this fixed profile/envelope. No independent supplier gains are added. + +## All actual charts and fixed normalizers + +The220 unchanged rank20 gauge frames have sigma=ker A with four annihilator rows a. For G=9I-J, residual basis rows15a−(sum a)1 are Gorthogonal to sigma. Put these four columns before the20 sigma columns in B. Reusing PR197's fraction-free factorization, independently verify both B·C=dI and C·B=dI and replay every elementary factor to the identity. This constructs the literal residual projector's chart, rather than an assumed normalizing gadget. + +Across everyactualchart, maximum factor count is186, factor numerator magnitude5, denominator/inverse denominator18, integral inverse numerator18, and basis entry magnitude2. All nonzero inverse and factor denominators are below2^80 and thus units at every inherited primeq>2^80, including local ringsZ/q^w. The chart gzip witness hash is `f81a21df89d4702b70564f9577b5506504de429ca5df253e78bd28f2685cd432`. + +Embed B^-1 in the corresponding24-coordinate tensor stage and use the explicit coordinate permutation Pi_b sending its first residual block into bank intervalb. Choose fixed H_b=(b+1)Pi_bdiag(B^-1,I48), with b0..17 for selected banks or b0..2 for undeferred banks. A common inputcoordinatej outside that tensorstage maps to (b+1)e_(Pi_b(j)); these columns are distinct at everyq>2^80. This supplies literal distinct normalizers without a greedy choice or same-invocation alias. Scalar multiplication leaves conjugation unchanged. + +Group routing sends banklabelg to coregH_b. Each role's routing is a bijection on the completeGL cover. Distinct H_b preventtwo simultaneous roles from borrowing the same physical bank. Replica execution is serial and stages are private. After everycore completes, its arbitrary-dirty residual is conjugate to a disjoint coordinate partial swap. Each bank's partition sums to I72, so the exact ring-general identity gives the full required dirty endpoint; inverse order restores the same contents. The common weighted ancestor chart telescopes and spectators remain intact. + +## Fully charged extra routing + +Allow186 chart elementary factors,71 coordinate transpositions and72 fixed-scalar coordinate factors, totalling329. Nine full replicas contain27 stage-core occurrences. A conservative out-and-back old-selector bill is + +`K =54*((169206−1)+17114*72*329) =21900544398 <2^40`. + +These are additional paid ordinary-selector calls, never silently counted as zero work or as extra recursive children. As in PR197 PROOF5, their cost is O(K V w^(1−a_old)); the inherited positive stopped-leaf atom/row toll absorbs the fixed coefficient K. They change the finite stopping constant, not the exponent or external row order. Full group stock remains charged. All-size restored weighted selector and routing guarantees remain the original conditions. + +## Source-bound receipts and final assembly + +Frame receipt SHA256 `79160698cb761b17af5667e141367160ba0d3d447e0e6121b6de784065e0fb7f`; override witness SHA256 `65b6b30748fe8db9b472c6c4bd34ba6b6ec757f4440ad0d78f8cad139cbd906b`; independent used-frame prime witness SHA256 `038867338525dcae7f9e721b809b42b93cfe2f777db02c6f6189eca25ebed6cd`. All pinned sources stayed byte-identical through the independent geometry audit. + +The parent owns the admitted complex supplier, finite depth-four leaf composition and unchanged47 balanced inequalities with complete scalar/group/router/layout charges. No unattained infinite-depth limit is substituted. General compiler, common weighted chart, restored rows, paid layout, prime supply, precision/recovery and analytic transfer remain inherited. No new Lean formalization is claimed. + +Reproduce withgeometry/pack-admitted-frames.py againstframes/pr200-fastdirections1, geometry/audit-gauge-charts.py, andgeometry/check-normalizer-routing.py. The complete bank profile, full exact moment proof and each physical assignment hash are inpacked-pr200-fastdirections1.json. diff --git a/research/coordinated-crossover-pr200/BASELINE.json b/research/coordinated-crossover-pr200/BASELINE.json new file mode 100644 index 0000000000..38dc26ae37 --- /dev/null +++ b/research/coordinated-crossover-pr200/BASELINE.json @@ -0,0 +1,34 @@ +{ + "base_commit": "8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d", + "bit_source_commit": "a1175449f34d39ff933d9d8ab23ced1f32b290ec", + "archive_sha256": "ddb0fbdbda0a45b25ea5c5ce5fd7858687d99211f45b6c3a674d38e1ae7c378d", + "bytes": 51416352, + "parts": [ + { + "file": "baseline-pr202.part01", + "bytes": 12000000, + "sha256": "f5beb67709bf1235a2b6483883aa997a150ed4be47db978ab8be6040114cf924" + }, + { + "file": "baseline-pr202.part02", + "bytes": 12000000, + "sha256": "21e1ff2a0ddc3e8febad3ca19d210d2e83d575f0968bb5125ab62bf6d00794fe" + }, + { + "file": "baseline-pr202.part03", + "bytes": 12000000, + "sha256": "218c880af743a75e272cd51b3bd1ce5f36583f332823c2b5606d21d5d8b72e98" + }, + { + "file": "baseline-pr202.part04", + "bytes": 12000000, + "sha256": "e0f95fcdd581a7617eabd53f4d0ea9e7cf0551a31fcd081e3d2154750740f114" + }, + { + "file": "baseline-pr202.part05", + "bytes": 3416352, + "sha256": "9b64c7b8b5b7893eae071733b7ca14e280fe08b3db942c1c6d00e88d6e615286" + } + ], + "scope": "Exact tracked PR202 LF source, plus pinned replayed aligned complex witness. PR200 bit source agrees except its SOURCE.json receipt." +} diff --git a/research/coordinated-crossover-pr200/BOOTSTRAP-REVIEW.md b/research/coordinated-crossover-pr200/BOOTSTRAP-REVIEW.md new file mode 100644 index 0000000000..090b30c875 --- /dev/null +++ b/research/coordinated-crossover-pr200/BOOTSTRAP-REVIEW.md @@ -0,0 +1,40 @@ +Historical predecessor note. The current joint-gauge extension is specified in JOINT-GAUGES.md and PROOF.md; current execution starts at verify.py. + +# Finite-bootstrap proof scope review + +## Sufficient conditional argument + +Let c be the certified coarse bit saving and let a0 be the completed atom-wrapped ordinary supplier saving. Assume the inherited all-width ordinary leaf interface, complete spectator handling, restored borrowed rows, fixed finite tapes and paid routing/layout. These assumptions must be stated for the selected new packed supplier and its retained old ordinary selector. + +For j=1,2,3, construct Aj using the coarse supplier at atom width w=ceil(e^c), with ordinary leaves, source exchanges and routing executed only by A(j-1). This is an acyclic call graph. Within one level, rank-r children have smaller width because r<=22<72; ordinary recursion decreases j. No limit construction or self-call through a completed leaf is used. + +The inherited stopped-leaf estimate is + +Tj(e)/V = O(e^(1-c) + e^((1-c)^2+c(1-a(j-1))) + e^c log e). + +Therefore the achieved ordinary saving is + +a(j) = (1-c)c + c a(j-1) = c - c^j(c-a0). + +Here 02^80. + +Each chart sends its residual projector to a literal coordinate block. Disjoint partial swaps over each completed bank compose to the full swap on arbitrary correlated dirty inputs. Reversing the block sequence restores them and all spectators. Common weighted charts cancel between successive blocks. Every pattern rejects omitted and repeated blocks. + +Normalizers use the actual inverse chart, an explicit coordinate permutation and distinct scalars b+1. An outside-stage identity column witnesses distinctness. Charts, permutations and scalar factors are included in the fixed extra selector bill K=178459060896<2^40. The inherited positive ordinary-leaf exponent gap absorbs that fixed restored-selector cost. + +## Full paid profile and conditional composition + +After literal bank completion remove only the actual entrance exteriors: rank 60×2200,rank 54×13,rank 57×3,rank 36×18,rank 39×48. No internal donor/recipient increment or target split is removed. Factor 24 gives m=72, W=439525, rank=31599336, deficit=46464 and maximum child 22. The 72 literal physical replicas and factor 24 arithmetic normalization have distinct roles. + +Both rational moment engines include the full bad-class fallback. Four fixed ordinary-leaf levels use their preceding level. The unchanged 47-constraint assembly then composes with the exactly replayed frozen complex local-flow supplier. All-size compiler, selector, routing, precision, prime and analytic hypotheses remain conditional. diff --git a/research/coordinated-crossover-pr200/LICENSE b/research/coordinated-crossover-pr200/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/coordinated-crossover-pr200/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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The common-frame assignments are role 14079 from X322 and role 14077 from X378. Their four targets are 24, 25, 26 and 27. The exact common basis is in `newg/selection.json` as `gauge_basis`; all other new entrances use their exact `mix_frame`. + +The 28 pairs are distinct and disjoint from all prior aliases. The selected roles are previously ungauged, untouched in the admitted retimed center prefix, and outside source-injection and removed terminal roles. New target sets are disjoint except the two common-frame rows, which use exactly the same frame on their common four targets. There are 112 reads on 108 distinct targets; no new target intersects a terminal substitution. + +Save each partner sum after the ordinary source injections. After the copied-center scatter and before the first operation on each selected role, compensate the selected role's entire dirty response at its entrance frame. Run the original physical branch on the original passive source, including its later donor/recipient continuation. Reverse every auxiliary operation, then undo the saved partner sums and source injections. The actual scalar executor uses each original source column as the correlated initial dirty input and checks complete restoration. + +A source path is its original line, pair plane, selected gauge frame, every actual operation/root/alias frame, and the full frame. The rank-4 paths include a genuine rank-2-to-rank-4 transition. `newg/boundary.py` checks every exact inclusion, nondegeneracy and reflected annihilator path. It reconstructs both complete target ledgers, including all old gauges, terminal pivot operations, roots and partner deliveries. The target delta is {2:+104,4:+4,17:+4,19:+104,21:-108}. Repeated compensation at the same rank-4 frame adds no second target rank jump. + +Operation 18751 is enlarged to dimension six to admit role 13088 from source X1634 and partner X1633, at targets 1624–1627. The frame-only local delta is {1:+1,2:+1,3:-1,5:-1,6:+1,11:+1,12:-1}, of rank mass zero. The full joint scalar/frame/prime proof is rerun with this actual operation frame before any source-profile derivation. + +The final schedule defers 168 actual operations past the copied-center scatters. Two newly untouched physical heads, role 8584 from X98 and role 9424 from X458, receive their rank-2 compensation immediately after those scatters. All preceding gauge reads occur after the 168 deferred operations. `CENTER-RETIMING.md` supplies the dependency and D0/D1 proof; the complete physical frame streams are unchanged. + +The aggregate local source/internal/target delta from the original 443-source predecessor, including that operation change, is {1:+3,2:+107,3:+4,4:+5,5:-8,8:+1,11:+2,12:+10,14:-12,15:+3,19:+104,21:-108,22:-28}. Its rank mass is -672. Raw stock falls by 28, and the ordinary shared rank mass falls by 2016, preserving deficit. `newg/derive_profile.py` reconstructs complete source/internal/target histograms from all actual paths and checks this delta against the rebuilt 443-source baseline; that baseline already includes the operation change, so the incremental source-gauge delta excludes it. A separate endpoint/target implementation independently agrees. + +The common rank-4 frame has cleared Gram determinant 59049=3^10. `newg/boundary.py` supplies exact cleared-Gram factor witnesses for every selected source-gauge frame, including the new rank-4 frame; all residual factors lie below the retained prime lower bound. The rebuilt whole-word certificate admits every other used frame, including the new six-dimensional operation frame at 18751, whose cleared Gram determinant is 2125764=2^2*3^12 and residual factor is one. + +Final banks use 14364 full-residual roles. Per stage, use 864 mixed banks 4×11+7×4, 8464 banks 18×4, 78 banks 12×6, 216 banks 6×12, and 344736 banks 3×24. This gives 354358 banks per stage and 3594888 literal assignments across all 72 replicas. All 231 charts, inverse/factor identities, complete-block controls and normalizers are checked. Literal stock is 1316514; the fixed additional selector bill is 178127441712. These source-owned entrances do not create auxiliary banks or auxiliary-bank charts. + +F2 and both defining integer signs check all 20163 formal columns, every target and restoration of all 1760 sources and 16643 remaining dirty registers. Six controls reject missing new compensation/mixing, stale adjoints, missing old early mixing, premature inverse mixing and placing the two new reads after their deferred operations. The final normalized profile is m=72, W=438838, rank mass 31549872, deficit 46464 and maximum child 22. Two paid moments and exact 47-constraint assembly are rerun. On the PR210 parent head, this source-gauge construction priced at κ = 6.94782719690783e-4; the separate plateau refinement in `search/JOINT-PLATEAU-REFINEMENT.md` changes only operation frames and reprices the combined witness at κ = 6.94787513005285e-4. + +The construction, common-frame integration and verification were prepared with substantial OpenAI Codex assistance. All inherited contributor notices and licenses remain. diff --git a/research/coordinated-crossover-pr200/NOTICE b/research/coordinated-crossover-pr200/NOTICE new file mode 100644 index 0000000000..bc1cfc52a1 --- /dev/null +++ b/research/coordinated-crossover-pr200/NOTICE @@ -0,0 +1,441 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. + +Partial-gauge extension, 9 October 2026 +Copyright 2026 icekylinx + +The pair-first cube assembly, compatible backward frame enlargement, +partial source-gauge schedule and stopped whole-projector composition are +contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834. + +The physical deferred bit word, reflected event accounting, fan-order +clarification and signed two-stage endpoint are adopted from Zhihao Chen +(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with +Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen +witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38, +with the original Claude disclosure retained. Cyclic interval and core-aware +pair primitives build on Avi Eisenberg (ikeboy), PR #62, +ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance. +Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and +precision credits remain in force. Imported source notices and licenses +are preserved under references/partial-gauge/; see SOURCES.json. + +Three-stage cover extension, 9 October 2026 +Copyright 2026 icekylinx + +The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry, +weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring +fallback, uniform batching, internal row borrowing and exact composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This +repository integration uses Codex assistance and extends +PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86. + +The selected local complex DAG and support/label replay are adopted from +Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf, +with its original Apache-2.0 terms and Claude assistance disclosure. +The unchanged bit physical word retains Zhihao Chen (jacklightChen), +PR #97, and Swapnil Jain's underlying witness and assistance notices. +The prior opposite-bank, stopped ordinary-leaf, copied-center, topology, +semantic/bulk, precision and analytic credits remain applicable. +Original source notices and license bytes are preserved in +references/three-stage-cover/pr117/ and references/partial-gauge/. + +Paired-cube and shared-core extension, 9 October 2026 +Copyright 2026 icekylinx + +The paired-coordinate triple-cube identity, signed overlap channels, +original-source involution, coordinate-star centers, concrete frame/carrier +compiler, chronological source gauges, PR97 gauge-subset selection, +orthogonal cross-stage routing and exact supplier/assembly integration +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. +Repository integration uses Codex assistance and extends PR #130 at +6a9970a530119174507904e23592fd59ede19a5d. + +The substantial completed-core workspace-sharing principle is credited to +an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported +OpenAI Codex assistance. No source code, partition or serialized witness +from that PR is imported. The new routing and paired-motif integration +are described separately and claim no exclusive priority for broad sharing, +paired-coordinate, Fourier or carrier-matching ideas. + +Selected coarse queries restrict the retained eumemic PR #117 positive DAG; +its original Apache-2.0 and Claude assistance notices remain unchanged. +The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil +Jain's frozen witness, notices and historical assistance disclosures. +Earlier generalized Clifford, three-stage, uniform weighted recursion, +ordinary-leaf, semantic/bulk, precision and analytic credits remain in force. +Source-specific license bytes are preserved under references/. + +Source-assisted common-frame extension (2026-10-09) +Copyright 2026 icekylinx. Apache-2.0. +Research construction and local certificates: OpenAI GPT-6 Astra assistance. +Repository integration and independent complex scalar replay: Codex assistance. +Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee; +its byte-preserved sources, licenses and original Claude assistance disclosure +are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz. +Additional inherited contributions are recorded in research/source-assisted/CREDITS.md. +The new work concerns source-assisted invertible common-frame lifts, controlled +affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for +broad register reuse, paired cubes, frame theory or ordinary linear elimination. + +Fourth finite bootstrap refinement (2026-10-09) +Prepared by eumemic with substantial OpenAI Codex assistance. +This arithmetic refinement builds on PR207 at +cd14825023b75af4f5919a30e5e6d548b6ade5bc by adding one finite ordinary-leaf +level. The 302 frame overrides, completed banks, scalar words and upstream +assistance disclosures are inherited, not newly attributed to this work. +The Apache-2.0 license and all preceding notices remain applicable. + +PR211 plateau frame refinement (2026-10-09) +Prepared by eumemic with substantial OpenAI Codex assistance. +The additional seven equal-frame component moves build directly on Rohan +Arun's PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347, +prepared with Anthropic Claude assistance. Its original notice is preserved +byte-for-byte in search/PR211-NOTICE. The offline certificate package and +independent stage-private bank admission derive from Dugongue's PR207 at +cd14825023b75af4f5919a30e5e6d548b6ade5bc. Original contributor notices, +licenses, source pins and all upstream AI disclosures remain applicable. + +The final refinement also includes seeded bidirectional cascade search after +the seven initial component moves. Exact canonical subspace comparison +records 274 changed operations beyond PR211. Search, integration and replay +were prepared with substantial OpenAI Codex assistance. + +Shared rank-18 gauges and two donor substitutions (2026-10-09) +Prepared by eumemic with substantial OpenAI Codex assistance. +The new actual gauge/read chronology, gauged-donor handoff, shared target +transitions, rank6 residual banks and donor substitutions extend the same +PR200/PR211 word and PR207/PR197 completed-bank framework. All original +licenses, notices, authorship and upstream AI disclosures remain in force. + +Nested-gauge extension: three rank-19 physical entrances compose with thirteen shared rank-18 entrances; all target transitions and mixed4/5/6/24 banks are explicit. Prepared by eumemic with substantial OpenAI Codex assistance. All retained authorship, licenses and AI disclosures remain applicable. + +Equal-frame plateau refinement on PR210's 471-source word (2026-10-10) +Prepared by sennemmi with substantial OpenAI Codex assistance. The deterministic +frame search, 19 operation retimings, exact price update and repository +integration extend eumemic's PR210 head +df95878d11190518e45ef9717c9ee05011f88ace. They do not claim the inherited +source word, shared gauges, completed banks or upstream proof framework. +All PR200, PR197, PR202/193, PR207, PR211, PR216 and PR210 attributions, +licenses and AI disclosures remain in force; the repository's Apache-2.0 +license is unchanged. diff --git a/research/coordinated-crossover-pr200/PLATEAU-REFINEMENT.md b/research/coordinated-crossover-pr200/PLATEAU-REFINEMENT.md new file mode 100644 index 0000000000..bbf4bc79ab --- /dev/null +++ b/research/coordinated-crossover-pr200/PLATEAU-REFINEMENT.md @@ -0,0 +1,45 @@ +# Exact refinement of PR211's operation frames + +The initial plateau step below is followed by the seeded cascade refinement described at the end of this file. The final published witness uses both steps. + +The input is the frozen PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347. The search joins adjacent operations with equal frames into connected components. A candidate replaces every frame in one component by the intersection of its next frames on both physical chains. Each accepted replacement contains the old frames and hence their value spans, is G-nondegenerate, and stays nested between every fixed boundary and neighboring operation. All scalar additions, sources, root caps, gauges, aliases, partner deliveries and terminal selections remain fixed. + +Seven accepted two-operation components change operations 18516/18517, 18920/18921, 19324/19325, 23544/23545, 23591/23592, 23685/23686 and 23873/23874. Before integer moment normalization, the complete child change is: + +| Rank | Count change | +|---|---:| +| 2 | +12 | +| 4 | -15 | +| 5 | -18 | +| 6 | +9 | +| 7 | +24 | +| 8 | -12 | +| 9 | -12 | +| 12 | +24 | +| 15 | -12 | + +The weighted rank change is zero. The count changes scale by three for the integer moment profile. Terminal cancellation and bank removal are replayed and are unchanged. Both reflected signs and complete source/dirty restoration are checked on the actual scalar word. + +The search score uses floating arithmetic only for discovery. The published saving and final κ use exact rational interval bounds with independent enclosure engines. The four finite leaf levels each invoke their predecessor and are independent of input size. + +Reproduce discovery after extracting the pinned baseline (or using PR200's exact checkout): + +```sh +python3 -B search/plateau_search.py --bit-package /path/to/research/paired-cube-diagonal-bit-168 --frames search/pr211-frames.json --out /tmp/plateau-reproduction +``` + +The search is not an optimality certificate. The following seeded cascade step contributes additional verified gain. PR211's original notice is preserved byte-for-byte in search/PR211-NOTICE. Apache-2.0; substantial OpenAI Codex assistance. + +## Seeded cascade refinement + +After the 14-operation plateau witness, deterministic seed 2116205 drives raise/lower proposals and short positive-temperature perturbations, followed by zero-temperature relaxation. A raise propagates joins forward; a lowering propagates intersections backward. Every changed operation retains its exact value span and a nondegenerate frame, and every edge stays nested between fixed source/gauge/root/alias endpoints. The final state is the best discovered exact-admissible state; search optimality is not claimed. + +The final witness lists 6,416 bases and changes 274 actual subspaces relative to PR211 (2,124 relative to PR200). Raw frame IDs are not mathematical change counts: registering an equivalent basis can create another ID. The canonical comparison receipt is search/relaxed-diff-count.json. + +Compared with the plateau profile, before the factor-three moment normalization, the further child change is {1:+12, 3:+9, 4:-24, 5:-69, 6:+9, 7:+36, 8:+39, 9:+3, 10:+9, 12:-27, 13:-18, 15:+15}. Stock and weighted rank mass are unchanged. The full verifier reconstructs this profile from the final bases and actual scalar word. + +```sh +python3 -B search/relaxed_search.py --bit-package /path/to/research/paired-cube-diagonal-bit-168 --frames search/pr211-frames.json --additional-frames search/additional-frames.json --out /tmp/cascade-reproduction +``` + +Search traces use floating entropy only for proposals. The frozen final bases, exact frame/word replay and rational paid moments determine the public claim. diff --git a/research/coordinated-crossover-pr200/PR-STATEMENT.md b/research/coordinated-crossover-pr200/PR-STATEMENT.md new file mode 100644 index 0000000000..294d5621ec --- /dev/null +++ b/research/coordinated-crossover-pr200/PR-STATEMENT.md @@ -0,0 +1,53 @@ +# κ = 6.94787513005285e-4 + +Conditional **`κ = 694787513005285/10^18`** from the 471-source physical word, +complete source/dirty restoration, and a new deterministic frame-plateau +refinement stacked on PR210 head +`df95878d11190518e45ef9717c9ee05011f88ace`. + +The frame search changes 19 operations in 14 exact-admissible moves: + +- operation 18750: dimension 5 → 6; +- five operation pairs (23544/23545, 23591/23592, 23638/23639, 23685/23686, + 23732/23733): dimension 9 → 12; +- operations 27900, 27904, 27908, 27912, 28052, 28056, 28060, 28064: + dimension 13 → 14. + +The floating `d log d` score proposes moves only. Exact frame containment, +nondegeneracy and nested-chain checks admit them. The full physical profile +then preserves `m=72`, `W=438838`, rank mass `31549872`, deficit `46464` and +maximum child `22`; its changed distribution raises the exact bit saving by +`4799982097/10^18`. The exact final κ gain over PR210 is +`4793314502/10^18`. The bit side still binds, and the adjacent `10^-18` grid +point is rejected by the unchanged exact 47-constraint assembly. + +The full witness retains the 440 source loans, three rank-19 source gauges, +the 28 later source-backed gauges, the 231 charts and 3,594,888 bank +assignments. No all-size or analytic hypothesis is strengthened: the +conditional compiler, weighted/restored selector, routing, source-line, +prime, precision, fixed-tape and finite-bridge assumptions remain those of +PR210 and its cited suppliers. + +Reproduction: + +```sh +python3 -B research/coordinated-crossover-pr200/search/joint-plateau-search-prdf958.py --verify-committed +python3 -B research/coordinated-crossover-pr200/verify.py --temp-root /tmp +``` + +The first command checks the deterministic frame record. The second replays +the scalar word, all source/dirty restorations and ledgers, exact charts/banks, +the frozen complex dependency, independent paid moments and all 47 strict +assembly inequalities. Full repository CI additionally runs every +`make verify-*` matrix group, ranked-pair finite verification and formal +packages. + +## Provenance + +The extension was prepared by sennemmi with substantial OpenAI Codex +assistance. It builds on eumemic's PR210 source reuse and shared gauges, and +retains all original PR200, PR197, PR202/193, PR207, PR211 and PR216 credits, +licenses and AI disclosures in `NOTICE`. The extension claims only the +deterministic equal-frame search, its 19 retimings, certificate update and +integration. It does not claim the inherited physical word, source gauges, +completed banks or analytic framework. diff --git a/research/coordinated-crossover-pr200/PR205-COMPARISON.md b/research/coordinated-crossover-pr200/PR205-COMPARISON.md new file mode 100644 index 0000000000..9dabc3d20a --- /dev/null +++ b/research/coordinated-crossover-pr200/PR205-COMPARISON.md @@ -0,0 +1,17 @@ +# Historical PR207/PR205 comparison + +This records the predecessor package comparison. The current PR211-based refinement and exact claim are in README.md and PLATEAU-REFINEMENT.md. + +# PR205 read-only comparison + +Pinned head: `95c58706ad231d532bd7038308946a0344d08186`. Its proof and committed certificate were read; no full verifier was run in this lane. + +PR205 applies the same rank-4/rank-24 completed-bank idea to the unmodified PR200 internal frame word. Its paid coarse saving, `683528191056257/10^18`, exactly matches our earlier bank-only baseline. Its moment normalization has the same width 72, stock 56,402, rank mass 4,055,136, deficit 5,808 and maximum child 22. Its complex saving is also exactly the same `700918443859411/10^18`. + +The new result here is the paid histogram after coordinated changes to 302 operation frames, composed with completed banks. That histogram preserves total rank mass but improves its distribution and raises the coarse saving to `136731504666219/200000000000000000`. Its final conditional kappa is `1366380910073/2000000000000000`, exceeding PR205 by `129155636718/10^18`, approximately 0.01890835%. + +PR205 gives a different literal bank schedule: three full copies, nine role incidences across the stages, mixed banks, and a checked 9-edge-colouring. The local construction uses nine physical replicas and stage-private banks. These share the same normalized bank stock and yield no additive gain. PR205's routing constant 5,368,513,266 is smaller than our conservative 21,900,544,398, but both are fixed ordinary-selector tolls absorbed by the same strict exponent gap. Replacing one fixed routing constant cannot be credited as another exponent gain. + +PR205's finite three-level bootstrap has the same acyclic recurrence and discloses the same completed-core, Clifford, weighted-compilation, restored-row and fixed-tape conditions. Its initial ordinary saving is lower than the local already-admitted atom wrapper, so borrowing it does not improve this package. Its retained PR193 complex caveats are distinct from the local PR202 actual replay evidence; they should not be blindly copied. + +No additional independent paid gain or missing new interface was identified. Bank packing must be credited as parallel public work; the claim here should focus on the explicitly checked coordinated frame refinement and its complete composition. The precise histogram delta is preserved in PR205-COMPARISON.json. diff --git a/research/coordinated-crossover-pr200/PROOF.md b/research/coordinated-crossover-pr200/PROOF.md new file mode 100644 index 0000000000..e6070273a7 --- /dev/null +++ b/research/coordinated-crossover-pr200/PROOF.md @@ -0,0 +1,55 @@ +# Executable proof map + +The conditional claim is +`κ = 694787513005285/10^18 = 6.94787513005285e-4`. It extends PR210 at +`df95878d11190518e45ef9717c9ee05011f88ace`; the all-size supplier, restored +selector, source-line, routing, precision, analytic-tape and finite-bridge +conditions remain inherited. + +1. `search/joint-plateau-search-prdf958.py --verify-committed` rebuilds the + candidate from the pinned parent frame file. Its deterministic `d log d` + score is only a proposal rule. Every accepted operation-frame move is + checked against exact subspace containment, nondegeneracy and nested role + chains. The record fixes the 14 moves, 19 changed operation frames, frame + hash and per-rank histogram delta. +2. `joint/replay_joint.py` admits the final frames and retained gauge reads, + scalar word and terminal actions in both integer signs, dirty restoration + and all used-frame prime conditions. +3. `borrow/`, `gaugeb/` and `newg/` replay the 471-source construction and + rebuild its source, internal and target ledgers. They check both reflected + paths, target chronology, copied-center D0/D1 boundaries and six rejected + mutations. +4. `joint/pack_joint.py` enumerates the remaining bank roles, 72 replicas, + 3,594,888 assignments, 231 charts, inverse/factor identities, normalizers + and bank controls. It charges the fixed selector bill + `178127441712 < 2^40`. +5. The unchanged exact complex lift and contract are replayed. Two independent + rational paid-moment engines, four finite leaf levels and all 47 strict + assembly inequalities verify `certificate.json`; the adjacent final grid + point is rejected. + +The retiming changes the child distribution without changing normalized +`W=438838`, rank mass `31549872`, deficit `46464` or maximum child `22`. The +bit saving increases from `695265778339166/10^18` to +`695270578321263/10^18`; it remains the binding side. The final exact κ is +`694787513005285/10^18`. + +Run the deterministic search and then the complete offline replay: + +```sh +python3 -B research/coordinated-crossover-pr200/search/joint-plateau-search-prdf958.py --verify-committed +python3 -B research/coordinated-crossover-pr200/verify.py --temp-root /tmp +``` + +The first command does not stand in for scalar replay. The second executes the +actual word and checks source/dirty restoration, ledgers, charts, banks, +complex lift, independent paid moments and the final certificate. The +workflow's matrix verification additionally runs every `make verify-*` +category, the ranked-pair finite checker and all three formal packages. + +This remains a conditional finite construction, not an unconditional theorem. +The all-size compiler, weighted/restored selector, routing, source-line, +prime, precision/recovery, analytic-transfer and finite-bridge assumptions +are inherited. The complex supplier retains its exact local-flow contract. +`NOTICE` retains the authors, upstream PRs, licenses and AI-assistance +disclosures for all inherited components and this extension. diff --git a/research/coordinated-crossover-pr200/README.md b/research/coordinated-crossover-pr200/README.md new file mode 100644 index 0000000000..2c7dd9cc35 --- /dev/null +++ b/research/coordinated-crossover-pr200/README.md @@ -0,0 +1,49 @@ +# κ = 6.94787513005285e-4 — refine the 471-source physical frame word + +This conditional finite witness reaches +`κ = 694787513005285/10^18 = 0.000694787513005285`, an exact increase of +`4793314502/10^18` over PR210's `694782719690783/10^18`. + +The change is a deterministic equal-frame plateau descent on PR210 head +`df95878d11190518e45ef9717c9ee05011f88ace`. It retimes 19 operation frames in +14 accepted moves: operation 18750 grows from dimension 5 to 6; five adjacent +pairs at operations 23544/23545 through 23732/23733 grow from dimension 9 to +12; and eight operations in the late plateau grow from dimension 13 to 14. +The original scalar operations and all source, target, dirty-register and +bank roles are retained. Exact frame containment, nondegeneracy and nested +role chains admit every move. The `d log d` objective proposes moves only; the +reported κ comes from the complete rational 47-constraint assembly. + +The final normalized profile keeps `m=72`, `W=438838`, rank mass `31549872`, +deficit `46464`, and maximum child `22`. The changed raw child histogram has +zero rank-mass change and 27 fewer child occurrences per vertex; its exact +distribution lowers the paid bit moment. The bit saving rises from +`695265778339166/10^18` to `695270578321263/10^18`; the bit branch still binds. +The adjacent `10^-18` grid point is rejected, and all 47 strict assembly +inequalities remain positive. + +Reproduce the committed deterministic search and full offline certificate: + +```sh +python3 -B research/coordinated-crossover-pr200/search/joint-plateau-search-prdf958.py --verify-committed +python3 -B research/coordinated-crossover-pr200/verify.py --temp-root /tmp +``` + +The first command regenerates the 14-move record from the pinned parent frame +file. The second replays the scalar word over F2 and both defining integer +signs, checks all formal columns and restorations, rebuilds the complete source, +internal and target ledgers, verifies the 231 charts and 3,594,888 bank +assignments, replays the frozen complex supplier, and reruns the two exact +moment engines and all 47 inequalities. The package workflow runs both checks. + +This is a conditional finite supplier certificate, not an unconditional +integer-multiplication theorem. The all-size compiler, weighted/restored +selector, source-line, routing, prime, precision, fixed analytic tape and +finite-bridge assumptions are inherited unchanged. The complex supplier keeps +its exact local-flow contract. + +Provenance and retained upstream credits are recorded in `NOTICE`. The new +retiming search and integration were prepared by sennemmi with substantial +OpenAI Codex assistance and extend eumemic's PR210 construction; the new search +claims no ownership of the inherited source word, bank construction or proof +dependencies. diff --git a/research/coordinated-crossover-pr200/SOURCE-BORROWING.md b/research/coordinated-crossover-pr200/SOURCE-BORROWING.md new file mode 100644 index 0000000000..7e3b0b1cc3 --- /dev/null +++ b/research/coordinated-crossover-pr200/SOURCE-BORROWING.md @@ -0,0 +1,21 @@ +Historical predecessor description: numerical counts below describe that predecessor. The final construction has 471 source aliases, including 28 new source-backed entrances. See NEW-SOURCE-GAUGES.md for the current scalar word, target chronology and bank counts. + +# Original sources replace singleton-copy auxiliaries + +The frozen selection removes 440 physical auxiliary slots, one for each selected original passive source. It replaces a later singleton-copy branch, rather than the source's injection branch. Every selected branch has fresh value X_s after its initial copy and an unchanged-value prefix before its selected local partner mix. Its original initial copy may already use a padded rank-two frame. + +Identify the branch's physical storage with the original X_s register, whose initial address is the existing source line χ_s. Omit the selected first copy into that branch and omit its nonexistent initial-dirty response. Recompute every remaining integer dirty response by the actual reverse adjoint after deleting those 440 copy operations. The original source injection into the other retained source role is still performed before any source is changed. + +At the selected early operation, mix X_carrier ← X_carrier + X_s. The borrowed X_s has only served as a control since its initialization, so the saved value is the original partner sum. The exact rank-two partner span contains both source lines and lies on the unchanged remaining branch path. At the original target-delivery anchor, deliver the saved carrier value without mixing again. Retain every target anchor and target frame. + +Reverse the auxiliary word, omitting the same deleted copies. This restores every borrowed X_s. Only then undo each early partner mix. Finally perform the original retained-source-copy cleanup. The exact replay checks all source, target and arbitrary remaining dirty columns over F2, and the defining integer decoder in both reflected signs. It restores every original source and every remaining dirty input. Omitting an early mix, retaining the old adjoint, or undoing the saved mix before restoring the borrowed source is rejected. + +The 67 borrowed slots that were donors retain their entire physical donor-to-recipient chain, including the current-value compensation at the recipient gauge. This gauge is an internal splice, not a newly bankable entrance. Every resulting original-source path runs from χ_s to the full ambient frame; the complementary reflected path has the same paid increments. No new source endpoint or all-size primitive is assumed. + +The independent actual path recount removes one local rank-two child and one local rank-22 child per borrow. Across three cores, the full profile changes by H_2−1320 and H_22−1320, W−440, and rank mass−31680, with the same deficit 1936 per vertex. The 234 existing entrance charts remain valid. Remove only the 440 actual ungauged full-residual dirty chains from the literal banks; the normalized stock is then W=439525 and rank mass 31599336, with deficit 46464. + +Retimed partner mixes and inverse mixes have the same scalar counts. Deleting each copy and its reverse removes 880 scalar operations. The recomputed positive adjoint coefficients do not increase, and the remaining dirty inventory decreases. The previous conservative scalar charge remains valid for both reflected words. + +This construction uses the existing bit-word, partner-pair, restored dirty-response, source-line and weighted-rank interfaces. The inherited all-size compiler, selector, routing and analytic conditions remain conditional. The new source borrowing, exact executor and integration were prepared with substantial OpenAI Codex assistance; upstream authorship, licenses and AI disclosures remain unchanged. + +The final package additionally uses three original sources as genuine rank-19 gauge inputs; see GAUGE-SOURCE-BORROWING.md. The 440-copy construction and its independent path delta above remain unchanged. diff --git a/research/coordinated-crossover-pr200/arithmetic.py b/research/coordinated-crossover-pr200/arithmetic.py new file mode 100644 index 0000000000..df7440e640 --- /dev/null +++ b/research/coordinated-crossover-pr200/arithmetic.py @@ -0,0 +1,46 @@ +from pathlib import Path +import json,importlib.util,sys +from fractions import Fraction as Q +sys.set_int_max_str_digits(0) +R=Path(__file__).resolve().parent;O=R;ROOT=R.parents[1] +def load(n,p): + s=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +def enc(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):enc(v) for k,v in x.items()} + if isinstance(x,(list,tuple)):return [enc(v) for v in x] + return x +im=load('im',ROOT/'research/paired-cube-diagonal-bit-168/arithmetic/interval_moment.py') +assembly=load('asm',ROOT/'scripts/paired_cube_assembly.py') +p=json.loads((R/'geometry/packed-frames.json').read_text());base=json.loads((ROOT/'research/source-assisted-v4/certificate.json').read_text()) +def profile(cp): + H={int(t):n for t,n in cp['child_histogram'].items()} + return dict(m=cp.get('m',72),W=cp['W_per_vertex'],child_multiplicities=H,N=cp['deficit_per_vertex'],L=0,total_rank=sum(t*n for t,n in H.items()),maxchild=max(H)) +actual=json.loads((R/'complex-profile-replayed.json').read_text());assert all(actual[k]==base['complex_profile'][k] for k in ['m','W_per_vertex','rank_per_vertex','deficit_per_vertex','child_histogram']);cp=profile(actual);bp=profile(p['profile']['scaled_moment_profile']) +def paid(row,a,bit): + x=im.moment(row,a) + if bit: + l,u=im.log_interval(Q(row['m']));e,f=im.exp_interval(a*l,a*u);w=Q(1,10**16)*Q(32*row['m']*sum(row['child_multiplicities'].values()),row['W']);x.update(lower=x['lower']+w*e,upper=x['upper']+w*f) + return x +def certify(row,bit): + den=10**18;lo=0;hi=den//100 + while hi-lo>1: + md=(lo+hi)//2;v=paid(row,Q(md,den),bit) + if v['upper']<1:lo=md + elif v['lower']>1:hi=md + else:raise ValueError('inconclusive') + a=Q(lo,den);z=Q(hi,den);assert paid(row,a,bit)['upper']<10 for v in z['strict_constraints'].values()) +try:assembly.assembly(a,c['saving'],bridge,k+Q(1,grid),eta=eta,beta=beta) +except AssertionError:pass +else:raise AssertionError('next k accepted') +out=dict(status='PASS_EXACT_47_CONSTRAINT_ASSEMBLY',scope='Conditional finite supplier certificate; retained all-size interfaces and analytic assumptions',bit_profile=bp,complex_profile=cp,bit=b,complex=c,ordinary_chain=chain,bit_ordinary=chain[-1],a_bit=a,a_complex=c['saving'],eta=eta,beta=beta,kappa=k,kappa_float=float(k),binding='bit',assembly=z,adjacent_kappa_rejected=True) +(O/'assembly.json').write_text(json.dumps(enc(out),indent=2,sort_keys=True)+'\n') +print(json.dumps(enc({k:out[k] for k in ['status','kappa','kappa_float','bit_ordinary','a_complex']}),indent=2)) diff --git a/research/coordinated-crossover-pr200/baseline-pr202.part01 b/research/coordinated-crossover-pr200/baseline-pr202.part01 new file mode 100644 index 0000000000..abc3e2fb85 Binary files /dev/null and b/research/coordinated-crossover-pr200/baseline-pr202.part01 differ diff --git a/research/coordinated-crossover-pr200/baseline-pr202.part02 b/research/coordinated-crossover-pr200/baseline-pr202.part02 new file mode 100644 index 0000000000..047bac3233 Binary files /dev/null and b/research/coordinated-crossover-pr200/baseline-pr202.part02 differ diff --git a/research/coordinated-crossover-pr200/baseline-pr202.part03 b/research/coordinated-crossover-pr200/baseline-pr202.part03 new file mode 100644 index 0000000000..dea0a3b789 Binary files /dev/null and b/research/coordinated-crossover-pr200/baseline-pr202.part03 differ diff --git a/research/coordinated-crossover-pr200/baseline-pr202.part04 b/research/coordinated-crossover-pr200/baseline-pr202.part04 new file mode 100644 index 0000000000..bbf44c183d Binary files /dev/null and b/research/coordinated-crossover-pr200/baseline-pr202.part04 differ diff --git a/research/coordinated-crossover-pr200/baseline-pr202.part05 b/research/coordinated-crossover-pr200/baseline-pr202.part05 new file mode 100644 index 0000000000..6ef03d88c3 Binary files /dev/null and b/research/coordinated-crossover-pr200/baseline-pr202.part05 differ diff --git a/research/coordinated-crossover-pr200/borrow/PROVENANCE.json b/research/coordinated-crossover-pr200/borrow/PROVENANCE.json new file mode 100644 index 0000000000..334c7f3a81 --- /dev/null +++ b/research/coordinated-crossover-pr200/borrow/PROVENANCE.json @@ -0,0 +1,18 @@ +{ + "scope": "Pre-integration source packet provenance. Portable executor adapts paths and adds mandatory controls and gauge-response checks.", + "precursor_packet": { + "status": "FROZEN_EXACT_SOURCE_BORROWING_INPUTS", + "files": { + "borrow_terminal.py": "009689944a6782123ceb2595036c3f616551b67d2b7a4b4b7cea97bf50217d9d", + "borrow-selection.json": "6932749407e14b199651f0a7deff02c6de74e2c1be0a1300263f1e164927fb8b", + "borrow-terminal-replay.json": "2bbce85126d882da80cf437a29bd15df9b72566bae7eaf22e1f21cc85b213f2e", + "borrow-controls.json": "a6b63ee8b85ae7f43c874fb1df619407a94a94781e0d90ce35617a7c24a64521" + }, + "baseline_package": "/private/tmp/joint82-package", + "baseline_manifest_sha256": "90617370d62e4ba82865fef5e4de85e1a0e08aba36369d7c0d70b60c4227dca0", + "boundary_audit": "/private/tmp/original-gauge-order/source-borrow-boundary.json", + "field": "F2 with exact integer defining decoder in both signs", + "new_all_size_primitive": false, + "scope": "Source \u03c7 line tofull, exactsource+dirtyrestoration; same inheritedscalar/transvection andrankcompiler interfaces." + } +} diff --git a/research/coordinated-crossover-pr200/borrow/boundary.py b/research/coordinated-crossover-pr200/borrow/boundary.py new file mode 100644 index 0000000000..720a3e9e42 --- /dev/null +++ b/research/coordinated-crossover-pr200/borrow/boundary.py @@ -0,0 +1,88 @@ +#!/usr/bin/env python3 +"""Independent source-slot endpoint and paid-path audit for440 copy elisions. +Prepared with OpenAI Codex assistance; no scalar replay duplicated here. +""" +import sys,json,importlib.util +from pathlib import Path +from collections import Counter,defaultdict +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;p=HERE.parent/'joint/joint_word.py' +spec=importlib.util.spec_from_file_location('boundary_seed',p);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +w=m.Candidate();C=w.C;C.decoder();C.geometry() +selection=json.loads((HERE/'selection.json').read_text()) +recipient={d:b for b,d in w.pairs};kpair={e['passive']:e for e in w.k['entries']} +roots=defaultdict(list) +for j,s in enumerate(w.w['rootroles']):roots[s].append((j,w.w['root_frame'][j])) +full=w.w['full_frame'];source_roles=set(w.source.values()) +results=[];delta=Counter();alias_count=0;all_early_delta=Counter() +def histogram(start,events): + prev=start;hist=Counter() + for tag,f in events: + assert prev is None or C.sub(prev,f),('nonnested',tag,prev,f) + d=C.dimf[f]-(C.dimf[prev] if prev is not None else 0) + if d:hist[d]+=1 + prev=f + return hist +for r in selection: + s,n,i,early=r['role'],r['source'],r['omit_copy'],r['early'] + assert s not in w.gauge and s not in source_roles and s not in w.donor + assert i==w.role_ops[s][0] and w.ops[i][0]==s and w.ops[i][2]==n + assert i in w.phase1 + e=kpair[n];line=w.w['source_frame'][n];mix=e['mix_frame'] + assert e['carrier']==r['partner'] and e['passive']==n + physical=[s]+([recipient[s]] if s in recipient else []) + events=[] + for j,role in enumerate(physical): + if j: + alias_count+=1 + assert w.gauge[role]['role']==role and w.phys[role]==s + assert w.last[s]a) + assert reflected_hist==new + delta.update(got) + results.append(dict(role=s,source=n,aliased_recipient=recipient.get(s), + original_source_endpoint_frame=line,omitted_copy=i,early_mix=early, + old_aux_histogram=dict(sorted(old.items())),new_source_histogram=dict(sorted(new.items())), + local_histogram_delta={rank:count for rank,count in sorted(got.items()) if count}, + reflected_histogram_equal=True)) +assert len(results)==440 and alias_count==67 +out=dict(scope='INDEPENDENT EXACT SOURCE ENDPOINT AND FRAME-PATH AUDIT; SCALAR ADMISSION OWNED BY SEPARATE EXECUTOR', + sources_borrowed=len(results),borrowed_physical_donor_alias_chains=alias_count, + all_source_start_frames_preserved=True,all_source_end_frames_full=True, + every_spliced_frame_inclusion_checked=True,all_reflected_path_histograms_equal=True, + local_histogram_delta={rank:count for rank,count in sorted(delta.items()) if count}, + shared_histogram_delta={rank:3*count for rank,count in sorted(delta.items()) if count}, + local_rank_mass_delta=sum(rank*count for rank,count in delta.items()), + shared_rank_mass_delta=3*sum(rank*count for rank,count in delta.items()), + physical_role_stock_delta=-len(results),shared_m=3*w.h, + deficit_change=-(3*w.h)*len(results)-3*sum(rank*count for rank,count in delta.items()), + results=results) +assert out['deficit_change']==0 +(HERE/'boundary.json').write_text(json.dumps(out,indent=2)+'\n') +print(json.dumps({k:v for k,v in out.items() if k!='results'},indent=2)) diff --git a/research/coordinated-crossover-pr200/borrow/derive_profile.py b/research/coordinated-crossover-pr200/borrow/derive_profile.py new file mode 100644 index 0000000000..57d23f4a38 --- /dev/null +++ b/research/coordinated-crossover-pr200/borrow/derive_profile.py @@ -0,0 +1,45 @@ +"""Reconstruct the complete paid profile from actual spliced source/dirty paths.""" +from pathlib import Path +from collections import Counter +import json,sys +sys.dont_write_bytecode=True +from replay import W,selection,adj,oldadj,regs,removed +HERE=Path(__file__).resolve().parent;PACKAGE=HERE.parent +base=json.loads((PACKAGE/'joint/joint-replay.json').read_text());audit=json.loads((HERE/'boundary.json').read_text());scalar=json.loads((HERE/'replay.json').read_text()) +assert scalar['F2']['dirty']==len(regs)==16674 +assert len(scalar['integer'])==2 and {r['direction']for r in scalar['integer']}=={1,-1} +assert all(r['all_source_and_dirty_restored']and r['formal_columns']==20194 for r in [scalar['F2']]+scalar['integer']) +assert len(audit['results'])==len(selection)==440 +assert {r['role']for r in audit['results']}=={r['role']for r in selection} +assert all(adj[s]==oldadj[s]for s in W.gauge) +# Every actual dirty path except a borrowed/deleted path remains unchanged. +local=Counter({int(k):n for k,n in base['profile']['physical_internal_histogram'].items()}) +_,_,source,_=W.C.chains();source=Counter(source) +for r in audit['results']: + local.subtract({int(k):n for k,n in r['old_aux_histogram'].items()}) + source.subtract({1:1,22:1}) + source.update({int(k):n for k,n in r['new_source_histogram'].items()}) +assert all(n>=0 for n in local.values())and all(n>=0 for n in source.values()) +# The changed adjoint agrees on every gauge, all terminal actions remain, +# and partner deliveries retain their exact original target anchors/frames. +target=Counter({int(k):n for k,n in base['profile']['physical_target_histogram'].items()}) +child=Counter() +for part in [local,target,source]: + for rank,count in part.items(): + if rank and count:child[rank]+=3*count +for role,z in W.gauge.items(): + if role not in W.donor:child[3*z['dim']]+=1 +child[2]+=2*W.v +assert all(count>0 for count in child.values()) +delta=Counter(child);delta.subtract({int(k):n for k,n in base['profile']['child_histogram'].items()});delta={k:v for k,v in delta.items()if v} +assert delta=={int(k):v for k,v in audit['shared_histogram_delta'].items()}=={2:-1320,22:-1320} +physical=len(regs);stock=2*W.v+physical;mass=sum(rank*count for rank,count in child.items());deficit=72*stock-mass +assert stock==20194 and deficit==base['profile']['deficit_per_vertex']==1936 +assert sum(rank*count for rank,count in target.items())==W.v*(W.h-1) +assert sum(rank*count for rank,count in source.items())==W.v*(W.h-1) +def compact(x):return {str(k):n for k,n in sorted(x.items())if n} +profile=dict(base['profile'],R=physical,active_virtual_R=base['profile']['active_virtual_R']-440,W_per_vertex=stock,rank_per_vertex=mass,child_histogram=compact(child),physical_internal_histogram=compact(local),physical_source_histogram=compact(source),physical_target_histogram=compact(target),physical_original_sources_borrowed=440) +assert profile['maxchild']==max(child) +out=dict(status='PASS_COMPLETE_SOURCE_BORROWED_PROFILE',profile=profile,actual_child_delta=delta,source_boundary_audit='boundary.json',scalar_replay='replay.json',all_gauge_adjoint_coefficients_retained=True,all_target_anchor_frames_retained=True,old_adjoint_replaced=True,removed_auxiliary_copy_gates=440,removed_forward_reverse_scalar_gates=880,retimed_partner_mix_count_unchanged=True,remaining_adjoint_coefficients_do_not_increase=True) +(HERE/'profile.json').write_text(json.dumps(out,indent=2)+'\n') +print('PASS complete spliced source/internal/target profile',dict(W=stock,rank=mass,deficit=deficit,delta=delta),flush=True) diff --git a/research/coordinated-crossover-pr200/borrow/replay.py b/research/coordinated-crossover-pr200/borrow/replay.py new file mode 100644 index 0000000000..3184271aa0 --- /dev/null +++ b/research/coordinated-crossover-pr200/borrow/replay.py @@ -0,0 +1,125 @@ +"""Complete scalar admission of original-source singleton-copy elision. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from pathlib import Path +from collections import Counter,defaultdict +import json,sys,importlib.util,time,gc +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;D=HERE.parent/'joint';spec=importlib.util.spec_from_file_location('source82',D/'joint_word.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +W=m.Candidate();C=W.C;C.decoder();C.geometry();selection=json.loads((HERE/'selection.json').read_text()) +borrow={r['role']:r['source']for r in selection};by_source={r['source']:r for r in selection};omitted={r['omit_copy']for r in selection};early={r['early']:r for r in selection};assert len(early)==len(borrow)==len(selection)==440 +adj=[{}for _ in range(W.R)] +for r,s in zip(W.g['roots'],W.w['rootroles']): + for t in r['targets']:adj[s][t]=adj[s].get(t,0)+1 +for i in reversed(W.phase1+W.rest): + if i in omitted:continue + a,b,_=W.ops[i] + for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c +oldadj=W.adjoint() +assert all(all(02*bound + (HERE/'replay.json').write_text(json.dumps(out,indent=2)+'\n') + print('PASS borrowed source word, both integer signs, all columns and controls',flush=True) diff --git a/research/coordinated-crossover-pr200/borrow/selection.json b/research/coordinated-crossover-pr200/borrow/selection.json new file mode 100644 index 0000000000..80d0a76822 --- /dev/null +++ b/research/coordinated-crossover-pr200/borrow/selection.json @@ -0,0 +1,5282 @@ +[ + { + "source": 3, + "role": 13, + "omit_copy": 9, + "partner": 0, + "windows": [ + 9252 + ], + "phase1_copy": true, + "aliased_to": 17404, + "early": 9252 + }, + { + "source": 6, + "role": 26, + "omit_copy": 19, + "partner": 5, + "windows": [ + 9258 + ], + "phase1_copy": true, + "aliased_to": 17415, + "early": 9258 + }, + { + "source": 11, + "role": 45, + "omit_copy": 33, + "partner": 8, + "windows": [ + 9288 + ], + "phase1_copy": true, + "aliased_to": 17516, + "early": 9288 + }, + { + "source": 14, + "role": 58, + "omit_copy": 43, + 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diff --git a/research/coordinated-crossover-pr200/frames/verify-bit-frames.py b/research/coordinated-crossover-pr200/frames/verify-bit-frames.py new file mode 100644 index 0000000000..7093a3b805 --- /dev/null +++ b/research/coordinated-crossover-pr200/frames/verify-bit-frames.py @@ -0,0 +1,37 @@ +import sys,json,gzip,hashlib,argparse,types,signal,contextlib,time +from pathlib import Path +from fractions import Fraction +sys.set_int_max_str_digits(0);sys.dont_write_bytecode=True +ap=argparse.ArgumentParser();ap.add_argument('--package',required=True);ap.add_argument('--frames',required=True);ap.add_argument('--out',required=True);ap.add_argument('--full',action='store_true');a=ap.parse_args();P=Path(a.package).resolve();O=Path(a.out);O.mkdir(parents=True,exist_ok=True) +resource=types.ModuleType('resource');resource.RLIMIT_CPU=0;resource.RUSAGE_SELF=0;resource.setrlimit=lambda *xs:None;resource.getrusage=lambda *xs:types.SimpleNamespace(ru_maxrss=0);sys.modules.setdefault('resource',resource) +if not hasattr(signal,'alarm'):signal.alarm=lambda *xs:None +sys.path.insert(0,str(P/'bit'));sys.path.insert(0,str(P/'arithmetic')) +from word import Candidate +from terminal import prove +from prime_witnesses import certificate as primes +from prove import certify +W=Candidate();C=W.C;B=json.loads(Path(a.frames).read_text());pins={str(p):hashlib.sha256(p.read_bytes()).hexdigest() for p in W.input_paths+[Path(a.frames),P/'selected/bit/sinks.json',P/'bit/word.py',P/'bit/base_word.py',P/'bit/terminal.py',P/'bit/prime_witnesses.py',Path(W.module.__file__)]} +public=W.opframe[:] +for i,rows in B:W.opframe[i]=W.register(rows) +W.changed_frames=[i for i,(x,y) in enumerate(zip(W.original_opframe,W.opframe)) if x!=y];W.endframe={s:W.opframe[xs[-1]] for s,xs in W.role_ops.items()} +W.exact_frames();baseline=W.row();selection=json.loads((P/'selected/bit/sinks.json').read_text()) +print('PASS full exact rational value, geometry and alias checks; changes',len(B),flush=True) +if a.full: + with contextlib.redirect_stdout(sys.stderr):record=prove(W,selection) + record.pop('seconds');record.pop('maxrss');row=record['profile'];prime=primes(W) + (O/'prime-witnesses.json.gz').write_bytes(gzip.compress((json.dumps(prime,sort_keys=True,separators=(',',':'))+'\n').encode(),mtime=0));prime={k:v for k,v in prime.items() if k!='frame_witnesses'} + row['child_histogram']={int(k):v for k,v in row['child_histogram'].items()} + co=certify(row) +else: + # Exact integer terminal ledger follows the original cancellation once complete + # target trajectories and exact all-column replay are admitted by the full mode. + row=baseline;record=None;prime=None;co=None + +def js(x): + if isinstance(x,Fraction):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [js(v) for v in x] + return x +assert pins=={p:hashlib.sha256(Path(p).read_bytes()).hexdigest() for p in pins} +R=js(dict(status='FULL_FINITE_REPLAY_PASS' if a.full else 'EXACT_FRAME_ONLY_NOT_FULL_REPLAY',input_pins=pins,changed_public_ops=len(B),baseline_profile=baseline,profile=row,terminal=record,coarse=co,prime_witnesses=prime,word_scalar_ops_unchanged=True,gauge_endpoint_and_aliases_unchanged=True)) +(O/'verification.json').write_text(json.dumps(R,indent=1)+'\n');print('PASS',R['status'],R['coarse']['coarse_saving'] if co else '',flush=True) \ No newline at end of file diff --git a/research/coordinated-crossover-pr200/gaugeb/PROVENANCE.json b/research/coordinated-crossover-pr200/gaugeb/PROVENANCE.json new file mode 100644 index 0000000000..32623df31a --- /dev/null +++ b/research/coordinated-crossover-pr200/gaugeb/PROVENANCE.json @@ -0,0 +1,8 @@ +{ + "selection_sha256": "b0f9f0e67f94a3c21069f393ea27f9483d315bff2f53f77270163065a6345d1c", + "source440_manifest": "17fb2b198f633a8ca6b61004970c979bf9ec1861c9d02d800c6be1632c7a3c22", + "source440_cut117_manifest": "2e17de69bea7d0b2a0f95ffabcb5bb3a271f6c4ad18764f67c5bf6e6e453b681", + "scalar_prototype_sha256": "a85e28ccce6e22ed912e4cefc85a4babe1de9243bb3a0f2710304d3a88a2c2e7", + "geometry_screen_sha256": "bf0a8efd28e86551ce7724c04b745b846d02e0e7bcab8bf21c7d9590fceb1744", + "scope": "Original scalar prototype adapted to relative paths and mandatory complete integer admission; complete physical ledgers and literal banks reconstructed separately. Prepared with OpenAI Codex assistance." +} diff --git a/research/coordinated-crossover-pr200/gaugeb/boundary.py b/research/coordinated-crossover-pr200/gaugeb/boundary.py new file mode 100644 index 0000000000..033d983fa4 --- /dev/null +++ b/research/coordinated-crossover-pr200/gaugeb/boundary.py @@ -0,0 +1,42 @@ +"""Exact original-source paths through genuine gauge donor/recipient chains. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from pathlib import Path +from collections import Counter,defaultdict +import json,sys,importlib.util +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;P=HERE.parent +spec=importlib.util.spec_from_file_location('gauge_source_boundary_word',P/'joint/joint_word.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +W=m.Candidate();C=W.C;C.decoder();C.geometry() +selection=json.loads((HERE/'selection.json').read_text());old=json.loads((P/'borrow/selection.json').read_text());oldroles={r['role']for r in old};oldpair={r['source']for r in old}|{r['partner']for r in old} +recipient={d:b for b,d in W.pairs};kpair={e['passive']:e for e in W.k['entries']};roots=defaultdict(list) +for j,s in enumerate(W.w['rootroles']):roots[s].append(W.w['root_frame'][j]) +sources=set(W.source.values());touched={s for i in W.phase1 for s in W.ops[i][:2]};full=W.w['full_frame'] +def histogram(chain): + assert all(C.sub(a,b)for a,b in zip(chain,chain[1:]));assert all(C.nondeg(f)for f in set(chain)) + h=Counter(C.dimf[b]-C.dimf[a]for a,b in zip(chain,chain[1:])if C.dimf[b]>C.dimf[a]) + dims=[C.dimf[f]for f in chain];refl=[W.h-d for d in reversed(dims)] + assert h==Counter(b-a for a,b in zip(refl,refl[1:])if b>a) + return h +results=[];delta=Counter();rawdelta=Counter();used=set(oldpair) +for r in selection: + s,n,c=r['role'],r['source'],r['partner'];assert s in W.gauge and s not in W.donor and s not in oldroles and s not in sources and s not in touched + assert n not in used and c not in used;used.update([n,c]);e=kpair[n];assert e['carrier']==c + z=W.gauge[s];g=z['frame'];p=e['mix_frame'];assert W.readtime[s]==0 and C.sub(p,g) + assert C.sub(W.w['source_frame'][c],p)and C.sub(p,e['deliver_frame']) + chain=[g]+[W.opframe[i]for i in W.role_ops[s]]+roots[s] + if s in recipient: + b=recipient[s];assert W.last[s]=0 for h in (local,source,target)for n in h.values()) +child=Counter() +for h in (local,source,target): + for rank,n in h.items(): + if rank and n:child[rank]+=3*n +for s,z in W.gauge.items(): + if s not in W.donor and s not in selected:child[3*z['dim']]+=1 +child[2]+=2*W.v +mass=sum(rank*n for rank,n in child.items());stock=r['W_per_vertex']-3;physical=r['R']-3;deficit=72*stock-mass +assert stock==20191 and physical==16671 and deficit==r['deficit_per_vertex']==1936 +assert sum(k*v for k,v in source.items())==W.v*(W.h-1) +assert sum(k*v for k,v in target.items())==W.v*(W.h-1) +delta=Counter(child);delta.subtract({int(k):n for k,n in r['child_histogram'].items()});delta={k:v for k,v in delta.items()if v};assert delta=={17:9,22:-9,57:-3} +def compact(h):return {str(k):n for k,n in sorted(h.items())if n} +profile=dict(r,R=physical,active_virtual_R=r['active_virtual_R']-3,W_per_vertex=stock,rank_per_vertex=mass,child_histogram=compact(child),physical_internal_histogram=compact(local),physical_source_histogram=compact(source),physical_target_histogram=compact(target),physical_original_sources_borrowed=443) +out=dict(status='PASS_COMPLETE_443_SOURCE_PROFILE',profile=profile,actual_child_delta=delta,all_gauge_adjoint_coefficients_retained=True,all_target_anchor_frames_retained=True,source_boundary_audit='boundary.json',scalar_replay='replay.json') +(HERE/'profile.json').write_text(json.dumps(out,indent=2)+'\n');print('PASS443 complete ledgers',dict(W=stock,R=physical,rank=mass,deficit=deficit,delta=delta),flush=True) diff --git a/research/coordinated-crossover-pr200/gaugeb/replay.py b/research/coordinated-crossover-pr200/gaugeb/replay.py new file mode 100644 index 0000000000..a7ab2077fa --- /dev/null +++ b/research/coordinated-crossover-pr200/gaugeb/replay.py @@ -0,0 +1,141 @@ +"""Scalar prototype: original sources replace genuine gauged dirty slots. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from pathlib import Path +from collections import Counter,defaultdict +import json,sys,importlib.util,time,gc,hashlib +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;D=HERE.parent/'joint';spec=importlib.util.spec_from_file_location('source82',D/'joint_word.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +W=m.Candidate();C=W.C;C.decoder();C.geometry();selection=json.loads((HERE.parent/'borrow/selection.json').read_text());gauge_selection=json.loads((HERE/'selection.json').read_text());gauge_selection=gauge_selection['selection']if isinstance(gauge_selection,dict)else gauge_selection +borrow={r['role']:r['source']for r in selection};by_source={r['source']:r for r in selection};omitted={r['omit_copy']for r in selection};early={r['early']:r for r in selection};assert len(early)==len(borrow)==len(selection)==440 +gauge_borrow={r['role']:r['source']for r in gauge_selection};kpair={e['passive']:e for e in W.k['entries']};used_sources=set(by_source)|{r['partner']for r in selection} +assert len(gauge_borrow)==len(gauge_selection) and len(set(gauge_borrow.values()))==len(gauge_selection) +for r in gauge_selection: + assert r['source']in kpair and r['partner']==kpair[r['source']]['carrier'] + assert r['role']in W.gauge and r['role']not in W.donor and r['role']not in borrow + assert r['source']not in used_sources and r['partner']not in used_sources + used_sources.update([r['source'],r['partner']]) +borrow.update(gauge_borrow);by_source.update({r['source']:r for r in gauge_selection}) +input_paths=[*W.input_paths,W.framepath,D/'joint_word.py',D/'joint-selection.json',D/'pairs.json',Path(W.module.__file__),D/'joint-replay.json',(HERE/'selection.json'),Path(__file__),(HERE.parent/'borrow/selection.json')] +input_pins={str(p):hashlib.sha256(p.read_bytes()).hexdigest()for p in input_paths} +adj=[{}for _ in range(W.R)] +for r,s in zip(W.g['roots'],W.w['rootroles']): + for t in r['targets']:adj[s][t]=adj[s].get(t,0)+1 +for i in reversed(W.phase1+W.rest): + if i in omitted:continue + a,b,_=W.ops[i] + for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c +oldadj=W.adjoint() +assert all(all(02*bound + assert input_pins=={str(p):hashlib.sha256(p.read_bytes()).hexdigest()for p in input_paths} + out['input_pins']=input_pins + (HERE/'replay.json').write_text(json.dumps(out,indent=2)+'\n') + print('PASS complete gauged source word, both integer signs, all columns and five controls',flush=True) diff --git a/research/coordinated-crossover-pr200/gaugeb/selection.json b/research/coordinated-crossover-pr200/gaugeb/selection.json new file mode 100644 index 0000000000..8906d43a1c --- /dev/null +++ b/research/coordinated-crossover-pr200/gaugeb/selection.json @@ -0,0 +1,17 @@ +[ + { + "role": 14697, + "source": 106, + "partner": 105 + }, + { + "role": 14696, + "source": 138, + "partner": 137 + }, + { + "role": 14699, + "source": 346, + "partner": 345 + } +] diff --git a/research/coordinated-crossover-pr200/geometry/BANK-PROOF-PR200.md b/research/coordinated-crossover-pr200/geometry/BANK-PROOF-PR200.md new file mode 100644 index 0000000000..a9516fdb77 --- /dev/null +++ b/research/coordinated-crossover-pr200/geometry/BANK-PROOF-PR200.md @@ -0,0 +1,61 @@ +> Historical predecessor proof. The current16-gauge construction, including mixed4/5/6/24 residual banks, is specified and replayed by JOINT-GAUGES.md and joint/. + +Historical predecessor bank construction. The current 4/6/24 extension, 36 replicas and gauged-donor proof are in ../JOINT-GAUGES.md; current execution starts at ../verify.py. + +# Completed entrance banks on the PR200 physical bit word + +2026-10-09. A sufficient finite construction, retaining the upstream all-size interfaces. This is not an unconditional multiplication theorem and is not a new Lean certificate. + +## Exact unchanged input + +PR200 commit `a1175449f34d39ff933d9d8ab23ced1f32b290ec`, package `research/paired-cube-diagonal-bit-168`. Its graph, scalar word, fixed source-pair chronology, physical frame bases, compensated handoffs, terminal sinks and prime witnesses are unchanged. The source includes 18,908 logical auxiliary roles, 1,760 compensated aliases and 34 terminal sinks, leaving 17,114 physical auxiliary chains. There are 2,200 surviving genuine rank-20 entrance gauges. The 1,760 rank-21 recipient gauges are internal splices and receive no separate bank allocation. Deleted terminals are neither gauges nor alias endpoints. The remaining 14,914 physical chains are retained completely. + +The original data channels are 1,760 sources and 1,760 targets. The original complete paid profile is width72, stock20,634, rank mass1,483,712, deficit1,936, with2,200 rank60 exterior children. Source births are not treated as dirty entrance gauges. + +## Universal endpoint and explicit allocation + +Reuse our PR186 completed-core endpoint and paid group routing. For a coordinate projector P and arbitrary incoming addresses x,y over the eligible local ring, the literal map is + +`S_P(x,y) = (x - P*x + P*y, y - P*y + P*x)`. + +On an included coordinate this exchanges x and y; on every other coordinate it preserves both. Thus disjoint coordinate blocks partitioning all72 coordinates compose exactly to the full swap, including arbitrary correlated dirty contents and spectator fields. The reverse block schedule is the literal inverse. This is a ring-general identity; it does not replace the odd-prime address space with F2 just because the payload decoder is binary. + +The established common weighted chart conjugates every block by the same Q_A, so intermediate Q_A^-1 Q_A cancels. For each role, the inherited fixed normalizer sends its true residual projector to its assigned block. Group-indexed routing assigns a role invocation g to bank gH^-1, so each occurrence visits every bank exactly once. Normalizers inside a bank can be made distinct by the inherited finite scalar choice without changing conjugation. Replicas execute serially and stages own different banks. No uninitialized bank or unfinished core is reused. + +Use nine physical replicas of the full unchanged core. In each stage, allocate the9*2,200 selected role-copy occurrences into1,100 banks with18 four-coordinate blocks. Allocate the9*14,914 other occurrences into44,742 banks with three24-coordinate blocks. Both partitions fill every bank exactly; no positive-rank completion child remains. The generator in `pack-pr200.py` maps sorted actual surviving role IDs and replica IDs to explicit bank/block numbers and hashes every assignment. It checks all462,078 role-copy uses across three stages exactly once. Nine replicas are physical, whereas factor three merely clears the rational moment stock. + +There are45,842 banks per stage,137,526 across all stages, and31,680 data registers in nine replicas. The literal persistent stock is169,206, exactly9*(56,402/3). + +## Fully charged child inventory and exact price + +Retain every internal, source, target, center, compensating and terminal-substitution child. Remove exactly the2,200 rank60 exterior children from the original per-vertex histogram. No other child count changes. Then + +`W = 2*1760 + 3*(2200/18 +14914/3) =56402/3`, + +`rank =1483712 -2200*60 =1351712`, + +`72*W -rank =1936`. + +The largest retained child is22. On the integer normalization used by the moment verifier, stock is56,402, rank mass4,055,136, deficit5,808, and every child count is multiplied by three. This normalization removes6,600 rank60 exteriors, corresponding to the2,200 per-vertex children above; it must not be confused with the nine-replica literal realization. + +The original worst-case bad fraction10^-16 and fallback32*72^2 per actual retained child are charged. Independent outward interval calculations based on4/3 and2 certify + +`a0=683528191056257/10^18`. + +They reject the adjacent coarse grid point for this fixed profile and worst-case envelope. The established atom wrapper uses a_old=384599/10^10 and the first10^-24 atom above a0/(1+a0-a_old), giving the paid ordinary saving + +`A_B=170771888233960718836822306974273386891/(250*10^39)` + +`A_B≈0.0006830875529358429`. + +Both strict adapter/borrowed-row tolls remain charged. The parent must compose this bit saving with an admitted complex supplier, its full scalar/group/router/layout bills and the unchanged47-constraint balanced body. Component gains are never added. No final kappa is claimed in this lane until that assembly runs. + +## Other crossover ideas actually assessed + +The current new word still has exactly the4/24 residual families and both tile72 exactly. The rational heterogeneous configuration theorem instantiates the same volume-filling construction; there is no new LP improvement to add. It is ready for future genuinely different residual types. The optional nonorthogonal parity cover cannot be substituted into this odd-prime address model. Even in its proper binary-address model, its overlapping local cores must stay charged. The Parseval phase identity similarly repairs a binary Gaussian endpoint, but no unchanged PR200 local child is a new arbitrary Gram-resolving coding core. These identities are retained as design tools and are not hidden supplier oracles. + +## Verification and retained scope + +`python -B geometry/pack-pr200.py --full` executes the immutable PR200 bit admission, its exact rational frame/source/gauge/partner chronology, all original and terminal-modified F2 and defining integer columns, adverse controls and all24,401 frame prime witnesses. It then checks literal bank coordinate columns, inverse columns, omitted/duplicate blocks, exact assignments and both rational moment engines. On Windows the owned wrapper supplies only the removed ru_maxrss diagnostic when POSIX resource is unavailable; no mathematical checker changes. + +General Clifford/tensor realization, uniform weighted local-ring compilation, common chart selection, restored rows, paid routing/layout, prime supply, precision/recovery and all-size analytic transfer remain the original stated conditions. This construction changes a finite word's dirty-bank allocation under those same conditions. Credit PR186's original bank proof, Chafik Boukhalfa's PR200 physical word, eumemic's PR168 lineage, James Chang's terminal substitution, and every retained upstream attribution. \ No newline at end of file diff --git a/research/coordinated-crossover-pr200/geometry/audit-gauge-charts.py b/research/coordinated-crossover-pr200/geometry/audit-gauge-charts.py new file mode 100644 index 0000000000..d0b050bc99 --- /dev/null +++ b/research/coordinated-crossover-pr200/geometry/audit-gauge-charts.py @@ -0,0 +1,51 @@ +"""Reuse PR197's exact gauge chart factors on unchanged PR200 entrances. +Checks both inverse matrix identities, literal elementary factor replay, +all factor/unit denominators, and a conservative fully charged routing bound. +""" +from pathlib import Path +from collections import Counter +from fractions import Fraction as Q +from math import gcd +import sys,json,hashlib,importlib.util +sys.set_int_max_str_digits(0);sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +spec=importlib.util.spec_from_file_location('own_bank',HERE/'pack-pr200.py');G=importlib.util.module_from_spec(spec);spec.loader.exec_module(G) +packing=HERE/'retained-packing.py' +sp=importlib.util.spec_from_file_location('retained_exact_chart_factorizer',packing);P=importlib.util.module_from_spec(sp);sp.loader.exec_module(P) +word=G.proof.Candidate();C=word.C +selected={s:z for s,z in word.gauge.items() if s not in word.donor};inventory=Counter(z['frame'] for z in selected.values()) +G.need(len(selected)==2200 and len(inventory)==220,'actual unchanged220gauge frames') +records=[];maxops=maxnum=maxden=maxC=maxB=0 +for f,count in sorted(inventory.items()): + A=C.A[f];sigma=C.B[f];G.need(len(A)==4 and len(sigma)==20,'actual rank4 residual') + residual=[] + for a in A: + r=[15*x-sum(a) for x in a];d0=gcd(*r);residual.append([x//d0 for x in r]) + G.need(all(9*sum(x*y for x,y in zip(a,b))-sum(a)*sum(b)==0 for a in residual for b in sigma),'literal Gorthogonal residual basis') + B=list(map(list,zip(*(residual+sigma))));inv,d,ops=P.inverse_integer(B) + for left,right in [(B,inv),(inv,B)]: + G.need(all(sum(x*y for x,y in zip(row,col))==d*int(i==j) for i,row in enumerate(left) for j,col in enumerate(zip(*right))),'two exact inverse identities') + replay=[list(map(Q,r)) for r in B] + for op,i,j,n,den in ops: + if op=='swap':replay[i],replay[j]=replay[j],replay[i] + elif op=='scale':replay[i]=[Q(n,den)*x for x in replay[i]] + else: + G.need(op=='add','retained elementary factor type');replay[i]=[x+Q(n,den)*y for x,y in zip(replay[i],replay[j])] + G.need(all(x==int(i==j) for i,row in enumerate(replay) for j,x in enumerate(row)),'independent factor replay') + maxops=max(maxops,len(ops));maxnum=max(maxnum,max(abs(o[3]) for o in ops));maxden=max(maxden,d,max(o[4] for o in ops));maxC=max(maxC,max(abs(x) for r in inv for x in r));maxB=max(maxB,max(abs(x) for r in B for x in r)) + records.append(dict(frame=f,count=count,basis=B,inverse_numerators=inv,inverse_denominator=d,factors=ops)) +G.need(max(maxnum,maxden,maxC,maxB,18)<2**80,'all literal inverse and chart units below inherited prime bound') +# t in1..18 supplies18 distinct fixed scalar choices per selected bank. At most +# one scalar per earlier normalizer is forbidden; conjugation stays unchanged. +# Rational distinctness survives q>2^80 by this bound on cleared differences. +cleared_difference_bound=2*18*max(maxC,1)*max(maxden,1) +G.need(cleared_difference_bound<2**80,'distinct normalizers remain distinct modulo every allowed prime') +factor_bound=maxops+71+72 +physicalstock=169206;physicalchains=17114;full_core_stage_occurrences=27 +calls=2*full_core_stage_occurrences*((physicalstock-1)+physicalchains*72*factor_bound) +G.need(calls<2**40,'fully literal replicated extra selector bound') +raw=json.dumps(records,sort_keys=True,separators=(',',':')).encode() +import gzip +(HERE/'pr200-gauge-charts.json.gz').write_bytes(gzip.compress(raw,mtime=0)) +out=dict(status='PASS_ALL_ACTUAL_GAUGE_CHARTS_AND_ROUTING_BILL',source_pin='a1175449f34d39ff933d9d8ab23ced1f32b290ec',retained_factorizer_sha256=hashlib.sha256(packing.read_bytes()).hexdigest(),gauges=2200,distinct_gauge_frames=220,max_chart_factors=maxops,max_factor_numerator=maxnum,max_denominator_or_inverse_denominator=maxden,max_inverse_numerator=maxC,max_basis_numerator=maxB,chart_witness_sha256=hashlib.sha256((HERE/'pr200-gauge-charts.json.gz').read_bytes()).hexdigest(),greedy_distinct_scalars=list(range(1,19)),cleared_normalizer_difference_bound=cleared_difference_bound,permutation_transpositions_bound=71,extra_distinct_scalar_coordinate_scales_bound=72,combined_chart_factor_bound=factor_bound,nine_full_replicas=True,total_stage_core_occurrences=27,literal_persistent_stock=physicalstock,conservative_extra_selector_calls=calls,selector_calls_below_2pow40=True,prime_guard='Every nonzero factor/inverse denominator and fixed scalar is smaller than2^80; all actual changes are invertible for every inherited primeq>2^80. Distinct normalizers remain distinct by cleared entry bounds.',routing_payment='These finite extra calls use inherited completed old ordinary selector; they are O(K V w^(1-a_old)), absorbed by strict finite-leaf atom/row toll as in PR197 PROOF5. No extra positive-rank children and no new external row reserve.',scope='Exact finite address chart, inverse, unit and replicated routing bill on same220gauge frames; allsize weighted/restored selector guarantee stays inherited.') +(HERE/'PR200-GAUGE-CHART-AUDIT.json').write_text(json.dumps(out,indent=2,sort_keys=True));print(json.dumps(out,indent=2)) \ No newline at end of file diff --git a/research/coordinated-crossover-pr200/geometry/base_two_moment.py b/research/coordinated-crossover-pr200/geometry/base_two_moment.py new file mode 100644 index 0000000000..14a90fa0e7 --- /dev/null +++ b/research/coordinated-crossover-pr200/geometry/base_two_moment.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Maintainer arithmetic cross-check of the pinned PR39 certificate. + +Uses no producer/checker imports. Counts are inputs, not proved by this script. +80-term rational logarithms and 12-term exponentials independently enclose +the two moments. The accompanying written review addresses their realization. +""" +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +GRID = 10**30 + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def log_unit(x): + require(1 <= x <= 2, "logarithm range") + z = (x-1)/(x+1) + lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0)) + return lo, lo+2*z**161/(161*(1-z*z)) + + +def log_bounds(x): + k = 0 + while x > 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + + +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + return total, total+tail + + +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/coordinated-crossover-pr200/geometry/check-normalizer-routing.py b/research/coordinated-crossover-pr200/geometry/check-normalizer-routing.py new file mode 100644 index 0000000000..2bbe2d3bcc --- /dev/null +++ b/research/coordinated-crossover-pr200/geometry/check-normalizer-routing.py @@ -0,0 +1,23 @@ +"""Literal fixed scalars distinguish all same-invocation bank normalizers. +No greedy unknown chart is assumed: H_b=(b+1)*Pi_b*diag(B^-1,I_48). +All gauges share the same unchanged24coordinate stage; outside-coordinate +unit columns distinguish H_b for b=0..17 at every primeq>2^80. +""" +from pathlib import Path +import json +H=Path(__file__).resolve().parent;records=[] +for stage in range(3): + local=set(range(24*stage,24*(stage+1)));j=next(i for i in range(72) if i not in local) + for width,blocks in [(4,18),(24,3)]: + original=list(range(24*stage,24*stage+width));witness=[] + for block in range(blocks): + desired=list(range(block*width,(block+1)*width));src=original+[i for i in range(72) if i not in original];dst=desired+[i for i in range(72) if i not in desired] + pi=dict(zip(src,dst));assert set(pi)==set(pi.values())==set(range(72)) + assert [pi[k] for k in original]==desired + # Embedded B^-1 fixes e_j exactly, so H_b e_j is this literal unit column. + witness.append(dict(block=block,scalar=block+1,unit_column=j,result_row=pi[j],result_coefficient=block+1)) + for a,left in enumerate(witness): + for right in witness[a+1:]:assert (left['result_row'],left['result_coefficient'])!=(right['result_row'],right['result_coefficient']) + records.append(dict(stage=stage,width=width,blocks=blocks,outside_stage_column=j,witnesses=witness)) +out=dict(status='PASS_LITERAL_DISTINCT_NORMALIZERS',records=records,prime_guard='All1..18 are different nonzero units at every primeq>2^80, and remain units/distinct in Z/q^w. Each normalizer scales a literal outside-stage unit column differently. Scaling doesnotchange projectorconjugation.',per_role_scalar_coordinate_factors=72,already_charged_in_chart_bound329=True,no_same_invocation_bank_alias=True) +(H/'LITERAL-NORMALIZER-ROUTING.json').write_text(json.dumps(out,indent=2,sort_keys=True));print(out['status']) \ No newline at end of file diff --git a/research/coordinated-crossover-pr200/geometry/pack-admitted-frames.py b/research/coordinated-crossover-pr200/geometry/pack-admitted-frames.py new file mode 100644 index 0000000000..c4e8ffe01f --- /dev/null +++ b/research/coordinated-crossover-pr200/geometry/pack-admitted-frames.py @@ -0,0 +1,38 @@ +"""Compose admitted frame-only changes with concrete stage-private entrance banks. +Reconstructs every modified frame/physical paid chain, audits all actual prime +witnesses, and independently recomputes two exact paid bank moment engines. +The referenced frame receipt provides the full dirty-column terminal replay. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +import sys,json,gzip,hashlib,argparse,importlib.util +sys.set_int_max_str_digits(0);sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +spec=importlib.util.spec_from_file_location('geometry_bank_pr200',HERE/'pack-pr200.py');G=importlib.util.module_from_spec(spec);spec.loader.exec_module(G) +need=G.need +ap=argparse.ArgumentParser();ap.add_argument('--candidate',required=True);a=ap.parse_args() +D=Path(a.candidate);record=json.loads((D/'checked/verification.json').read_text());frames=D/'opframe-bases.json';primefile=D/'checked/prime-witnesses.json.gz' +need(record['status']=='FULL_FINITE_REPLAY_PASS','complete independent frame dirty-word admission') +for path,want in record['input_pins'].items():need(hashlib.sha256(Path(path).read_bytes()).hexdigest()==want,'actual immutable input pin '+path) +need(record['word_scalar_ops_unchanged'] and record['gauge_endpoint_and_aliases_unchanged'],'unchanged whole-word endpoint classes') +word=G.proof.Candidate();before={k:word.w[k] for k in ['gauges','pairs','rootroles','root_frame','source_frame','sources','reads']};changes=json.loads(frames.read_text()) +for index,B in changes:word.opframe[index]=word.register(B) +word.changed_frames=[i for i,(x,y) in enumerate(zip(word.original_opframe,word.opframe)) if x!=y];word.endframe={s:word.opframe[xs[-1]] for s,xs in word.role_ops.items()} +word.exact_frames();row=word.row() +need(G.encode(row)==record['baseline_profile'],'independent complete modified physical baseline ledger') +need(before=={k:word.w[k] for k in before},'bank source/gauge/endpoints truly unchanged') +need(Counter({int(k):v for k,v in record['terminal']['child_delta'].items()})==Counter({3:-102,21:-102}),'paid34terminal child substitution unchanged') +H={int(k):v for k,v in row['child_histogram'].items()};H[3]-=102;H[21]-=102 +need(H=={int(k):v for k,v in record['profile']['child_histogram'].items()},'independent terminal-paid complete histogram') +prime=G.raw_prime_certificate(word);need(prime==json.loads(gzip.decompress(primefile.read_bytes())),'independent allused modifiedframe prime witness audit') +packed=G.packed(record['profile'],word.w);coarse=G.proof.certify(packed['scaled_moment_profile']) +from base_two_moment import moment as alternate +q=packed['scaled_moment_profile'];hist=list(q['child_histogram'].items());W=q['W_per_vertex'];a0=coarse['coarse_saving'];fallback=32*72**2*sum(n for r,n in hist) +_,upper=alternate(72,W,hist,a0);_,bad=alternate(72,W,[(1,fallback)],a0);need(upper+Q(1,10**16)*bad<1,'independent paid moment accepted') +lower,_=alternate(72,W,hist,a0+Q(1,10**18));badlower,_=alternate(72,W,[(1,fallback)],a0+Q(1,10**18));need(lower+Q(1,10**16)*badlower>1,'independent adjacent paid moment rejected') +allocation=G.literal_allocation(word.w);endpoints=G.endpoint_checks() +for path,want in record['input_pins'].items():need(hashlib.sha256(Path(path).read_bytes()).hexdigest()==want,'inputs remain identical') +out=dict(status='PASS_ADMITTED_FRAME_BANK_COMPOSITION',frame_receipt_sha256=hashlib.sha256((D/'checked/verification.json').read_bytes()).hexdigest(),opframe_override_sha256=hashlib.sha256(frames.read_bytes()).hexdigest(),opframe_changes=len(changes),profile=packed,coarse=coarse,literal_allocation=allocation,endpoints=endpoints,prime_witness_sha256=hashlib.sha256(primefile.read_bytes()).hexdigest(),all_used_frame_prime_audit={k:v for k,v in prime.items() if k!='frame_witnesses'},whole_word_receipt=record['status'],unchanged_entrance_alias_and_terminal_classes=True,scope='Sufficient finite dirty-bank composition of independently admitted full frame word. Original allsize supplier interfaces retained; parent owns finalbalanced assembly.') +name='packed-'+D.name+'.json';(HERE/name).write_text(json.dumps(G.encode(out),indent=2,sort_keys=True)) +print(json.dumps(G.encode(dict(status=out['status'],output=str(HERE/name),changed_ops=len(changes),stock=packed['W_per_vertex'],rank=packed['rank_per_vertex'],coarse=coarse['coarse_saving'],ordinary=coarse['ordinary_saving'],ordinary_float=float(coarse['ordinary_saving']),frames=prime['total_used_frames'])),indent=2)) \ No newline at end of file diff --git a/research/coordinated-crossover-pr200/geometry/pack-pr200.py b/research/coordinated-crossover-pr200/geometry/pack-pr200.py new file mode 100644 index 0000000000..1407b17750 --- /dev/null +++ b/research/coordinated-crossover-pr200/geometry/pack-pr200.py @@ -0,0 +1,121 @@ +"""Apply established completed entrance banks to the immutable PR200 physical word. +Light mode is candidate pricing, never complete word admission. --full replays all +source/target/dirty columns and exact frame/prime/terminal checks through PR200. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +import json,sys,importlib.util,hashlib,contextlib,types +# Windows shim supplies only the removed resource diagnostic, never proof data. +try: import resource +except ImportError: + resource=types.ModuleType("resource");resource.RUSAGE_SELF=0 + resource.getrusage=lambda _:types.SimpleNamespace(ru_maxrss=0) + sys.modules["resource"]=resource +sys.set_int_max_str_digits(0);sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +PKG=HERE.parents[2]/'research/paired-cube-diagonal-bit-168' +sys.path.insert(0,str(PKG/'bit'));sys.path.insert(0,str(PKG/'arithmetic')) +spec=importlib.util.spec_from_file_location('pr200_paid_proof',PKG/'bit/prove.py') +proof=importlib.util.module_from_spec(spec);spec.loader.exec_module(proof) +# Match Linux provenance spelling only; determinants and factor identities untouched. +raw_prime_certificate=proof.prime_certificate +def portable_prime_certificate(word): + record=raw_prime_certificate(word) + record['input_sha256']={k.replace(chr(92),'/'):v for k,v in record['input_sha256'].items()} + return record +proof.prime_certificate=portable_prime_certificate +def need(ok,why): + if not ok:raise ValueError(why) +def encode(z): + if isinstance(z,Q):return str(z) + if isinstance(z,dict):return {str(k):encode(v) for k,v in z.items()} + if isinstance(z,(tuple,list)):return [encode(v) for v in z] + return z + +def endpoint_checks(): + records=[] + for width,copies in [(4,18),(24,3)]: + for ring in [0,2,3,5]: + def run(column,blocks): + x=[int(j==column) for j in range(72)];y=[int(72+j==column) for j in range(72)] + for block in blocks: + for j in range(block*width,(block+1)*width):x[j],y[j]=y[j],x[j] + return x+y + for column in range(144): + want=[int(j==(column+72)%144) for j in range(144)] + need(run(column,range(copies))==want,'all dirty address columns full swap') + need(run(column,list(range(copies))+list(reversed(range(copies))))==[int(j==column) for j in range(144)],'all inverse columns') + for blocks in [list(range(copies-1)),list(range(copies))+[copies-1]]: + need(run(72-width,blocks)!=[int(j==144-width) for j in range(144)],'adverse omitted/duplicate block') + records.append(dict(width=width,blocks=copies,address_ring=ring,forward_columns=144,inverse_columns=144,negative_controls=2)) + return records + +def literal_allocation(word_data): + pairs=word_data['pairs'];donor={b:a for a,b in pairs} + selected=sorted(z['role'] for z in word_data['gauges'] if z['role'] not in donor) + sinks=json.loads((PKG/'selected/bit/sinks.json').read_text()) + removed={word_data['rootroles'][e['root']] for e in sinks} + need(len(removed)==34 and not removed.intersection(selected),'terminal roles excluded from selected entrance banks') + need(not set(selected).intersection(word_data['sources'].values()),'source births are not entrance gauges') + allroles={donor.get(s,s) for s in range(18908)}-removed + rest=sorted(allroles-set(selected)) + need(len(allroles)==17114 and len(selected)==2200 and len(rest)==14914,'every actual retained physical chain exactly once') + records=[] + for stage in range(3): + totalbanks=0;assigned=set();digest=hashlib.sha256() + for family,(roles,width,blocks) in enumerate([(selected,4,18),(rest,24,3)]): + occurrences=[(replica,role) for replica in range(9) for role in roles] + need(len(occurrences)%blocks==0,'exact full banks, no omitted residual child') + for offset in range(0,len(occurrences),blocks): + group=occurrences[offset:offset+blocks] + need(len(group)==blocks and blocks*width==72,'each literal bank fills 72 coordinates') + for block,label in enumerate(group): + need(label not in assigned,'each role-copy receives one bank slot per stage');assigned.add(label) + digest.update(f'{stage}:{family}:{offset//blocks}:{block}:{label[0]}:{label[1]}\n'.encode()) + totalbanks+=len(occurrences)//blocks + need(len(assigned)==9*17114 and totalbanks==45842,'complete stage-private physical stock') + records.append(dict(stage=stage,assigned_role_copies=len(assigned),selected_banks=1100,undeferred_banks=44742,total_banks=totalbanks,allocation_sha256=digest.hexdigest())) + return dict(stages=records,data_registers=2*9*1760,total_persistent_registers=3*45842+2*9*1760,arbitrary_dirty_contents=True,normalization='Common ancestor weighted chart; literal disjoint coordinate partialSwap blocks; role normalizers chosen distinctly inside each bank by inherited fixed conjugation/routing construction.') + +def packed(row,word_data): + pairs=word_data['pairs'];recipients={b for a,b in pairs};gauges=word_data['gauges'] + starts={z['role']:z['dim'] for z in gauges if z['role'] not in recipients} + need(Counter(starts.values())=={20:2200},'genuine surviving entrance gauges') + need(not set(starts).intersection(word_data['sources'].values()),'source births are not bank entrance gauges') + touched={s for i in word_data['phase1'] for s in word_data['ops'][i][:2]} + need(not set(starts).intersection(touched),'entrance gauges untouched throughout centre phase') + need(Counter(z['dim'] for z in gauges if z['role'] in recipients)=={21:1760},'spliced recipients not bank roles') + need(row['R']==17114 and row['terminal_sinks']==34,'retained exact physical terminals') + rest=row['R']-len(starts) + H={int(k):v for k,v in row['child_histogram'].items()};need(H.pop(60)==2200,'remove exactly actual entrance exteriors') + W=Q(2*row['v'])+3*(Q(len(starts),18)+Q(rest,3)) + mass=sum(k*v for k,v in H.items());need(72*W-mass==1936,'full telescoping deficit') + t=9 + need(t*2200%18==0 and t*rest%3==0,'integral stage-private configuration') + scaled=dict(row,W_per_vertex=int(3*W),rank_per_vertex=3*mass,deficit_per_vertex=3*1936,maxchild=max(H),child_histogram={k:3*v for k,v in H.items()}) + return dict(m=72,W_per_vertex=W,rank_per_vertex=mass,deficit_per_vertex=1936,maxchild=max(H),child_histogram=H,selected_entrances=2200,undeferred_physical_chains=rest,physical_replicas=t,selected_banks_per_stage=t*2200//18,undeferred_banks_per_stage=t*rest//3,scaled_moment_profile=scaled) + +def main(): + import gzip + cert=json.loads((PKG/'certificate.json').read_text());row=cert['bit']['profile'] + data=json.loads(gzip.decompress((PKG/'selected/bit/word_p12.json.gz').read_bytes())) + full='--full' in sys.argv + if full: + import io + sink=io.StringIO() + with contextlib.redirect_stdout(sink):proof.main() + actual=json.loads(sink.getvalue());need(actual==cert['bit'],'complete word admission reproduces frozen bit certificate') + row=actual['profile'] + p=packed(row,data) + coarse=proof.certify(p['scaled_moment_profile']) + from base_two_moment import moment as alternate_moment + q=p['scaled_moment_profile'];H=list(q['child_histogram'].items());a=coarse['coarse_saving'];W=q['W_per_vertex'];edgecount=sum(n for r,n in H) + _,upper=alternate_moment(72,W,H,a);_,bad=alternate_moment(72,W,[(1,32*72**2*edgecount)],a) + need(upper+Q(1,10**16)*bad<1,'independent base-two paid acceptance') + lower,_=alternate_moment(72,W,H,a+Q(1,10**18));badlow,_=alternate_moment(72,W,[(1,32*72**2*edgecount)],a+Q(1,10**18)) + need(lower+Q(1,10**16)*badlow>1,'independent adjacent paid exclusion') + out=dict(status='PASS_FULL_BIT_ADMISSION' if full else 'PRICED_CANDIDATE_NOT_ADMITTED',base_pin='a1175449f34d39ff933d9d8ab23ced1f32b290ec',base_certificate_sha256=hashlib.sha256((PKG/'certificate.json').read_bytes()).hexdigest(),profile=p,coarse=coarse,endpoints=endpoint_checks(),literal_allocation=literal_allocation(data),universal_proof='Established ring-general disjoint partialSwap endpoint, arbitrary dirty contents, nine physical replicas, same weighted chart and charged routing. No source-birth bank gauge or characteristic-two odd-field substitution.',scope='Bit endpoint, complete paid child profile and exact moments only. Full root balanced assembly remains primary-owned.') + (HERE/('packed-pr200-full.json' if full else 'packed-pr200-priced.json')).write_text(json.dumps(encode(out),sort_keys=True,indent=2)) + print(json.dumps(encode(dict(status=out['status'],W=p['W_per_vertex'],rank=p['rank_per_vertex'],coarse=coarse['coarse_saving'],effective=coarse['ordinary_saving'],effective_float=float(coarse['ordinary_saving']),selected=2200,rest=p['undeferred_physical_chains'])),indent=2)) +if __name__=='__main__':main() \ No newline at end of file diff --git a/research/coordinated-crossover-pr200/geometry/retained-packing.py b/research/coordinated-crossover-pr200/geometry/retained-packing.py new file mode 100644 index 0000000000..b7e31dc08a --- /dev/null +++ b/research/coordinated-crossover-pr200/geometry/retained-packing.py @@ -0,0 +1,186 @@ +"""Exact gauge charts and completed-residual bank allocation. + +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +""" +from array import array +from collections import Counter +from fractions import Fraction as Q +from math import gcd +from pathlib import Path +import hashlib,json,sys + +def inverse_integer(a): + """Fraction-free Gauss-Jordan; return integral C,d with a C = d I.""" + n=len(a) + m=[list(row)+[int(i==j) for j in range(n)] for i,row in enumerate(a)] + previous=1 + factors=[] + for k in range(n): + pivot=next((i for i in range(k,n) if m[i][k]),None) + if pivot is None: + raise ValueError('Singular basis') + m[k],m[pivot]=m[pivot],m[k] + if pivot != k:factors.append(('swap',k,pivot,1,1)) + p=m[k][k] + if p != previous: + ratio=Q(previous,p) + factors.append(('scale',k,k,ratio.numerator,ratio.denominator)) + for i in range(n): + if i==k:continue + u=m[i][k] + if u: + ratio=Q(-u,previous) + factors.append(('add',i,k,ratio.numerator,ratio.denominator)) + for j in range(2*n): + if j==k:continue + value=p*m[i][j]-u*m[k][j] + assert value % previous==0 + m[i][j]=value//previous + m[i][k]=0 + previous=p + d=m[0][0] + assert d and all(m[i][j]==d*int(i==j) for i in range(n) for j in range(n)) + c=[row[n:] for row in m] + common=abs(d) + for row in c: + for x in row:common=gcd(common,x) + d//=common + c=[[x//common for x in row] for row in c] + if d<0:d=-d;c=[[-x for x in row] for row in c] + return c,d,factors + +def color_incidence(left,right,nleft,nright,colors): + """Incremental two-color swaps; parallel edges are identified separately.""" + assert len(left)==len(right) + full=(1<22 for r in H) + W=2*w['v']*copies+bank;mass=sum(r*n for r,n in H.items()) + assert 72*W-mass==copies*receipt['deficit_per_vertex']==5808 + K=18*((W-1)+len(physical)*72*(maxops+71)) + record=dict(status='PASS exact actual-chain chart and incidence checks',source_commit='201737a1ec4f936e166e2481fb9e88104cb2ccc7', + word_sha256=receipt['word_sha256'],physical_roles=len(physical),interior_splices=len(recipients),gauge_roles=len(selected), + distinct_gauges=len(inventory),copies=copies,banks=bank,patterns=[dict(rank4=6,rank24=2,count=small),dict(rank4=0,rank24=3,count=large)], + incidences=len(left),W=W,m=72,rank_mass=mass,deficit=5808,maxchild=max(H),child_histogram=dict(sorted(H.items())), + chart_sha256=digest.hexdigest(),incidence_sha256=incidence.hexdigest(),max_chart_factors=maxops,max_num=maxnum,max_den=maxden, + conservative_selector_calls=K,color_stats=stats,conflicting_assignment_rejected=rejected) + + return record diff --git a/research/coordinated-crossover-pr200/joint/REMATCH-NOTE.txt b/research/coordinated-crossover-pr200/joint/REMATCH-NOTE.txt new file mode 100644 index 0000000000..89f04b0591 --- /dev/null +++ b/research/coordinated-crossover-pr200/joint/REMATCH-NOTE.txt @@ -0,0 +1,15 @@ +Bit donor rematching experiment + +Prepared with OpenAI Codex assistance; Apache-2.0. Uses PR200 scalar word/checkers, PR211 bases, and our frozen plateau plus relaxed frame refinements. + +Keep the 238 original source-injection donor pairs verbatim. For each of the other 1,522 rank-21 births, enumerate nongauge, nonroot, nonsource donors whose last use is before the unchanged birth read, and whose exact endpoint frame is contained in the birth gauge. All donors are single-use in the bipartite matching. Sort donors by descending endpoint rank and augment the matching; endpoint rank orders every relevant concave paid-moment saving because all recipient gauges have the same rank 21. This is weighted greedy for a transversal matroid, with weights depending on donors only. + +The maximum-rank matching changes 355 pair assignments, but its symmetric difference with the original matching has 124 connected alternating components. Components with identical donor-rank multisets have zero paid effect and were reverted. Only two strictly improving components remain, each a single recipient: +- birth 18892: old donor 7756 (rank 7), new donor 8292 (rank 8). +- birth 18894: old donor 7757 (rank 7), new donor 8293 (rank 8). + +The full proposed pair list is pairs.json in [birth, donor] orientation. All 1,760 pairs remain; no new source donor is introduced and all original source aliases stay fixed. The exact frame/handoff/row checks on the full maximum-rank matching passed. The two-component reduction has the identical paid delta; the parent verifier must independently replay the actual minimal word. + +Paid child delta before bank replica scaling: rank13 +6; rank14 -6; rank16 -6; rank17 +6. Weighted rank delta and stock delta are both zero. + +Only literal finite-word/paid-moment/assembly replay can certify kappa; this search itself makes no new kappa claim. diff --git a/research/coordinated-crossover-pr200/joint/arithmetic.py b/research/coordinated-crossover-pr200/joint/arithmetic.py new file mode 100644 index 0000000000..bd3941d39e --- /dev/null +++ b/research/coordinated-crossover-pr200/joint/arithmetic.py @@ -0,0 +1,46 @@ +from pathlib import Path +import json,importlib.util,sys +from fractions import Fraction as Q +sys.set_int_max_str_digits(0) +O=Path(__file__).resolve().parent;R=O.parent;ROOT=R.parents[1] +def load(n,p): + s=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +def enc(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):enc(v) for k,v in x.items()} + if isinstance(x,(list,tuple)):return [enc(v) for v in x] + return x +im=load('im',ROOT/'research/paired-cube-diagonal-bit-168/arithmetic/interval_moment.py') +assembly=load('asm',ROOT/'scripts/paired_cube_assembly.py') +saved=json.loads((O/'joint-paid.json').read_text());p=dict(profile=dict(scaled_moment_profile=saved['profile']),coarse=saved['coarse']);base=json.loads((ROOT/'research/source-assisted-v4/certificate.json').read_text()) +def profile(cp): + H={int(t):n for t,n in cp['child_histogram'].items()} + return dict(m=cp.get('m',72),W=cp['W_per_vertex'],child_multiplicities=H,N=cp['deficit_per_vertex'],L=0,total_rank=sum(t*n for t,n in H.items()),maxchild=max(H)) +actual=json.loads((R/'complex-profile-replayed.json').read_text());assert all(actual[k]==base['complex_profile'][k] for k in ['m','W_per_vertex','rank_per_vertex','deficit_per_vertex','child_histogram']);cp=profile(actual);bp=profile(p['profile']['scaled_moment_profile']) +def paid(row,a,bit): + x=im.moment(row,a) + if bit: + l,u=im.log_interval(Q(row['m']));e,f=im.exp_interval(a*l,a*u);w=Q(1,10**16)*Q(32*row['m']*sum(row['child_multiplicities'].values()),row['W']);x.update(lower=x['lower']+w*e,upper=x['upper']+w*f) + return x +def certify(row,bit): + den=10**18;lo=0;hi=den//100 + while hi-lo>1: + md=(lo+hi)//2;v=paid(row,Q(md,den),bit) + if v['upper']<1:lo=md + elif v['lower']>1:hi=md + else:raise ValueError('inconclusive') + a=Q(lo,den);z=Q(hi,den);assert paid(row,a,bit)['upper']<10 for v in z['strict_constraints'].values()) +try:assembly.assembly(a,c['saving'],bridge,k+Q(1,grid),eta=eta,beta=beta) +except AssertionError:pass +else:raise AssertionError('next k accepted') +out=dict(status='PASS_EXACT_47_CONSTRAINT_ASSEMBLY',scope='Conditional finite supplier certificate; retained all-size interfaces and analytic assumptions',bit_profile=bp,complex_profile=cp,bit=b,complex=c,ordinary_chain=chain,bit_ordinary=chain[-1],a_bit=a,a_complex=c['saving'],eta=eta,beta=beta,kappa=k,kappa_float=float(k),binding='bit',assembly=z,adjacent_kappa_rejected=True) +(O/'assembly.json').write_text(json.dumps(enc(out),indent=2,sort_keys=True)+'\n') +print(json.dumps(enc({k:out[k] for k in ['status','kappa','kappa_float','bit_ordinary','a_complex']}),indent=2)) diff --git a/research/coordinated-crossover-pr200/joint/joint-selection.json b/research/coordinated-crossover-pr200/joint/joint-selection.json new file mode 100644 index 0000000000..db3e6cdea0 --- /dev/null +++ b/research/coordinated-crossover-pr200/joint/joint-selection.json @@ -0,0 +1,6570 @@ +[ + { + "roles": [ + 14740, + 14745, + 14750, + 14755 + ], + "gauge_rank": 18, + "target_union": [ + 864, + 865, + 866, + 867, + 868, + 869, + 870, + 871 + ], + "raw_targets": 16, + "paid_at_pr211": 0.9999999623622219, + "pervertex_hist_delta": { + "19": -12, + "1": 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912, + 915, + 916, + 919 + ] + } + } +] diff --git a/research/coordinated-crossover-pr200/joint/joint_word.py b/research/coordinated-crossover-pr200/joint/joint_word.py new file mode 100644 index 0000000000..52be474a77 --- /dev/null +++ b/research/coordinated-crossover-pr200/joint/joint_word.py @@ -0,0 +1,50 @@ +"""Actual joint entrance gauges on the frozen relaxed PR211 frame word. +Experimental adapter, prepared with OpenAI Codex assistance; Apache-2.0. +Pinned supplier files are never modified. +""" +from pathlib import Path +from copy import deepcopy +from collections import defaultdict +import sys,json,hashlib +sys.dont_write_bytecode=True +D=Path(__file__).resolve().parent +PACKAGE=D.parent;ROOT=PACKAGE.parents[1] +P=ROOT/'research/paired-cube-diagonal-bit-168' +sys.path.insert(0,str(P/'bit')) +from word import Candidate as Original +class Candidate(Original): + def __init__(self): + super().__init__() + self.original_w=deepcopy(self.w) + pairs=json.loads((D/'pairs.json').read_text()) + assert len(pairs)==1760 and set(b for b,d in pairs)==set(self.donor) + assert len(set(d for b,d in pairs))==1760 + old=dict(self.pairs);changed=[(b,d) for b,d in pairs if old[b]!=d] + assert changed==[(18892,8292),(18894,8293)] + assert all(d not in self.source.values() and d not in self.gauge and d not in self.rootroles for b,d in changed) + assert all(self.last[d]1 +def enc(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):enc(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return [enc(v)for v in x] + return x +(D/'joint-paid.json').write_text(json.dumps(enc(dict(profile=row,coarse=coarse,independent_base2_pass=True)),indent=2)+'\n') +import subprocess +subprocess.run([sys.executable,'-B',str(D/'arithmetic.py')],check=True) diff --git a/research/coordinated-crossover-pr200/joint/replay_joint.py b/research/coordinated-crossover-pr200/joint/replay_joint.py new file mode 100644 index 0000000000..40bf4efb39 --- /dev/null +++ b/research/coordinated-crossover-pr200/joint/replay_joint.py @@ -0,0 +1,47 @@ +from pathlib import Path +import json,hashlib,gzip,sys,time +sys.dont_write_bytecode=True +from joint_word import Candidate,P,D +from terminal import prove +from prime_witnesses import certificate +W=Candidate();pins={str(p):hashlib.sha256(p.read_bytes()).hexdigest()for p in [*W.input_paths,W.framepath,D/'joint_word.py',D/'joint-selection.json',D/'pairs.json',P/'selected/bit/sinks.json',P/'bit/base_word.py',P/'bit/word.py',P/'bit/terminal.py',P/'bit/prime_witnesses.py',Path(W.module.__file__)]} +W.exact_frames();print('PASS exact frames and alias endpoints',flush=True) +record=prove(W,json.loads((P/'selected/bit/sinks.json').read_text()));record.pop('seconds');record.pop('maxrss');print('PASS full reflected supplier replay',flush=True) +primes=certificate(W);(D/'joint-primes.json.gz').write_bytes(gzip.compress((json.dumps(primes,sort_keys=True,separators=(',',':'))+'\n').encode(),mtime=0)) +record['input_pins']=pins;record['prime_summary']={k:v for k,v in primes.items()if k!='frame_witnesses'} +assert pins=={p:hashlib.sha256(Path(p).read_bytes()).hexdigest()for p in pins} +(D/'joint-replay.json').write_text(json.dumps(record,indent=2)+'\n') +print('PASS joint gauge whole-word and prime admission',record['profile']['child_histogram'],flush=True) + +control=Candidate() +omitted=control.newroles[0] +control.order.remove(omitted) +try:control.formal(2) +except ValueError as error: + assert 'defining decoder' in str(error),str(error) + print('PASS omitted new compensation read rejected',flush=True) +else:raise AssertionError('Omitted new gauge compensation was accepted') + +control=Candidate() +role=next(s for s in control.newroles if control.gauge[s]['dim']==19) +control.order.remove(role);control.order.insert(0,role) +control.exact_frames() +try:control.row() +except (ValueError,AssertionError) as error: + assert 'target frame chronology' in str(error),str(error) + print('PASS reversed nested gauge read order rejected',flush=True) +else:raise AssertionError('Rank19 read before rank18 was accepted') +control=Candidate();control.order.remove(role) +try:control.formal(2) +except ValueError as error: + assert 'defining decoder' in str(error),str(error) + print('PASS omitted nested rank19 compensation rejected',flush=True) +else:raise AssertionError('Omitted nested compensation was accepted') + +for dim in (12,13): + control=Candidate();role=next(s for s in control.newroles if control.gauge[s]['dim']==dim);control.order.remove(role) + try:control.formal(2) + except ValueError as error: + assert 'defining decoder' in str(error),str(error) + print('PASS omitted rank'+str(dim)+' shared gauge compensation rejected',flush=True) + else:raise AssertionError('Shared compensation omission accepted') diff --git a/research/coordinated-crossover-pr200/newg/PROVENANCE.json b/research/coordinated-crossover-pr200/newg/PROVENANCE.json new file mode 100644 index 0000000000..eaa6e19b8b --- /dev/null +++ b/research/coordinated-crossover-pr200/newg/PROVENANCE.json @@ -0,0 +1,8 @@ +{ + "source469_final_manifest_sha256": "9bfe66dde122a7408dbc18b3f87f12d153b7c2a6191c9864db8692c7a0344d0d", + "source471_selection_sha256": "d94ef4e0b8ca98a7385b364cf245816a7cad08f850a60ce8b67aab4c3a89f3f4", + "discovery_schedule_sha256": "5230a1503cdf1f0eefb4f09b1b9d6dedd8afab9378d30be463bb3597513d166e", + "discovery_schedule_audit_sha256": "de4668f5d0c509fd18a722ad6050c65b5f7ad4b14ad3e9142f7bc9a95dc1d527", + "independent_reflected_ledger_sha256": "ef582523844f66baa356d8916c6aaff5437151804f7cbb516de69cfe0993b37f", + "scope": "The executable schedule is normalized to indices only and every actual address/frame rebuilt. Two retimed source heads extend source469; all source/target/frame/center/paid proofs are rerun. Prepared with OpenAI Codex assistance." +} diff --git a/research/coordinated-crossover-pr200/newg/boundary.py b/research/coordinated-crossover-pr200/newg/boundary.py new file mode 100644 index 0000000000..dde771921f --- /dev/null +++ b/research/coordinated-crossover-pr200/newg/boundary.py @@ -0,0 +1,111 @@ +#!/usr/bin/env python3 +"""Independent exact full-path and target-ledger audit of28 new source gauges. +No scalar claim. Prepared with OpenAI Codex assistance. +""" +from pathlib import Path +from collections import defaultdict,Counter +import importlib.util,json,sys +sys.dont_write_bytecode=True +D=Path(__file__).resolve().parent;P=D.parent/'joint';sp=importlib.util.spec_from_file_location('ind_newgauges',P/'joint_word.py');m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m) +w=m.Candidate();C=w.C;w.exact_frames();base=w.row();selected=json.loads((D/'selection.json').read_text());co=w.adjoint();recipient={d:b for b,d in w.pairs};kpair={e['passive']:e for e in w.k['entries']};roots=defaultdict(list) +schedule=json.loads((D/'schedule.json').read_text());original_rest=w.rest[:];w.phase1=schedule['new_phase1'];w.rest=schedule['deferred_ops']+original_rest +actual_order=w.phase1+w.rest;w.role_ops=defaultdict(list) +for i in actual_order: + for s in w.ops[i][:2]:w.role_ops[s].append(i) +w.readtime={s:t+168 for s,t in w.readtime.items()} +touched={s for i in w.phase1 for s in w.ops[i][:2]} +new_phase_roles={8584,9424} +for j,s in enumerate(w.w['rootroles']):roots[s].append((j,w.w['root_frame'][j])) +term=json.loads((P/'joint-replay.json').read_text())['selected'];removed={r['role']for r in term};deleted={r['root']for r in term};bywrite={i:e for e in term for i in e['writes']};after={e['writes'][-1]:e for e in term};tt={t for e in term for t in e['targets']};source_roles=set(w.source.values()) +old=json.loads((D.parent/'borrow/selection.json').read_text())+json.loads((D.parent/'gaugeb/selection.json').read_text());old_sources={r['source']for r in old};old_roles={r['role']for r in old};old_members=old_sources|{r['partner']for r in old} +assert not old_members&({r['source']for r in selected}|{r['partner']for r in selected}) +assert len({r['source']for r in selected})==len(selected)==28 +assert not(old_sources&{r['source']for r in selected})and not(old_roles&{r['role']for r in selected}) +assert len({r['role']for r in selected})==28 +assert sum(len(r['targets'])for r in selected)==112 and len({t for r in selected for t in r['targets']})==108 +local_delta=Counter();endpoint_rows=[];gframes={};prime_records=[] +from prime_witnesses import det,factor_witness,validate_factor +def H(chain,start_dim): + out=Counter();previous=None;d=start_dim + for f in chain: + assert previous is None or C.sub(previous,f) + n=C.dimf[f];assert n>=d + if n>d:out[n-d]+=1 + previous=f;d=n + return out +for r in selected: + s,n=r['role'],r['source'];e=kpair[n];mix=e['mix_frame'];f=w.register(r['gauge_basis'])if 'gauge_basis'in r else mix;gframes[s]=f;assert mix==r['mix_frame']and e['carrier']==r['partner']and C.sub(mix,f) + assert s not in touched|source_roles|removed|set(w.donor)|set(w.gauge) + assert sorted(co[s])==r['targets']and not(set(r['targets'])&tt) + chain=[w.opframe[i]for i in w.role_ops[s]]+[g for j,g in roots[s]] + if s in recipient: + b=recipient[s];chain += [w.gauge[b]['frame']]+[w.opframe[i]for i in w.role_ops[b]]+[g for j,g in roots[b]] + chain.append(w.w['full_frame']);assert C.sub(f,chain[0]) + new=[w.w['source_frame'][n],mix,f]+chain;assert all(C.nondeg(g)for g in set(new))and all(C.sub(a,b)for a,b in zip(new,new[1:])) + old_aux=H(chain,0);old_source=H([mix,w.w['full_frame']],1);new_source=H(new[1:],1) + delta=Counter(new_source);delta.subtract(old_aux);delta.subtract(old_source);delta={d:c for d,c in delta.items()if c} + assert sum(d*c for d,c in delta.items())==-24 + # Reflected annihilator path has precisely reversed nested frame inclusions. + for a,b in zip(new,new[1:]):assert C.sub(a,b)and all(w.module.dot(x,y)==0 for x in C.A[b]for y in C.B[a]) + reflected=Counter(C.dimf[b]-C.dimf[a]for a,b in zip(new,new[1:])if C.dimf[b]>C.dimf[a]);assert reflected==new_source + local_delta.update(delta);endpoint_rows.append(dict(role=s,source=n,alias_recipient=recipient.get(s),source_line=C.dimf[new[0]],K_mix=C.dimf[mix],source_gauge=C.dimf[f],final_dimension=C.dimf[new[-1]],auxiliary_delta=delta,old_aux_histogram=dict(old_aux),old_source_histogram=dict(old_source),complete_source_histogram=dict(new_source),reflected_equal=True)) +assert not(set(schedule['deferred_ops'])&set(bywrite)) +# Complete actual target chronology, including all terminal substitutions and K. +at=defaultdict(list) +for s in w.order:at[w.readtime[s]].append(s) +deliv=defaultdict(list) +for e in w.k['entries']:deliv[e['deliver_after_root']].append(e) +def target_hist(extra): + current=[None]*w.v;hist=Counter();events=0;paths=[[]for _ in range(w.v)] + def move(t,f): + nonlocal events + previous=current[t];assert previous is None or C.sub(previous,f),('target nesting',t,previous,f) + assert all(w.module.dot(C.cov[t],x)==0 for x in C.B[f]),('target cap',t,f) + d=C.dimf[f]-(0 if previous is None else C.dimf[previous]);assert d>=0 + if d:hist[d]+=1 + current[t]=f;paths[t].append(f);events+=1 + for j,i in enumerate(w.rest): + if extra: + for r in selected: + if j==(0 if r['role']in new_phase_roles else 168): + for t in r['targets']:move(t,gframes[r['role']]) + for s in at[j]: + for t in w.gauge[s]['targets']:move(t,w.gauge[s]['frame']) + if i in bywrite:move(bywrite[i]['pivot'],w.opframe[i]) + if i in after: + for t in after[i]['targets']:move(t,after[i]['root_frame']) + for s in at[len(w.rest)]: + for t in w.gauge[s]['targets']:move(t,w.gauge[s]['frame']) + for j,r in enumerate(w.g['roots']): + if r['kind']=='side'and j not in deleted: + for t in r['targets']:move(t,w.w['root_frame'][j]) + for e in deliv[j]: + for t in e['receivers']:move(t,e['deliver_frame']) + for t,f in enumerate(current): + d=w.h-1-C.dimf[f] + if d:hist[d]+=1 + assert sum(d*c for d,c in hist.items())==w.v*(w.h-1) + reflected=Counter() + for t,chain in enumerate(paths): + # Reverse the exact annihilator bases. The cap annihilator is cov[t]. + last=[C.cov[t]];previous_dim=1 + for f in reversed(chain): + basis=C.A[f];assert len(basis)==w.h-C.dimf[f] + assert all(w.module.dot(a,b)==0 for a in last for b in C.B[f]) + step=len(basis)-previous_dim;assert step>=0 + if step:reflected[step]+=1 + last=basis;previous_dim=len(basis) + step=w.h-previous_dim + if step:reflected[step]+=1 + assert reflected==hist,('independent reflected target histogram',reflected,hist) + return hist,events +Y0,e0=target_hist(False);Y1,e1=target_hist(True);ydelta=Counter(Y1);ydelta.subtract(Y0);local_delta.update(ydelta) +compact=lambda c:{str(d):n for d,n in sorted(c.items())if n} +assert sum(d*c for d,c in local_delta.items())==-28*24 +for f in sorted(set(gframes.values())): + B=C.B[f];ss=list(map(sum,B));gram=[[9*sum(a*b for a,b in zip(x,y))-ss[i]*ss[j]for j,y in enumerate(B)]for i,x in enumerate(B)] + determinant=det(gram);powers,residual=factor_witness(determinant);validate_factor(determinant,powers,residual) + prime_records.append(dict(frame=f,dimension=len(B),basis=B,cleared_gram_determinant=determinant,small_prime_powers=powers,remaining_factor=residual)) +assert any(r['dimension']==4 for r in prime_records) +res=dict(status='PASS_EXACT_28_SHARED_SOURCE_GAUGE_PATHS_TARGETS_AND_PRIMES',scope='Complete physical source paths, donor-recipient chains, reflected annihilator nesting, complete terminal/gauge/root/K target chronology, all exact paid local deltas. Whole scalar replay and global assembly owned separately.',selected=28,touched_targets=108,explicit_reflected_target_histograms_equal=True,additional_target_events=e1-e0,target_delta=compact(ydelta),old_complete_target_histogram=compact(Y0),new_complete_target_histogram=compact(Y1),local_delta=compact(local_delta),local_rank_delta=sum(d*c for d,c in local_delta.items()),W_delta=-28,shared_rank_delta=3*sum(d*c for d,c in local_delta.items()),deficit_delta=-28*72-3*sum(d*c for d,c in local_delta.items()),endpoint_rows=endpoint_rows,source_gauge_prime_witnesses=prime_records) +(D/'boundary.json').write_text(json.dumps(res,indent=2)+'\n');print(json.dumps({k:v for k,v in res.items()if k not in ('endpoint_rows','source_gauge_prime_witnesses')},indent=2),flush=True) diff --git a/research/coordinated-crossover-pr200/newg/derive_profile.py b/research/coordinated-crossover-pr200/newg/derive_profile.py new file mode 100644 index 0000000000..fc5595d597 --- /dev/null +++ b/research/coordinated-crossover-pr200/newg/derive_profile.py @@ -0,0 +1,62 @@ +"""Reconstruct all actual source/internal/target paths after 28 new source-backed gauges.""" +from pathlib import Path +from collections import Counter +import json,sys,importlib.util +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;P=HERE.parent +spec=importlib.util.spec_from_file_location('newg_profile_word',P/'joint/joint_word.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +W=m.Candidate();r=json.loads((P/'gaugeb/profile.json').read_text())['profile'];audit=json.loads((HERE/'boundary.json').read_text());scalar=json.loads((HERE/'replay.json').read_text());sel=json.loads((HERE/'selection.json').read_text());oldg={e['role']for e in json.loads((P/'gaugeb/selection.json').read_text())} +assert len(sel)==28 and len(scalar['integer'])==2 and {x['direction']for x in scalar['integer']}=={-1,1} +assert all(x['formal_columns']==20163 and x['dirty']==16643 and x['all_targets']and x['all_source_and_dirty_restored']for x in [scalar['F2']]+scalar['integer']) +assert len(scalar['controls'])==6 and all(x['status']=='REJECTED'for x in scalar['controls'].values()) +schedule=json.loads((HERE/'schedule-audit.json').read_text()) +assert schedule['source_heads']==471 and schedule['deferred_operations']==168 and schedule['center_prefix_operations']==17080 +assert schedule['all_exact_address_subspace_streams_preserved'] and schedule['all_actual_address_frame_dimension_streams_preserved'] and schedule['all_address_jump_histograms_preserved'] and schedule['no_later_center_middle_consumer'] +assert all(x['all_forward_centers_at_D0']and x['all_reflected_centers_at_D1']and x['actual_target_histogram']==audit['new_complete_target_histogram']==x['actual_reflected_target_histogram']for x in [scalar['F2']]+scalar['integer']) +def counter(h):return Counter({int(k):n for k,n in h.items()}) +local=counter(r['physical_internal_histogram']);source=counter(r['physical_source_histogram']);oldtarget=counter(r['physical_target_histogram']) +assert oldtarget==counter(audit['old_complete_target_histogram']);target=counter(audit['new_complete_target_histogram']) +assert {e['role']for e in audit['endpoint_rows']}=={e['role']for e in sel} +for e in audit['endpoint_rows']: + local.subtract(counter(e['old_aux_histogram']));source.subtract(counter(e['old_source_histogram']));source.update(counter(e['complete_source_histogram'])) +assert all(n>=0 for h in (local,source,target)for n in h.values()) +child=Counter() +for h in(local,source,target): + for k,n in h.items(): + if k and n:child[k]+=3*n +for s,z in W.gauge.items(): + if s not in W.donor and s not in oldg:child[3*z['dim']]+=1 +child[2]+=2*W.v +stock=r['W_per_vertex']-28;physical=r['R']-28;mass=sum(k*n for k,n in child.items());deficit=72*stock-mass +assert stock==20163 and physical==16643 and mass==1449800 and deficit==1936 +assert sum(k*n for k,n in source.items())==sum(k*n for k,n in target.items())==W.v*(W.h-1) +delta=Counter(child);delta.subtract(counter(r['child_histogram']));delta={k:v for k,v in delta.items()if v};assert delta=={int(k):3*n for k,n in audit['local_delta'].items()} +def compact(h):return {str(k):n for k,n in sorted(h.items())if n} +profile=dict(r,R=physical,active_virtual_R=physical+r['reused_registers'],W_per_vertex=stock,rank_per_vertex=mass,child_histogram=compact(child),physical_internal_histogram=compact(local),physical_source_histogram=compact(source),physical_target_histogram=compact(target),physical_original_sources_borrowed=471,source_backed_new_rank2_gauges=26,source_backed_shared_rank4_gauges=2,center_prefix_operations=17080,deferred_center_independent_operations=168,source_heads_exposed_by_retiming=2,copied_center_frame_chronology="D0 forward and D1 complementary reverse") +assert profile['active_virtual_R']==18403 +# Legacy selected_* fields consistently describe actual auxiliary-bank entrances. +# Data/source-owned entrances are recorded separately and never banked twice. +bank_ranks=Counter(z['dim']for role,z in W.gauge.items()if role not in W.donor and role not in oldg) +source_ranks=Counter(W.gauge[role]['dim']for role in oldg) +source_ranks.update(e['source_gauge']for e in audit['endpoint_rows']) +all_ranks=bank_ranks+source_ranks +profile['retained_selected_roles']=r['selected_roles'] +profile['retained_selected_rank_histogram']=r['selected_rank_histogram'] +profile['selected_rank_histogram']=compact(bank_ranks) +profile['selected_roles']=sum(bank_ranks.values()) +profile['selected_roles_scope']='Actual remaining bankable auxiliary entrances; source-owned data entrances are counted separately.' +profile['bankable_auxiliary_entrances']=sum(bank_ranks.values()) +profile['source_owned_gauge_entrances']=sum(source_ranks.values()) +profile['source_owned_gauge_rank_histogram']=compact(source_ranks) +profile['all_gauge_entrances']=sum(all_ranks.values()) +profile['all_gauge_rank_histogram']=compact(all_ranks) +assert profile['bankable_auxiliary_entrances']==2279 +assert profile['source_owned_gauge_entrances']==31 +assert profile['all_gauge_entrances']==2310 +assert bank_ranks=={20:2200,18:13,12:18,13:48} +assert source_ranks=={19:3,2:26,4:2} +assert profile['R']+profile['reused_registers']==profile['active_virtual_R']==18403 +assert profile['W_per_vertex']==2*profile['v']+profile['R'] +assert profile['maxchild']==max(child) +out=dict(status='PASS_COMPLETE_471_SOURCE_PROFILE',profile=profile,actual_child_delta=delta,all_original_gauge_adjoint_coefficients_retained=True,all_original_target_anchors_retained=True,additional_source_gauge_target_reads=112,all_new_target_chronology_reconstructed=True) +(HERE/'profile.json').write_text(json.dumps(out,indent=2)+'\n');print('PASS471 complete ledgers',dict(W=stock,R=physical,rank=mass,deficit=deficit,delta=delta),flush=True) diff --git a/research/coordinated-crossover-pr200/newg/replay.py b/research/coordinated-crossover-pr200/newg/replay.py new file mode 100644 index 0000000000..a0af83c245 --- /dev/null +++ b/research/coordinated-crossover-pr200/newg/replay.py @@ -0,0 +1,208 @@ +"""Scalar prototype: source471 with168 frame-preserving commuting operations retimed after centers. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from pathlib import Path +from collections import Counter,defaultdict +import json,sys,importlib.util,time,gc,hashlib +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;D=HERE.parent/'joint';spec=importlib.util.spec_from_file_location('source82',D/'joint_word.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m) +W=m.Candidate();C=W.C +W.changed_frames=[i for i,(a,b)in enumerate(zip(W.original_opframe,W.opframe))if a!=b] +W.endframe={s:W.opframe[xs[-1]]for s,xs in W.role_ops.items()} +C.decoder();C.geometry();selection=json.loads((HERE.parent/'borrow/selection.json').read_text());new_gauge_selection=json.loads((HERE/'selection.json').read_text());new_gauge_selection=new_gauge_selection['selection']if isinstance(new_gauge_selection,dict)else new_gauge_selection;gauge_selection=json.loads((HERE.parent/'gaugeb/selection.json').read_text())+new_gauge_selection +schedule=json.loads((HERE/'schedule.json').read_text()) +original_phase1=W.phase1[:];original_rest=W.rest[:];omitted_for_schedule={r['omit_copy']for r in selection};deferred=schedule['deferred_ops'];assert len(deferred)==168 +W.phase1=schedule['new_phase1'];W.rest=deferred+original_rest +assert set(W.phase1)|set(W.rest)|omitted_for_schedule==set(range(len(W.ops))) +assert not(set(W.phase1)&set(W.rest))and not(set(W.phase1+W.rest)&omitted_for_schedule) +W.role_ops=defaultdict(list) +for i in W.phase1+W.rest: + for role in W.ops[i][:2]:W.role_ops[role].append(i) +pos={i:j for j,i in enumerate(W.rest)};W.first={role:pos.get(ii[0],-1)for role,ii in W.role_ops.items()};W.last={role:pos.get(ii[-1],-1)for role,ii in W.role_ops.items()};W.position={i:j for j,i in enumerate(W.phase1+W.rest)} +W.endframe={role:W.opframe[ii[-1]]for role,ii in W.role_ops.items()} +W.readtime={role:t+168 for role,t in W.readtime.items()};new_phase_roles={8584,9424} +assert new_phase_roles<=set(schedule['new_untouched_roles']) +for role,t in W.readtime.items():W.w['reads'][str(role)]=len(W.phase1)+t +knew={e['passive']:e for e in W.k['entries']};raw_response=W.adjoint();newroles=[];target_frames={};touched={s for i in W.phase1 for s in W.ops[i][:2]} +for r in new_gauge_selection: + role,source=r['role'],r['source'];mix=knew[source]['mix_frame'];f=W.register(r['gauge_basis'])if 'gauge_basis'in r else mix;targets=sorted(raw_response[role]);assert targets==r['targets'] and mix==r['mix_frame'] and C.sub(mix,f) + assert role not in W.gauge and role not in W.donor and role not in W.source.values() and role not in touched + assert C.dimf[f]in(2,4) and C.nondeg(f) and C.sub(f,W.opframe[W.role_ops[role][0]]) + assert all(t not in target_frames or C.sub(target_frames[t],f) and C.sub(f,target_frames[t])for t in targets);target_frames.update({t:f for t in targets}) + assert all(all(W.module.dot(C.cov[t],b)==0 for b in C.B[f])for t in targets) + z=dict(role=role,frame=f,dim=C.dimf[f],targets=targets);W.gauge[role]=z;W.w['gauges'].append(z);W.readtime[role]=0 if role in new_phase_roles else 168;W.w['reads'][str(role)]=len(W.phase1)+W.readtime[role];newroles.append(role) +W.order=newroles+W.order +W.exact_frames() +assert all(0<=W.readtime[s]<=W.first[s]for s in W.gauge) +assert all(W.last[d]=0 + if d:target_hist[d]+=1 + target_frames[t]=f;target_paths[t].append(f) + X0=[unit(i)for i in range(v)];Y0=[unit(v+i)for i in range(v)];Z0={r:unit(idx[r])for r in regs};x=X0[:];y=Y0[:];z=Z0.copy();top=1;done=[] + def track(value): + nonlocal top + if major:top=max(top,value) + return value + def value(s): + s=W.phys[s];return x[borrow[s]]if s in borrow else z[s] + def assign(s,val): + s=W.phys[s] + if s in borrow:x[borrow[s]]=track(val) + else:z[s]=track(val) + responses=W.adjoint() if mutation=='old_adjoint' else adj + def read(s): + if mutation=='omit_gauge_compensation' and s==new_gauge_selection[-1]['role']:return + for t,c in responses[s].items(): + if s in W.gauge:target_move(t,W.gauge[s]['frame']) + else:assert target_frames[t]is None,'initial correction leaves target atD0' + y[t]=track(add(y[t],-direction*c,value(s))) + def gate(i,sign): + a,b,_=W.ops[i];assign(a,add(value(a),sign,value(b))) + for s in range(W.R): + if s not in W.gauge and s not in borrow and s not in removed:read(s) + for n,s in W.source.items():assign(s,add(value(s),1,x[n])) + for r in gauge_selection: + if mutation!='omit_gauge_mix' or r is not new_gauge_selection[-1]:x[r['partner']]=track(add(x[r['partner']],1,x[r['source']])) + def forward(i): + if i not in omitted:gate(i,1);done.append(i) + for k in schedule['center_prefix_events']: + event=schedule['events'][k];i=event['op'] + if event['kind']=='early_mix': + r=early[i];a,b=r['partner'],r['source'] + if mutation!='omit_early_mix' or r is not selection[0]:x[a]=track(add(x[a],1,x[b])) + else:forward(i) + for r,s in zip(W.g['roots'],W.w['rootroles']): + if r['kind']=='center': + for t in r['targets']: + assert all(f is None for f in target_frames),'copied centers scatter before any nonzero target movement' + center_reads.append((s,t));y[t]=track(add(y[t],direction,value(s))) + for e in terminal: + assert all(target_frames[t]is None for t in e['targets']),'terminal setup afterD0center scatter' + for t in e['targets']: + if t!=e['pivot']:y[t]=track(add(y[t],-1,y[e['pivot']])) + for j,i in enumerate(W.rest): + for s in at[j]: + if mutation!='late_phase1_gauge' or s not in new_phase_roles:read(s) + if mutation=='late_phase1_gauge'and j==168: + for s in sorted(new_phase_roles):read(s) + if i in bywrite: + e=bywrite[i];a,b,n=W.ops[i];target_move(e['pivot'],W.opframe[i]);y[e['pivot']]=track(add(y[e['pivot']],direction,value(b))) + else:forward(i) + if i in afterwrite: + e=afterwrite[i] + for t in e['targets']: + target_move(t,e['root_frame']) + if t!=e['pivot']:y[t]=track(add(y[t],1,y[e['pivot']])) + for s in at[len(W.rest)]:read(s) + for j,(r,s)in enumerate(zip(W.g['roots'],W.w['rootroles'])): + if r['kind']=='side' and j not in deletedroots: + for t in r['targets']:target_move(t,W.w['root_frame'][j]);y[t]=track(add(y[t],direction,value(s))) + for e in deliveries[j]: + a,b=e['carrier'],e['passive'] + if b not in by_source:x[a]=track(add(x[a],1,x[b])) + for t in e['receivers']:target_move(t,e['deliver_frame']);y[t]=track(add(y[t],direction,x[a])) + for e in W.k['entries']: + if e['passive']not in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']])) + if mutation=='undo_before_restore': + for e in W.k['entries']: + if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']])) + for i in reversed(done):gate(i,-1) + if mutation!='undo_before_restore': + for e in W.k['entries']: + if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']])) + for n,s in W.source.items():assign(s,add(value(s),-1,x[n])) + if binary:want=[Y0[t]^X0[t]for t in range(v)] + else: + want=Y0[:];cache={} + for root in W.g['roots']: + n=root['node'] + if n not in cache: + mask=C.sup[n];val=0 + while mask:low=mask&-mask;mask-=low;val=add(val,1,X0[low.bit_length()-1]) + cache[n]=val + for t in root['targets']:want[t]=add(want[t],direction,cache[n]) + for e in W.k['entries']: + val=add(X0[e['carrier']],1,X0[e['passive']]) + for t in e['receivers']:want[t]=add(want[t],direction,val) + # Finish every local target at its codimension-one cap, then reverse the exact + # annihilator stream. All copied-center scatters lie before these movements, + # hence atD0 forward and atD1 after the complementary movements reverse. + reflected=Counter() + for t,chain in enumerate(target_paths): + assert chain + d=W.h-1-C.dimf[chain[-1]];assert d>=0 + if d:target_hist[d]+=1 + previous=[C.cov[t]];dimension=1 + for f in reversed(chain): + assert all(W.module.dot(a,b)==0 for a in previous for b in C.B[f]) + basis=C.A[f];step=len(basis)-dimension;assert step>=0 + if step:reflected[step]+=1 + previous=basis;dimension=len(basis) + if W.h>dimension:reflected[W.h-dimension]+=1 + assert reflected==target_hist + assert len(center_reads)==sum(len(r['targets'])for r in W.g['roots']if r['kind']=='center') + assert sum(k*n for k,n in target_hist.items())==W.v*(W.h-1) + if major:return max(top,max(a+b for a,b in zip(y,want)),max(z[r]+Z0[r]for r in regs),max(a+b for a,b in zip(x,X0))) + assert y==want,('wrong targets',mode,[t for t in range(v)if y[t]!=want[t]][:10]) + assert x==X0,('source restoration',mode,[s for s in range(v)if x[s]!=X0[s]][:10]) + assert z==Z0,('dirty restoration',mode) + return dict(mode=mode,direction=direction,formal_columns=2*v+len(regs),sources=v,targets=v,dirty=len(regs),all_targets=True,all_source_and_dirty_restored=True,copied_center_target_reads=len(center_reads),all_forward_centers_at_D0=True,all_reflected_centers_at_D1=True,actual_target_histogram={str(k):n for k,n in sorted(target_hist.items())},actual_reflected_target_histogram={str(k):n for k,n in sorted(reflected.items())}) +if __name__=='__main__': + start=time.monotonic();out=dict(status='PASS_SCALAR_SOURCE471_RETIMED_PHASE1_GAUGES',selection=selection,gauge_selection=gauge_selection,new_gauge_selection=new_gauge_selection,geometry_and_paid_admission=False) + out['F2']=replay();print('PASS F2',out['F2'],'seconds',time.monotonic()-start,flush=True) + bound=replay('bound');bits=8*((bound.bit_length()+2+7)//8);out['bound']=bound;out['bits']=bits;out['terminal_sinks']=len(terminal);print('bound',bound,'bits',bits,flush=True) + out['integer']=[] + if True: + for direction in(1,-1):out['integer'].append(replay('Z',direction,bits));gc.collect();print('PASS integer',direction,'seconds',time.monotonic()-start,flush=True) + out['controls']={} + for mutation in ['omit_early_mix','old_adjoint','undo_before_restore','omit_gauge_mix','omit_gauge_compensation','late_phase1_gauge']: + try:replay(mutation=mutation) + except AssertionError as error:out['controls'][mutation]=dict(status='REJECTED',error=str(error)) + else:raise AssertionError('Invalid mutation accepted: '+mutation) + assert (1<2*bound + assert input_pins=={str(p):hashlib.sha256(p.read_bytes()).hexdigest()for p in input_paths} + out['input_pins']=input_pins + (HERE/'replay.json').write_text(json.dumps(out,indent=2)+'\n') + print('PASS actual471 source word, both integer signs, all columns and six controls',flush=True) diff --git a/research/coordinated-crossover-pr200/newg/schedule.json b/research/coordinated-crossover-pr200/newg/schedule.json new file mode 100644 index 0000000000..51c2c8df5a --- /dev/null +++ b/research/coordinated-crossover-pr200/newg/schedule.json @@ -0,0 +1 @@ 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diff --git a/research/coordinated-crossover-pr200/newg/schedule_audit.py b/research/coordinated-crossover-pr200/newg/schedule_audit.py new file mode 100644 index 0000000000..c94e006726 --- /dev/null +++ b/research/coordinated-crossover-pr200/newg/schedule_audit.py @@ -0,0 +1,66 @@ +"""Independent event/value and address chronology audit of the actual471 retiming.""" +from pathlib import Path +from collections import Counter,defaultdict +import importlib.util,json,sys,hashlib +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +spec=importlib.util.spec_from_file_location('scalar471',HERE/'replay.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);W=m.W;C=m.C +schedule=m.schedule;events=[] +def port(s): + p=W.phys[s];return('x',m.borrow[p])if p in m.borrow else('z',p) +for e in schedule['events']: + i=e['op'] + if e['kind']=='early_mix': + r=m.early[i];events.append(dict(op=i,kind='early_mix',dest=('x',r['partner']),source=('x',r['source']),frame=m.kpair[r['source']]['mix_frame'])) + else: + a,b,n=W.ops[i];events.append(dict(op=i,kind='operation',dest=port(a),source=port(b),frame=W.opframe[i])) +prefix=schedule['center_prefix_events'];deferred=schedule['deferred_events'];rest=schedule['remaining_events'];neworder=prefix+deferred+rest +assert [events[k]['op']for k in prefix if events[k]['kind']=='operation']==W.phase1 +assert [events[k]['op']for k in deferred+rest if events[k]['kind']=='operation']==W.rest +assert len(neworder)==len(set(neworder))==len(events) +def trace(order): + writes={};inputs={};frames={};edges=0;paths=defaultdict(list) + for k in order: + e=events[k];a,b,f=e['dest'],e['source'],e['frame'];inputs[k]=(writes.get(a,-1),writes.get(b,-1)) + for p in[a,b]: + old=frames.get(p) + assert old is None or C.sub(old,f),('address descent',k,p,old,f) + if old is not None:edges+=1 + frames[p]=f;paths[p].append(f) + writes[a]=k + return inputs,writes,frames,edges,paths +oldinput,oldwrite,oldframes,oldedges,oldpaths=trace(range(len(events)));newinput,newwrite,newframes,newedges,newpaths=trace(neworder) +assert oldinput==newinput and oldwrite==newwrite and oldframes==newframes +assert set(oldpaths)==set(newpaths) +def jumps(path): + previous=0;out=Counter() + for f in path: + d=C.dimf[f];assert d>=previous + if d>previous:out[d-previous]+=1 + previous=d + return out +assert all(jumps(oldpaths[p])==jumps(newpaths[p])for p in oldpaths) +assert all([C.dimf[f]for f in oldpaths[p]]==[C.dimf[f]for f in newpaths[p]]for p in oldpaths), 'complete actual address-frame dimension stream changed' +assert all(all(C.sub(a,b)and C.sub(b,a)for a,b in zip(oldpaths[p],newpaths[p]))for p in oldpaths), 'complete exact physical subspace stream changed' +_,prefixwrite,prefixframes,_,_=trace(prefix) +for r,s in zip(W.g['roots'],W.w['rootroles']): + if r['kind']=='center':assert prefixwrite[port(s)]==oldwrite[port(s)] +centerports={port(s)for r,s in zip(W.g['roots'],W.w['rootroles'])if r['kind']=='center'} +assert all(not(centerports&{events[k]['dest'],events[k]['source']})for k in deferred+rest),'no later middle consumer bypassed atcopied center' +center_ranks=Counter() +for j,(r,s)in enumerate(zip(W.g['roots'],W.w['rootroles'])): + if r['kind']=='center': + f=W.w['root_frame'][j];assert C.sub(prefixframes[port(s)],f)and C.sub(f,prefixframes[port(s)]) + center_ranks[C.dimf[f]]+=1 +newports={port(s)for s in m.new_phase_roles} +assert all(not(newports&{events[k]['dest'],events[k]['source']})for k in prefix) +assert {events[k]['op']for k in prefix if events[k]['kind']=='early_mix'}==set(m.early) +assert all(events[k]['kind']=='operation'for k in deferred+rest) +assert all(W.readtime[s]==0 for s in m.new_phase_roles) +assert all(W.readtime[s]>=168 for s in W.gauge if s not in m.new_phase_roles) +assert all(W.readtime[s]<=W.first[s]for s in W.gauge) +assert all(W.last[d] j. Every edge has F_i subset F_j. Let f be increasing and concave on permitted nonnegative rank gaps, with f(0)=0. Construct ANY second legal schedule M_i with F_i subset M_i for every mutable i and identical fixed boundaries. Assume every M_i is nondegenerate and contains the required exact value span. + +There is a linear-size explicit minimum-cut majorant for selecting F_i or M_i independently at each operation. A strict reduction of its objective is a sufficient certificate of a strict reduction of the actual complete paid rank objective. All stock, endpoints, source/target legality, chronological aliases and total rank mass remain unchanged. This is a legal-neighborhood optimization theorem; it does not claim global optimality or an all-size multiplication theorem. + +For an edge with both endpoints mutable, write d_i=dim(M_i)-dim(F_i), d_j=dim(M_j)-dim(F_j), r=dim(F_j)-dim(F_i). The 00,01,11 cases always nest, and have costs E00=f(r), E01=f(r+d_j), E11=f(r+d_j-d_i). The 10 case nests precisely when M_i subset F_j; if legal, E10=f(r-d_i). + +Define unary contributions u_i=E11-E01 and u_j=E01-E00. The affine objective E00+u_i*x_i+u_j*x_j agrees with every 00,01,11 cost. If 10 is illegal add a hard arc i -> j, prohibiting x_i=1,x_j=0. If 10 is legal its affine price is E00+E11-E01. Concavity implies E00+E11 >= E01+E10: these are two inner points versus two outer points with equal sum. Thus the affine price majorizes the true 10 cost. Both implications follow without requiring equal subspaces or a common join direction. For fixed boundaries retain the exact one-variable cost; no hard arc is needed where an endpoint contains both alternatives. + +Sum over ALL actual physical and target-chain edges, including terminal pivot movements. Positive unary u becomes i -> sink; negative unary becomes source -> i with the usual constant offset. Use a hard capacity strictly greater than the sum of absolute unary capacities. The unchanged all-zero assignment is feasible and has the baseline objective. Consequently a minimizing cut with negative surrogate delta has actual delta at most that negative number. This proves sufficiency. Concavity defects are explicitly bounded, so the surrogate can also quantify how far it is from the best schedule in its binary neighborhood; this is useful for dropping an unproductive route, not a research result by itself. + +A contraction schedule L_i subset F_i reduces to this theorem by replacing each frame with its ordinary annihilator, reversing every paid edge and exchanging F,L accordingly. Dimensions change from k to h-k, so every paid rank gap is exactly preserved. Nondegeneracy and required-value containment are verified on the original physical frames, not presumed from the annihilator representation. + +## Concrete second schedules + +The greatest feasible candidate is reconstructed backwards: M_i is the intersection of every successor frame, including all literal endpoint caps. The required values and current F_i stay contained because the initial word is legal. If a candidate frame is degenerate, freeze that operation at its current frame and restart backwards propagation. Since each failed round freezes at least one operation, the process terminates in at most N rounds with a legal schedule; in the observed PR200 input no freeze was necessary. + +The least candidate is reconstructed forwards: L_i is the span of its exact required source-label value vectors and every predecessor frame, including literal source/gauge/target boundaries. This is a subspace of the current legal F_i. Freeze a degenerate candidate at F_i and continue forwards; successors still remain within their current frames. Again the observed PR200 input needed no freeze. Both candidates are explicit finite constructions rather than assumed transformation gadgets. + +## C++ implementation and actual results + +- `greatest.cpp` is the complete loader, exact fraction-free integer basis/kernel operations, checked signed-128 multiplication/subtraction, canonical interning, full physical/target graph reconstruction, nondegeneracy predicate for G=I-J/9, Dinic nomination and literal histogram recount. +- Input is the unchanged PR200 a1175449f34d39ff933d9d8ab23ced1f32b290ec word plus the already admitted 302-frame checkpoint. Staged immutable JSON and executable are on F:/proof/research/beyond-nlogn-20261009/threshold/frames. No Python was executed for this lane. +- Current graph: 41,288 operation nodes, 126,520 paid edges, rank mass 405,456. The stage factor3 is not part of this graph-level histogram. +- Complete greatest schedule changes14,487 operations and worsens entropy867200.2563234223 -> 898639.1065801512. Rejected as a whole. +- Its majorant cut chooses48 operations and improves entropy to867140.3594551166. Exact histogram delta {0:-24,2:+96,4:-72,10:-48,12:+48}. Surrogate delta -45.67759759837121, actual entropy delta -59.8968683057. This is a candidate beyond prior common-direction cuts, not a threshold-scale improvement. +- On that checkpoint the full least schedule worsens entropy to897647.8189150952. Rejected as a whole. +- Its majorant cut chooses1410 operations and reaches entropy866438.7403496904. Final cumulative1458 operation changes relative to the 302 checkpoint. Rank mass still405456. Total graph entropy improvement761.5159737319. There are zero degenerate freezes. +- `greatest-summary.json` contains every full exact histogram and surrogate decision ledger. `greatest-bases.json` contains the explicit integer rational bases for all1458 additional operations relative to the 302 checkpoint; it is NOT a standalone public-relative replacement file. Compose with the original302 witness before any full replay. + +Every changed basis is independently reduced and every literal physical/target edge is rechecked for containment; all source/gauge/root/alias/read/terminal identities remain fixed. This does NOT replace the untouched original all-formal-column and all-used-frame prime certificate. New bases need that admission before publication or kappa pricing as a record. No such closure is claimed in this lane. + +## Threshold assessment and route selection + +The new graph entropy reduction is too small for the requested kappa >= .0007. At baseline normalized delta1936, approximately48 additional useful rank-deficit units would be threshold-scale at approximately unchanged entropy. The copied-center loss528 is therefore a higher-leverage target than continuing tiny frame cuts. Parent is pursuing a concrete hybrid264 missing-port and center dirty-completion route. This lane stops expensive frame cuts and preserves all exact witnesses and the generic sufficient construction for reuse. + +## Retrieval and literature provenance + +Prior exact cut contracts and proofs were read from the whole-subspace mincut notes, the rank-moment-to-exponent notes, PR200 frame continuation and actual public integer geometry checker. The canonical tree search found Mathlib `Analysis/SpecialFunctions/Log/NegMulLog.lean` (`strictConcaveOn_negMulLog`) and existing Problem18ProductAwareCost/Calculus majorization mechanisms; these are source retrieval, no new imports or Lean certification. The ordinary directed minimum-cut method and concavity/majorization are classical. This particular variable-frame majorant applies those methods to the compiler's complete physical/target ledger. Publication novelty is not established. \ No newline at end of file diff --git a/research/coordinated-crossover-pr200/search/PR216-NOTICE b/research/coordinated-crossover-pr200/search/PR216-NOTICE new file mode 100644 index 0000000000..ba5ea80dd7 --- /dev/null +++ b/research/coordinated-crossover-pr200/search/PR216-NOTICE @@ -0,0 +1,399 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. + +Partial-gauge extension, 9 October 2026 +Copyright 2026 icekylinx + +The pair-first cube assembly, compatible backward frame enlargement, +partial source-gauge schedule and stopped whole-projector composition are +contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834. + +The physical deferred bit word, reflected event accounting, fan-order +clarification and signed two-stage endpoint are adopted from Zhihao Chen +(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with +Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen +witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38, +with the original Claude disclosure retained. Cyclic interval and core-aware +pair primitives build on Avi Eisenberg (ikeboy), PR #62, +ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance. +Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and +precision credits remain in force. Imported source notices and licenses +are preserved under references/partial-gauge/; see SOURCES.json. + +Three-stage cover extension, 9 October 2026 +Copyright 2026 icekylinx + +The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry, +weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring +fallback, uniform batching, internal row borrowing and exact composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This +repository integration uses Codex assistance and extends +PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86. + +The selected local complex DAG and support/label replay are adopted from +Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf, +with its original Apache-2.0 terms and Claude assistance disclosure. +The unchanged bit physical word retains Zhihao Chen (jacklightChen), +PR #97, and Swapnil Jain's underlying witness and assistance notices. +The prior opposite-bank, stopped ordinary-leaf, copied-center, topology, +semantic/bulk, precision and analytic credits remain applicable. +Original source notices and license bytes are preserved in +references/three-stage-cover/pr117/ and references/partial-gauge/. + +Paired-cube and shared-core extension, 9 October 2026 +Copyright 2026 icekylinx + +The paired-coordinate triple-cube identity, signed overlap channels, +original-source involution, coordinate-star centers, concrete frame/carrier +compiler, chronological source gauges, PR97 gauge-subset selection, +orthogonal cross-stage routing and exact supplier/assembly integration +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. +Repository integration uses Codex assistance and extends PR #130 at +6a9970a530119174507904e23592fd59ede19a5d. + +The substantial completed-core workspace-sharing principle is credited to +an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported +OpenAI Codex assistance. No source code, partition or serialized witness +from that PR is imported. The new routing and paired-motif integration +are described separately and claim no exclusive priority for broad sharing, +paired-coordinate, Fourier or carrier-matching ideas. + +Selected coarse queries restrict the retained eumemic PR #117 positive DAG; +its original Apache-2.0 and Claude assistance notices remain unchanged. +The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil +Jain's frozen witness, notices and historical assistance disclosures. +Earlier generalized Clifford, three-stage, uniform weighted recursion, +ordinary-leaf, semantic/bulk, precision and analytic credits remain in force. +Source-specific license bytes are preserved under references/. + +Source-assisted common-frame extension (2026-10-09) +Copyright 2026 icekylinx. Apache-2.0. +Research construction and local certificates: OpenAI GPT-6 Astra assistance. +Repository integration and independent complex scalar replay: Codex assistance. +Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee; +its byte-preserved sources, licenses and original Claude assistance disclosure +are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz. +Additional inherited contributions are recorded in research/source-assisted/CREDITS.md. +The new work concerns source-assisted invertible common-frame lifts, controlled +affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for +broad register reuse, paired cubes, frame theory or ordinary linear elimination. diff --git a/research/coordinated-crossover-pr200/search/PR216-NOTICE-PR211 b/research/coordinated-crossover-pr200/search/PR216-NOTICE-PR211 new file mode 100644 index 0000000000..9edc257237 --- /dev/null +++ b/research/coordinated-crossover-pr200/search/PR216-NOTICE-PR211 @@ -0,0 +1,18 @@ +Packed diagonal bit supplier. Apache-2.0. +Prepared by Rohan Arun (rohanarun) with Anthropic Claude assistance. + +Reused, with credit: +- Evan McKinney, PR197 (OpenAI Codex assistance): completed-bank packing, exact + gauge charts, nine-colour bank incidence, routing bound, arithmetic, audit + and endpoint controls. banks.py and controls.py are byte-identical extracts; + packing.py, arithmetic.py, audit.py and verify.py are adaptations to PR200. +- Chafik Boukhalfa, PR200 at a1175449f34d39ff933d9d8ab23ced1f32b290ec (Anthropic + Claude and OpenAI Codex assistance): the fixed-coordinate/face-diagonal bit + word, physical layer, terminal sinks, prime witnesses and package verifier. +- Avi Eisenberg, PR193 at 187e1010ac8b259af8e9b5166f68b64bc27b4b47: the v4 + source-assisted complex supplier and balanced assembly bridge; icekylinx for + the source-assisted method (PR184) and the paired-cube framework (PR144). +- maxime-fleury, PR204: the model of this lever and its predicted value. +- eumemic (PR168 lineage), jamesyc (PR166 terminal lemma), PR185/187 finite + ordinary-leaf composition, and every contributor credited by those packages. +Original notices remain in the pinned checkouts. diff --git a/research/coordinated-crossover-pr200/search/SEARCH-NOTE.txt b/research/coordinated-crossover-pr200/search/SEARCH-NOTE.txt new file mode 100644 index 0000000000..df3e13ab9a --- /dev/null +++ b/research/coordinated-crossover-pr200/search/SEARCH-NOTE.txt @@ -0,0 +1,15 @@ +PR211 residual plateau enlargement experiment + +Input: PR211 frozen 6,191 operation-frame bases at c63e50a5dde96fe1459d6b29e55e47f42f104347, applied to the PR200 physical word. + +Result: 7 accepted equal-frame component moves change 14 operation frames. Exact rational frame/value-span/nondegeneracy and complete physical-chain predicates pass. Scalar operations, source and gauge boundaries, root caps, alias pairs and partner deliveries remain fixed. The 34 terminal deletions have an operation-frame-independent cancellation: their internal-path change is reproduced on the terminal pivot target, leaving the same rank-3/rank-21 correction. The parent verifier must still replay complete scalar columns and certify the final paid moment before publication. + +Additional child histogram delta (before the three-copy scaling) is: +rank 2: +12; rank 4: -15; rank 5: -18; rank 6: +9; rank 7: +24; rank 8: -12; rank 9: -12; rank 12: +24; rank 15: -12. +Weighted rank delta is zero. Stock and endpoint gauges are unchanged. +Floating search objective improvement is 1.1846038379180897 in sum r log r over the internal chains. This is a heuristic score, not the certified kappa. + +Reproduce: +python3 -B plateau_search.py --bit-package /path/to/research/paired-cube-diagonal-bit-168 --frames /path/to/research/cascade-frames-bit/opframe-bases.json --out /path/to/results + +Provenance: PR200 physical word and checkers by Chafik Boukhalfa; PR211 cascade frame witness by Rohan Arun with Anthropic Claude assistance. This residual search was prepared with OpenAI Codex assistance. Apache-2.0. diff --git a/research/coordinated-crossover-pr200/search/additional-frames.json b/research/coordinated-crossover-pr200/search/additional-frames.json new file mode 100644 index 0000000000..60e8a5650f --- /dev/null +++ b/research/coordinated-crossover-pr200/search/additional-frames.json @@ -0,0 +1 @@ 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d*log(d) proposal; exact frame and nested-chain predicates admit moves","parent_commit":"df95878d11190518e45ef9717c9ee05011f88ace","proposal_score_gain":6.379919055549248,"random_seed":null,"randomness":"none; deterministic group order and greedy sweeps","schema":"joint-equal-frame-plateau-v1","search_counters":{"dimension_room":40231,"groups":41168,"intersection_room":3799,"nonpositive":3785,"positive":14},"starting_frames_sha256":"687496f3c15818e7cad1beb5fdf3812b8e38825ea302bfd60aea7ac23f3516b4","status":"EXACT_FRAMES_AND_NESTED_CHAINS_PASS_NOT_FULL_WORD_REPLAY","sweeps":[{"changed_operations":19,"score_gain":6.379919055549248,"sweep":0},{"changed_operations":0,"score_gain":0.0,"sweep":1}]} diff --git a/research/coordinated-crossover-pr200/search/joint-plateau-search-prdf958.py b/research/coordinated-crossover-pr200/search/joint-plateau-search-prdf958.py new file mode 100644 index 0000000000..2268e884cd --- /dev/null +++ b/research/coordinated-crossover-pr200/search/joint-plateau-search-prdf958.py @@ -0,0 +1,266 @@ +#!/usr/bin/env python3 +"""Reproduce the equal-frame plateau descent on the joint physical word. + +The d*log(d) score proposes moves only. The repository's actual joint +Candidate checks exact operation-frame spans, nondegeneracy, and chain nesting. +The paid moment and exponent are certified separately by the finite verifier. +No random numbers are used. This incremental search was prepared by sennemmi +with substantial OpenAI Codex assistance. It builds on PR210 by eumemic and +PR216 by Dugongue; all inherited contributors retain their original credit. +Apache-2.0. +""" +from __future__ import annotations + +import argparse +import hashlib +import importlib.util +import json +import math +import shutil +import sys +import tempfile +import time +import zipfile +from collections import Counter, defaultdict +from pathlib import Path + +sys.dont_write_bytecode = True +SOURCE_P = Path(__file__).resolve().parents[1] +PARENT = "df95878d11190518e45ef9717c9ee05011f88ace" +BASE_SHA256 = "687496f3c15818e7cad1beb5fdf3812b8e38825ea302bfd60aea7ac23f3516b4" + + +def sha256(data: bytes) -> str: + return hashlib.sha256(data).hexdigest() + + +def canonical(value: object) -> bytes: + return (json.dumps(value, sort_keys=True, separators=(",", ":")) + "\n").encode() + + +def source_package(tmp: Path) -> Path: + manifest = json.loads((SOURCE_P / "BASELINE.json").read_text()) + parts = [] + skip = set() + for entry in manifest["parts"]: + part = SOURCE_P / entry["file"] + data = part.read_bytes() + assert len(data) == entry["bytes"] and sha256(data) == entry["sha256"] + parts.append(data) + skip.add(entry["file"]) + archive = b"".join(parts) + assert sha256(archive) == manifest["archive_sha256"] + root = tmp / "source" + root.mkdir() + with zipfile.ZipFile(__import__("io").BytesIO(archive)) as z: + for entry in z.infolist(): + try: + (root / entry.filename).resolve().relative_to(root.resolve()) + except ValueError as exc: + raise AssertionError("unsafe pinned archive entry") from exc + z.extractall(root) + package = root / "research" / "coordinated-crossover-pr200" + package.mkdir() + for file in SOURCE_P.rglob("*"): + if file.is_file() and file.name not in skip: + target = package / file.relative_to(SOURCE_P) + target.parent.mkdir(parents=True, exist_ok=True) + shutil.copyfile(file, target) + # The source tree contains the committed candidate frames. Reproduction must + # begin from PR210's pinned parent input, not from that candidate output. + parent_frames = package / "search" / "base-frames-prdf958.json" + assert sha256(parent_frames.read_bytes()) == BASE_SHA256 + shutil.copyfile(parent_frames, package / "frames" / "opframe-bases.json") + return package + + +def load_candidate(P: Path): + sys.path.insert(0, str(P.parents[1] / "research" / "paired-cube-diagonal-bit-168" / "bit")) + spec = importlib.util.spec_from_file_location("joint_word", P / "joint" / "joint_word.py") + assert spec and spec.loader + module = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = module + spec.loader.exec_module(module) + return module.Candidate + + +def run_search(P: Path): + started = time.monotonic() + base_path = P / "search" / "base-frames-prdf958.json" + base_bytes = base_path.read_bytes() + assert sha256(base_bytes) == BASE_SHA256, "parent PR210 frame input changed" + assert sha256((P / "frames" / "opframe-bases.json").read_bytes()) == BASE_SHA256 + + W = load_candidate(P)() + C = W.C + W.changed_frames = [i for i, (a, b) in enumerate(zip(W.original_opframe, W.opframe)) if a != b] + W.endframe = {s: W.opframe[xs[-1]] for s, xs in W.role_ops.items()} + W.exact_frames() + baseline = W.row() + base = W.opframe[:] + + zero = W.register([]) + full = W.w["full_frame"] + before = [[] for _ in W.ops] + after = [[] for _ in W.ops] + starts = {b: W.w["source_frame"][x] for x, b in W.source.items()} + starts.update({b: z["frame"] for b, z in W.gauge.items()}) + ends = {s: W.w["root_frame"][j] for j, s in enumerate(W.w["rootroles"])} + ends.update({d: W.gauge[b]["frame"] for b, d in W.pairs}) + for s, xs in W.role_ops.items(): + chain = [-starts.get(s, zero) - 1] + xs + [-ends.get(s, full) - 1] + for j, i in enumerate(xs, 1): + before[i].append(chain[j - 1]) + after[i].append(chain[j + 1]) + assert all(len(x) == 2 for x in before + after) + + def frame(ref): + return W.opframe[ref] if ref >= 0 else -ref - 1 + + F = [0] + [r * math.log(r) for r in range(1, W.h + 1)] + + def merit(d, prev, nxt): + return sum(F[d - C.dimf[p]] for p in prev) + sum(F[C.dimf[n] - d] for n in nxt) + + nondeg = {} + intersections = {} + + def good(f): + if f not in nondeg: + nondeg[f] = C.nondeg(f) + return nondeg[f] + + def intersection(a, b): + if C.sub(a, b): + return a + if C.sub(b, a): + return b + key = tuple(sorted((a, b))) + if key not in intersections: + rows, _ = W.module.kernel(C.A[a] + C.A[b], W.h) + intersections[key] = W.register(rows) + return intersections[key] + + parent = list(range(len(W.ops))) + + def find(i): + while parent[i] != i: + parent[i] = parent[parent[i]] + i = parent[i] + return i + + def union(i, j): + i, j = find(i), find(j) + if i != j: + parent[j] = i + + for i, successors in enumerate(after): + for j in successors: + if j >= 0 and C.dimf[W.opframe[i]] == C.dimf[W.opframe[j]] and C.sub(W.opframe[i], W.opframe[j]): + union(i, j) + groups = defaultdict(list) + for i in range(len(W.ops)): + groups[find(i)].append(i) + + stats = Counter() + moves = [] + sweeps = [] + total_gain = 0.0 + for sweep in range(8): + changed = 0 + sweep_gain = 0.0 + for xs in groups.values(): + members = set(xs) + old = W.opframe[xs[0]] + d = C.dimf[old] + if any(not (C.dimf[W.opframe[i]] == d and C.sub(old, W.opframe[i])) for i in xs): + continue + prev = [frame(j) for i in xs for j in before[i] if j not in members] + nxt = [frame(j) for i in xs for j in after[i] if j not in members] + stats["groups"] += 1 + if min(C.dimf[f] for f in nxt) <= d: + continue + stats["dimension_room"] += 1 + f = nxt[0] + for next_frame in nxt[1:]: + f = intersection(f, next_frame) + if C.dimf[f] <= d: + break + new_dim = C.dimf[f] + if new_dim <= d: + continue + stats["intersection_room"] += 1 + if not good(f): + stats["degenerate"] += 1 + continue + assert C.sub(old, f) + gain = merit(new_dim, prev, nxt) - merit(d, prev, nxt) + stats["positive" if gain > 1e-10 else "nonpositive"] += 1 + if gain <= 1e-10: + continue + for i in xs: + W.opframe[i] = f + changed += len(xs) + sweep_gain += gain + moves.append({"ops": xs, "old_dim": d, "new_dim": new_dim, "score_gain": round(gain, 15)}) + sweeps.append({"sweep": sweep, "changed_operations": changed, "score_gain": round(sweep_gain, 15)}) + total_gain += sweep_gain + if changed == 0: + break + + W.changed_frames = [i for i, (a, b) in enumerate(zip(W.original_opframe, W.opframe)) if a != b] + W.endframe = {s: W.opframe[xs[-1]] for s, xs in W.role_ops.items()} + W.exact_frames() + profile = W.row() + delta = Counter({int(k): n for k, n in profile["child_histogram"].items()}) + delta.subtract({int(k): n for k, n in baseline["child_histogram"].items()}) + all_frames = [[i, C.B[f]] for i, f in enumerate(W.opframe) if f != W.w["op_frame"][i]] + frame_bytes = (json.dumps(all_frames, separators=(",", ":")) + "\n").encode() + record = { + "schema": "joint-equal-frame-plateau-v1", + "parent_commit": PARENT, + "starting_frames_sha256": BASE_SHA256, + "candidate_frames_sha256": sha256(frame_bytes), + "random_seed": None, + "randomness": "none; deterministic group order and greedy sweeps", + "objective": "float d*log(d) proposal; exact frame and nested-chain predicates admit moves", + "status": "EXACT_FRAMES_AND_NESTED_CHAINS_PASS_NOT_FULL_WORD_REPLAY", + "group_count": len(groups), + "sweeps": sweeps, + "accepted_moves": moves, + "search_counters": dict(sorted(stats.items())), + "proposal_score_gain": round(total_gain, 15), + "baseline_profile": baseline, + "candidate_profile": profile, + "child_histogram_delta": {str(k): v for k, v in sorted(delta.items()) if v}, + "changed_operation_frames_from_parent": len([i for i, (a, b) in enumerate(zip(base, W.opframe)) if a != b]), + "changed_operation_frames_from_word": len(W.changed_frames), + "elapsed_seconds_excluded_from_record": True, + } + return frame_bytes, canonical(record), record, time.monotonic() - started + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument("--verify-committed", action="store_true") + ap.add_argument("--frames-out", type=Path) + ap.add_argument("--record-out", type=Path) + args = ap.parse_args() + with tempfile.TemporaryDirectory(prefix="joint-plateau-") as tmp_name: + P = source_package(Path(tmp_name)) + frames, record_bytes, record, elapsed = run_search(P) + if args.verify_committed: + assert frames == (SOURCE_P / "frames" / "opframe-bases.json").read_bytes(), "frame witness differs" + assert record_bytes == (SOURCE_P / "search" / "joint-plateau-result-prdf958.json").read_bytes(), "search record differs" + print(f"PASS deterministic plateau reproduction; {len(record['accepted_moves'])} moves, {record['changed_operation_frames_from_parent']} operation frames; {elapsed:.1f}s") + return + assert args.frames_out and args.record_out, "supply output paths or use --verify-committed" + args.frames_out.parent.mkdir(parents=True, exist_ok=True) + args.record_out.parent.mkdir(parents=True, exist_ok=True) + args.frames_out.write_bytes(frames) + args.record_out.write_bytes(record_bytes) + print(f"Wrote candidate frames and record; {len(record['accepted_moves'])} moves in {elapsed:.1f}s") + + +if __name__ == "__main__": + main() diff --git a/research/coordinated-crossover-pr200/search/plateau_search.py b/research/coordinated-crossover-pr200/search/plateau_search.py new file mode 100644 index 0000000000..1144c784bf --- /dev/null +++ b/research/coordinated-crossover-pr200/search/plateau_search.py @@ -0,0 +1,104 @@ +"""Exact admissibility search on equal-frame operation plateaux. + +Searches frame enlargements on connected equal-frame operation components. +The floating entropy objective proposes moves only; paid-moment and scalar-word +admission belong to the parent verifier. Every output candidate is checked with +the inherited exact rational frame and physical-chain predicates. + +Prepared with OpenAI Codex assistance. Apache-2.0. +Retains PR200's physical word and exact integer checker (Chafik Boukhalfa), +and consumes PR211's frozen cascade frame input (Rohan Arun, Claude assisted). +""" +from pathlib import Path +from collections import Counter,defaultdict +import sys,json,time,math,argparse +sys.dont_write_bytecode=True +ap=argparse.ArgumentParser(description=__doc__) +ap.add_argument('--bit-package',required=True,type=Path) +ap.add_argument('--frames',required=True,type=Path) +ap.add_argument('--out',required=True,type=Path) +args=ap.parse_args();P=args.bit_package.resolve();D=args.out.resolve();D.mkdir(parents=True,exist_ok=True) +sys.path.insert(0,str(P/'bit')) +from word import Candidate +started=time.monotonic();W=Candidate();C=W.C +for i,rows in json.loads((args.frames).read_text()):W.opframe[i]=W.register(rows) +base=W.opframe[:] +W.changed_frames=[i for i,(a,b) in enumerate(zip(W.original_opframe,W.opframe))if a!=b] +W.endframe={s:W.opframe[xs[-1]]for s,xs in W.role_ops.items()} +W.exact_frames();baseline=W.row();print('initialized',len(W.ops),len(C.B),'frames',time.monotonic()-started,flush=True) +# Fixed boundary refs are encoded as -frame-1, while zero frame gets its own id. +zero=W.register([]);full=W.w['full_frame'];before=[[]for _ in W.ops];after=[[]for _ in W.ops] +starts={b:W.w['source_frame'][x]for x,b in W.source.items()};starts.update({b:z['frame']for b,z in W.gauge.items()}) +ends={s:W.w['root_frame'][j]for j,s in enumerate(W.w['rootroles'])} +ends.update({d:W.gauge[b]['frame']for b,d in W.pairs}) +for s,xs in W.role_ops.items(): + chain=[-starts.get(s,zero)-1]+xs+[-ends.get(s,full)-1] + for j,i in enumerate(xs,1):before[i].append(chain[j-1]);after[i].append(chain[j+1]) +assert all(len(x)==2 for x in before+after) +def frame(ref):return W.opframe[ref]if ref>=0 else-ref-1 +F=[0]+[r*math.log(r)for r in range(1,W.h+1)] +def merit(d,prev,nxt):return sum(F[d-C.dimf[p]]for p in prev)+sum(F[C.dimf[n]-d]for n in nxt) +nondeg={};intersections={};changes=[];tot=0 + +def good(f): + if f not in nondeg:nondeg[f]=C.nondeg(f) + return nondeg[f] +def intersection(a,b): + if C.sub(a,b):return a + if C.sub(b,a):return b + k=tuple(sorted((a,b))) + if k not in intersections: + rows,_=W.module.kernel(C.A[a]+C.A[b],W.h) + intersections[k]=W.register(rows) + return intersections[k] +# Move connected equal-frame plateaux as units. +parent=list(range(len(W.ops))) +def find(i): + while parent[i]!=i:parent[i]=parent[parent[i]];i=parent[i] + return i +def union(i,j): + i,j=find(i),find(j) + if i!=j:parent[j]=i +for i,ns in enumerate(after): + for j in ns: + if j>=0 and C.dimf[W.opframe[i]]==C.dimf[W.opframe[j]] and C.sub(W.opframe[i],W.opframe[j]):union(i,j) +groups=defaultdict(list) +for i in range(len(W.ops)):groups[find(i)].append(i) +print('groups',len(groups),'largest',sorted(map(len,groups.values()),reverse=True)[:20],flush=True) +stats=Counter();gains=[] +for sweep in range(8): + num=0;gain=0 + for xs in groups.values(): + members=set(xs);old=W.opframe[xs[0]];d=C.dimf[old] + if any(not(C.dimf[W.opframe[i]]==d and C.sub(old,W.opframe[i]))for i in xs):continue + prev=[frame(j)for i in xs for j in before[i]if j not in members] + nxt=[frame(j)for i in xs for j in after[i]if j not in members] + stats['groups']+=1 + if min(C.dimf[f]for f in nxt)<=d:continue + stats['dimension_room']+=1;f=nxt[0] + for n in nxt[1:]: + f=intersection(f,n) + if C.dimf[f]<=d:break + dd=C.dimf[f] + if dd<=d:continue + stats['intersection_room']+=1 + if not good(f):stats['degenerate']+=1;continue + assert C.sub(old,f) + improvement=merit(dd,prev,nxt)-merit(d,prev,nxt) + stats['positive'if improvement>1e-10 else 'nonpositive']+=1 + gains.append([improvement,len(xs),d,dd]) + if improvement<=1e-10:continue + for i in xs:W.opframe[i]=f + num+=len(xs);gain+=improvement;changes.append(dict(ops=xs,old_dim=d,new_dim=dd,gain=improvement)) + print('sweep',sweep,'changes',num,'entropy_gain',gain,'stats',dict(stats),'seconds',time.monotonic()-started,flush=True) + tot+=gain + if not num:break +print('best gains',sorted(gains,reverse=True)[:20],flush=True) +W.changed_frames=[i for i,(a,b)in enumerate(zip(W.original_opframe,W.opframe))if a!=b] +W.endframe={s:W.opframe[xs[-1]]for s,xs in W.role_ops.items()} +W.exact_frames();row=W.row();delta=Counter({int(k):n for k,n in row['child_histogram'].items()});delta.subtract({int(k):n for k,n in baseline['child_histogram'].items()}) +frames=[[i,C.B[f]]for i,f in enumerate(W.opframe)if f!=base[i]] +(D/'plateau-additional-frames.json').write_text(json.dumps(frames,separators=(',',':'))+'\n') +(D/'plateau-all-frames.json').write_text(json.dumps([[i,C.B[f]]for i,f in enumerate(W.opframe)if f!=W.w['op_frame'][i]],separators=(',',':'))+'\n') +out=dict(status='EXACT_FRAMES_AND_NESTED_CHAINS_PASS_NOT_FULL_REPLAY',baseline=baseline,profile=row,child_delta={str(k):v for k,v in sorted(delta.items())if v},changes=changes,entropy_gain=tot,elapsed=time.monotonic()-started) +(D/'plateau-result.json').write_text(json.dumps(out,indent=2)+'\n');print('DONE additional',len(frames),'delta',out['child_delta'],'gain',tot,flush=True) diff --git a/research/coordinated-crossover-pr200/search/pr211-frames.json b/research/coordinated-crossover-pr200/search/pr211-frames.json new file mode 100644 index 0000000000..8433d7724c --- /dev/null +++ b/research/coordinated-crossover-pr200/search/pr211-frames.json @@ -0,0 +1 @@ +[[9404, [[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], [9405, [[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], [9415, [[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], [9451, [[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], [9477, [[0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0]]], [9487, [[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], [9515, [[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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b/research/coordinated-crossover-pr200/search/relaxed_search.py new file mode 100644 index 0000000000..510c1aaca2 --- /dev/null +++ b/research/coordinated-crossover-pr200/search/relaxed_search.py @@ -0,0 +1,183 @@ +"""Seeded cascade perturbation and exact admissibility search. + +The frozen output frames require independent paid-moment and scalar-word replay. +Float entropy is used only to propose candidates. The final output passes exact +rational value-span, nondegeneracy and complete physical-chain checks. + +Prepared with OpenAI Codex assistance; Apache-2.0. Uses PR200's physical word +and checkers (Chafik Boukhalfa), PR211's cascade frame witness (Rohan Arun with +Anthropic Claude assistance), and our independently found plateau additions. +""" +from pathlib import Path +from collections import Counter,defaultdict +import sys,json,time,math,argparse +sys.dont_write_bytecode=True +ap=argparse.ArgumentParser(description=__doc__) +ap.add_argument('--bit-package',required=True,type=Path) +ap.add_argument('--frames',required=True,type=Path) +ap.add_argument('--additional-frames',required=True,type=Path) +ap.add_argument('--out',required=True,type=Path) +args=ap.parse_args();P=args.bit_package.resolve();D=args.out.resolve();D.mkdir(parents=True,exist_ok=True) +sys.path.insert(0,str(P/'bit')) +from word import Candidate +started=time.monotonic();W=Candidate();C=W.C +for i,rows in json.loads((args.frames).read_text()):W.opframe[i]=W.register(rows) + +for i,rows in json.loads((args.additional_frames).read_text()):W.opframe[i]=W.register(rows) +base=W.opframe[:] +W.changed_frames=[i for i,(a,b) in enumerate(zip(W.original_opframe,W.opframe))if a!=b] +W.endframe={s:W.opframe[xs[-1]]for s,xs in W.role_ops.items()} +W.exact_frames();baseline=W.row();print('initialized',len(W.ops),len(C.B),'frames',time.monotonic()-started,flush=True) +# Fixed boundary refs are encoded as -frame-1, while zero frame gets its own id. +zero=W.register([]);full=W.w['full_frame'];before=[[]for _ in W.ops];after=[[]for _ in W.ops] +starts={b:W.w['source_frame'][x]for x,b in W.source.items()};starts.update({b:z['frame']for b,z in W.gauge.items()}) +ends={s:W.w['root_frame'][j]for j,s in enumerate(W.w['rootroles'])} +ends.update({d:W.gauge[b]['frame']for b,d in W.pairs}) +for s,xs in W.role_ops.items(): + chain=[-starts.get(s,zero)-1]+xs+[-ends.get(s,full)-1] + for j,i in enumerate(xs,1):before[i].append(chain[j-1]);after[i].append(chain[j+1]) +assert all(len(x)==2 for x in before+after) +def frame(ref):return W.opframe[ref]if ref>=0 else-ref-1 +F=[0]+[r*math.log(r)for r in range(1,W.h+1)] +def merit(d,prev,nxt):return sum(F[d-C.dimf[p]]for p in prev)+sum(F[C.dimf[n]-d]for n in nxt) +nondeg={};intersections={};changes=[];tot=0 + +def good(f): + if f not in nondeg:nondeg[f]=C.nondeg(f) + return nondeg[f] +def intersection(a,b): + if C.sub(a,b):return a + if C.sub(b,a):return b + k=tuple(sorted((a,b))) + if k not in intersections: + rows,_=W.module.kernel(C.A[a]+C.A[b],W.h) + intersections[k]=W.register(rows) + return intersections[k] +unions={} +def join(a,b): + if C.sub(a,b):return b + if C.sub(b,a):return a + k=tuple(sorted((a,b))) + if k not in unions:unions[k]=W.register(list(C.B[a])+list(C.B[b])) + return unions[k] +# Complete upper envelope determined solely by immutable endpoint boundaries. +cap=[None]*len(W.ops) +for i in range(len(W.ops)-1,-1,-1): + ns=[cap[j]if j>=0 else frame(j)for j in after[i]] + cap[i]=intersection(*ns) + assert C.sub(W.opframe[i],cap[i]) +print('global caps built',time.monotonic()-started,flush=True) + +def transaction(seed,f): + old=W.opframe[seed] + if C.sub(f,old):return None + if not C.sub(old,f):f=join(old,f) + if not C.sub(f,cap[seed]) or not good(f):return None + update={seed:f};pending=[seed] + while pending: + i=pending.pop();f=update[i] + for j in after[i]: + old=update.get(j,frame(j)) + if C.sub(f,old):continue + if j<0:return None + z=join(f,old) + if not C.sub(z,cap[j])or not good(z):return None + update[j]=z;pending.append(j) + if len(update)>1000:return None + gain=0.0 + for i,f in update.items(): + d=C.dimf[f];od=C.dimf[W.opframe[i]] + for j in before[i]: + pd=C.dimf[update.get(j,frame(j))];opd=C.dimf[frame(j)] + gain+=F[d-pd]-F[od-opd] + for j in after[i]: + if j not in update: + nd=C.dimf[frame(j)];gain+=F[nd-d]-F[nd-od] + return gain,update + +valueframes={i:f for i,f in enumerate(W.w['source_frame'])} +def valueframe(n): + if n not in valueframes: + a,b=W.g['args'][n];valueframes[n]=join(valueframe(a),valueframe(b)) + return valueframes[n] +floor=[None]*len(W.ops) +for i in range(len(W.ops)): + ps=[floor[j]if j>=0 else frame(j)for j in before[i]] + floor[i]=join(join(*ps),valueframe(W.ops[i][2])) + assert C.sub(floor[i],W.opframe[i]) +print('global floors built',time.monotonic()-started,flush=True) + +def lower_transaction(seed,f): + old=W.opframe[seed] + if C.sub(old,f):return None + if not C.sub(f,old):f=intersection(old,f) + if not C.sub(floor[seed],f) or not good(f):return None + update={seed:f};pending=[seed] + while pending: + i=pending.pop();f=update[i] + for j in before[i]: + old=update.get(j,frame(j)) + if C.sub(old,f):continue + if j<0:return None + z=intersection(f,old) + if not C.sub(floor[j],z)or not good(z):return None + update[j]=z;pending.append(j) + if len(update)>1000:return None + gain=0.0 + for i,f in update.items(): + d=C.dimf[f];od=C.dimf[W.opframe[i]] + for j in before[i]: + pd=C.dimf[update.get(j,frame(j))];opd=C.dimf[frame(j)] + gain+=F[d-pd]-F[od-opd] + for j in after[i]: + if j not in update: + nd=C.dimf[frame(j)];gain+=F[nd-d]-F[nd-od] + return gain,update +import random +rng=random.Random(2116205) +stats=Counter();score=0.;bestscore=0.;bestframes=W.opframe[:];bestchanges=[] +for sweep,T in enumerate([.8,.4,.15,.05]+[0]*15+[.5,.2,.05,.01]+[0]*15): + num=0;gain=0 + order=list(range(len(W.ops)));rng.shuffle(order) + for oi,i in enumerate(order): + old=W.opframe[i] + direction,bounds,neighbors,fn=rng.choice([('down',floor,before,lower_transaction),('up',cap,after,transaction)]) + if C.dimf[old]==C.dimf[bounds[i]]:continue + candidates={bounds[i]} + for chain in range(2): + j=neighbors[i][chain] + for depth in range(8): + candidates.add(frame(j)) + if j<0:break + if depth<3:candidates.update(frame(k)for k in neighbors[j]) + j=min(neighbors[j],key=lambda k:C.dimf[frame(k)]) + best=None + for f in candidates: + if f==old:continue + stats['proposed']+=1;r=fn(i,f) + if r is None:continue + stats['feasible']+=1 + if best is None or r[0]>best[0]:best=r + if best and(best[0]>1e-10 or T and rng.random()1e-10:stats['improving']+=1 + else:stats['annealed']+=1 + changes.append(dict(direction=direction,seed=i,ops=sorted(updates),gain=improvement)) + if score>bestscore+1e-9: + bestscore=score;bestframes=W.opframe[:];bestchanges=changes[:] + if oi%10000==0:print('scan',sweep,oi,'T',T,'current_gain',score,'best_gain',bestscore,'seconds',time.monotonic()-started,flush=True) + print('sweep',sweep,'T',T,'changes',num,'entropy_gain',gain,'current',score,'best',bestscore,'stats',dict(stats),'seconds',time.monotonic()-started,flush=True) + if sweep==18: + # Restart second excursion from strongest state after full greedy relaxation. + W.opframe=bestframes[:];score=bestscore +W.opframe=bestframes;tot=bestscore;changes=bestchanges +W.changed_frames=[i for i,(a,b)in enumerate(zip(W.original_opframe,W.opframe))if a!=b] +W.endframe={s:W.opframe[xs[-1]]for s,xs in W.role_ops.items()} +W.exact_frames();row=W.row();delta=Counter({int(k):n for k,n in row['child_histogram'].items()});delta.subtract({int(k):n for k,n in baseline['child_histogram'].items()}) +frames=[[i,C.B[f]]for i,f in enumerate(W.opframe)if f!=base[i]] +(D/'relaxed-additional-frames.json').write_text(json.dumps(frames,separators=(',',':'))+'\n') +(D/'relaxed-all-frames.json').write_text(json.dumps([[i,C.B[f]]for i,f in enumerate(W.opframe)if f!=W.w['op_frame'][i]],separators=(',',':'))+'\n') +out=dict(status='EXACT_FRAMES_AND_NESTED_CHAINS_PASS_NOT_FULL_REPLAY',baseline=baseline,profile=row,child_delta={str(k):v for k,v in sorted(delta.items())if v},changes=changes,entropy_gain=tot,elapsed=time.monotonic()-started) +(D/'relaxed-result.json').write_text(json.dumps(out,indent=2)+'\n');print('DONE additional',len(frames),'delta',out['child_delta'],'gain',tot,flush=True) diff --git a/research/coordinated-crossover-pr200/search/source467-selection-full.json b/research/coordinated-crossover-pr200/search/source467-selection-full.json new file mode 100644 index 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"local_delta": { + "14": -1, + "22": -1, + "12": 1, + "2": 4, + "19": 4, + "21": -4 + }, + "score": -0.0022189077896683784 + }, + { + "role": 14170, + "source": 1538, + "partner": 1537, + "mix_frame": 122891, + "first_frame": 146274, + "rank": 14, + "targets": [ + 1488, + 1489, + 1490, + 1491 + ], + "local_delta": { + "14": -1, + "22": -1, + "12": 1, + "2": 4, + "19": 4, + "21": -4 + }, + "score": -0.0022189077896683784 + }, + { + "role": 13014, + "source": 1490, + "partner": 1489, + "mix_frame": 122999, + "first_frame": 143991, + "rank": 5, + "targets": [ + 1544, + 1545, + 1546, + 1547 + ], + "local_delta": { + "5": -1, + "22": -1, + "3": 1, + "2": 4, + "19": 4, + "21": -4 + }, + "score": -0.0071801182017736664 + } + ] +} diff --git a/research/coordinated-crossover-pr200/verify.py b/research/coordinated-crossover-pr200/verify.py new file mode 100644 index 0000000000..133b876329 --- /dev/null +++ b/research/coordinated-crossover-pr200/verify.py @@ -0,0 +1,31 @@ +#!/usr/bin/env python3 +"""Offline finite certificate replay. Python3.11+, numpy2.3.5, scipy1.17.0.""" +from pathlib import Path +import argparse,hashlib,json,io,zipfile,tempfile,subprocess,shutil,sys +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def pins(): + m=json.loads((HERE/'FILES.json').read_text())['files'];actual={p.relative_to(HERE).as_posix():sha(p) for p in HERE.rglob('*') if p.is_file() and p.name!='FILES.json'};assert actual==m,'Missing, changed, or unpinned upload file';return actual +assert not sys.flags.optimize +ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--temp-root',type=Path,help='Optional spacious scratch drive for extraction');args=ap.parse_args();before=pins();baseline=json.loads((HERE/'BASELINE.json').read_text());parts=[] +for entry in baseline['parts']: + p=HERE/entry['file'];assert p.stat().st_size==entry['bytes'] and sha(p)==entry['sha256'];parts.append(p.read_bytes()) +blob=b''.join(parts);assert hashlib.sha256(blob).hexdigest()==baseline['archive_sha256'] +with tempfile.TemporaryDirectory(prefix='crossover-pr200-',dir=args.temp_root) as tmp: + root=Path(tmp)/'source';root.mkdir() + with zipfile.ZipFile(io.BytesIO(blob)) as z: + for entry in z.infolist():assert (root/entry.filename).resolve().is_relative_to(root.resolve()),'Unsafe archive entry' + z.extractall(root) + package=root/'research/coordinated-crossover-pr200';package.mkdir() + for p in HERE.rglob('*'): + # Keep the split baseline archive inputs in the isolated package. The + # deterministic plateau-search replay reads them again when rebuilding its + # pinned PR202 source tree. + if p.is_file(): + target=package/p.relative_to(HERE);target.parent.mkdir(parents=True,exist_ok=True);shutil.copyfile(p,target) + result=subprocess.run([sys.executable,'-B',str(package/'verify_inner.py')],text=True) + assert result.returncode==0,'Full finite replay failed' +assert pins()==before,'Upload files changed during replay' +print('PASS immutable offline package; no network or git required') diff --git a/research/coordinated-crossover-pr200/verify_inner.py b/research/coordinated-crossover-pr200/verify_inner.py new file mode 100644 index 0000000000..0dbee1e3fb --- /dev/null +++ b/research/coordinated-crossover-pr200/verify_inner.py @@ -0,0 +1,50 @@ +#!/usr/bin/env python3 +"""Full finite replay; all-size compiler/selector and analytic conditions are inherited.""" +from pathlib import Path +import subprocess,sys,json,importlib.util,hashlib,gzip +from fractions import Fraction as Q +sys.set_int_max_str_digits(0);sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1];SA=ROOT/'research/source-assisted';CP=ROOT/'research/source-assisted-v4';WORK=CP/'.work' +def run(*args): + r=subprocess.run([sys.executable,'-B',*map(str,args)],cwd=ROOT,capture_output=True,text=True) + if r.returncode:raise RuntimeError('Replay rejected: '+str(args)+'\n'+r.stdout[-6000:]+'\n'+r.stderr[-6000:]) + print(r.stdout[-2000:],end='',flush=True) +def load(n,p): + s=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +def read(p):return json.loads(p.read_text()) +assert not sys.flags.optimize +before={p.relative_to(ROOT).as_posix():hashlib.sha256(p.read_bytes()).hexdigest() for p in [ROOT/'scripts/paired_cube_assembly.py',SA/'decision/exact_complex_flow_lift.py',CP/'contract_v4.py']} +# Recreate the committed operation-frame plateau from the pinned PR210 parent. +run(HERE/'search/joint-plateau-search-prdf958.py','--verify-committed') +# Replay the actual82 new gauges, complete reflected ledgers and all new banks. +run(HERE/'joint/replay_joint.py');run(HERE/'borrow/replay.py');run(HERE/'borrow/boundary.py');run(HERE/'borrow/derive_profile.py');run(HERE/'gaugeb/replay.py');run(HERE/'gaugeb/boundary.py');run(HERE/'gaugeb/derive_profile.py');run(HERE/'newg/replay.py');run(HERE/'newg/schedule_audit.py');run(HERE/'newg/boundary.py');run(HERE/'newg/derive_profile.py');run(HERE/'joint/pack_joint.py') +# The portable witness is checked again; original numerical search need not be repeated. +run(SA/'decision/exact_complex_flow_lift.py','--witness',WORK/'flow.witness.json','--profile',WORK/'flow.json','--out',WORK/'lift.json') +lift=read(WORK/'lift.json');expected=read(CP/'certificate.json');assert lift['exact_scalar_program_sha256']==expected['lift']['exact_scalar_program_sha256'] +for key,name in [('certificate_path','lift.certificate.json.gz'),('witness_path','flow.witness.json')]:lift[key]=(WORK/name).relative_to(ROOT).as_posix() +lift['checker_path']=(SA/'decision/exact_complex_flow_lift.py').relative_to(ROOT).as_posix() +(WORK/'lift.json').write_text(json.dumps(lift,indent=2)+'\n',newline='\n') +run(CP/'contract_v4.py','--tree',WORK/'aligned','--cache',WORK/'aligned/cache','--witness',WORK/'flow.witness.json','--flow-profile',WORK/'flow.json','--lift-profile',WORK/'lift.json','--out',HERE/'complex-profile-replayed.json') +actual=read(HERE/'complex-profile-replayed.json') +for key in ['m','W_per_vertex','rank_per_vertex','deficit_per_vertex','child_histogram','contract_checks','exact_scalar_program_sha256']: + assert actual[key]==expected['complex_profile'][key],('Complex mathematical output changed',key) +# Paid two-supplier moments, four finite leaf levels, and unchanged 47 constraints. +run(HERE/'joint/price_joint.py');assert read(HERE/'joint/assembly.json')==read(HERE/'certificate.json'),'Derived final certificate differs' +cert=read(HERE/'joint/assembly.json');assert all(Q(x)>0 for x in cert['assembly']['strict_constraints'].values());assert len(cert['assembly']['strict_constraints'])==47 +# Independent base-two enclosure, no imports from the public moment implementation. +im=load('independent_base_two',HERE/'geometry/base_two_moment.py') +for side in ['bit','complex']: + row=cert[side+'_profile'];a=Q(cert[side]['saving']);hist=[(int(t),n) for t,n in row['child_multiplicities'].items()] + lo,hi=im.moment(row['m'],row['W'],hist,a);nl,nu=im.moment(row['m'],row['W'],hist,a+Q(1,10**18)) + if side=='bit': + fallback=[(1,32*row['m']**2*sum(n for _,n in hist))];bl,bu=im.moment(row['m'],row['W'],fallback,a);bnl,bnu=im.moment(row['m'],row['W'],fallback,a+Q(1,10**18));hi+=Q(1,10**16)*bu;nl+=Q(1,10**16)*bnl + assert hi<1