diff --git a/.github/workflows/residual-bank-run1.yml b/.github/workflows/residual-bank-run1.yml new file mode 100644 index 0000000000..6d377d743a --- /dev/null +++ b/.github/workflows/residual-bank-run1.yml @@ -0,0 +1,25 @@ +name: residual-bank-run1 + +on: + push: + paths: + - 'research/residual-bank-run1/**' + - '.github/workflows/residual-bank-run1.yml' + pull_request: + paths: + - 'research/residual-bank-run1/**' + - '.github/workflows/residual-bank-run1.yml' + +jobs: + verify: + runs-on: ubuntu-latest + strategy: + matrix: + python-version: ['3.11', '3.14'] + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python-version }} + - name: Offline accounting replay + run: python3 -B research/residual-bank-run1/verify.py diff --git a/research/residual-bank-run1/NOTICE.md b/research/residual-bank-run1/NOTICE.md new file mode 100644 index 0000000000..03c71d90f2 --- /dev/null +++ b/research/residual-bank-run1/NOTICE.md @@ -0,0 +1,36 @@ +# NOTICE + +## Provenance + +Package construction and the enumeration/schedule/arithmetic/verification code: +prepared for the CrocSwap/integer-mult-bounds queue with **OpenAI Codex +assistance**, 2026-10-10. + +## Vendored sources (byte-identical, sha256-pinned in SOURCE.json) + +- `interval_moment.py` — PR200's exact rational interval moment engine + (Chafik Boukhalfa, `research/paired-cube-diagonal-bit-168/arithmetic/`, + package Apache-2.0). +- `paired_cube_assembly.py` — the unchanged balanced assembly + (PR168-v4/PR184 lineage via ikeboy's PR193 tree; original attributions retained). +- `banks.py` — incidence colouring helpers (Evan McKinney, PR197, Apache-2.0; + vendored via rohanarun's PR205 package). +- `references/pr193-source-assisted-v4.certificate.json` — ikeboy's PR193 complex + supplier certificate (unchanged; its own credits and AI disclosures stand). +- `references/pr200-bit.certificate.json` — Chafik Boukhalfa's PR200 bit word + certificate (unchanged). +- `references/pr205-packed.certificate.json` — rohanarun's PR205 packed-row + certificate (unchanged). + +All mathematical content of the vendored files is the work of their authors as +credited in the upstream packages. The new content of this package is the rank-22 +enumeration (derived from the pinned PR200 word), the absorption schedule, the +retained-ledger arithmetic and the obligation statement. + +## AI assistance disclosure + +The new code, enumeration and text in this package were prepared with OpenAI Codex +(GPT-class model) assistance. The exact arithmetic is machine-replayed by +`verify.py`; the mathematical claims remain conditional as stated in PROOF.md. + +Apache-2.0. diff --git a/research/residual-bank-run1/PROOF.md b/research/residual-bank-run1/PROOF.md new file mode 100644 index 0000000000..63d45a6d98 --- /dev/null +++ b/research/residual-bank-run1/PROOF.md @@ -0,0 +1,94 @@ +# Construction argument and scope + +## Claim + +On the retained multiplication interfaces, absorbing the rank-22 residual family of +the PR200/PR205 terminal-modified bit word into the banks yields the conditional +exponent + + kappa = 700427501305159 / 10^18 = 0.000700427501305159 + +with the complex supplier binding. This is certified **at the accounting level** +(Steps 1–4 below, all machine-replayed by `verify.py`) and is **conditional on the +physical realization obligations R1–R4** (`obligations.json`). + +## Step 1 — the absorbed family is exactly enumerated + +`inputs/absorbed-occurrences.json` lists every rank-22 ledger child of the per-vertex +histogram with its provenance, derived from the pinned PR200 word +(`word_p12.json`, `frames_p12.json`, the bit certificate and the base checker, all +sha256-pinned in that file): 1,320 physical-chain frame jumps, 24 copied-centre +children, 880 source-chain frame jumps, 0 target jumps — 2,224 per vertex, i.e. the +full `hist[22] = 6,672` bin under the row's factor-3 normalization. No other bin is +touched. + +## Step 2 — whole-bank volume and retained ledger + +Under the three-copy integer normalization of the published packed row +(W = 56,402, rank mass 4,055,136, deficit 5,808, 877,638 children): + +* absorbed volume `22 × 20,016 = 440,352` registers = `72 × 6,116` whole banks; +* retained mass `3,614,784`, retained children `857,622`, largest child 21; +* row identity `72·50,286 − 3,614,784 = 5,808`, deficit unchanged, stock drop + `56,402 − 50,286 = 6,116` exactly the bank count. + +This is the accounting form of "absorbing a family into the banks drops its dirt +and, by the row identity W = (mass + D)/m, drops the stock with it" (PR #208). +`schedule.py` also enumerates every block tiling of width 72 over the word's +residual families {4, 24} plus the new 22-blocks and checks pattern divisibility. + +## Step 3 — exact paid moments + +`arithmetic.py` prices the absorbed profile with PR200's exact rational interval +moment engine, including the complete worst-case envelope (bad fraction 10^-16, +fallback `32·72²` per retained child). Before the absorption is applied the same +pipeline reproduces PR #205's certified packed coarse saving +`683528191056257/10^18` **to the digit**, which validates the engine against a +published certificate. + +* complex coarse saving (unchanged): `700918443859411/10^18`; +* bit coarse saving before absorption: `683528191056257/10^18`; +* bit coarse saving after absorption: `728251090009891/10^18` — the bit word now + clears the complex cap `7.009184e-4`; +* three-level finite ordinary composition from PR200's completed ordinary supplier + gives the bit leaf `≈ 7.282510899902281e-4`, strictly above the complex cap. + +## Step 4 — balanced assembly + +The unchanged 47-constraint balanced assembly (eta = beta = 10^-24, weak = 10^-30) +takes `a = min(bit leaf, (1−β)·b − weak)`. The bit leaf clears the cap, so +`a = (1−β)·b − weak` and the complex branch binds: + + kappa = 700427501305159 / 10^18 = 0.000700427501305159 + +All 47 strict constraints and 7 margins are positive; the adjacent grid point +`kappa + 10^-18` is rejected by the same assembly. This is the exact 10^-18-grid +sharpening of PR #208's priced rung-1 target `7004273/10^10`. + +## What remains conditional (R1–R4) + +The rank-22 bin is not the gauge-exterior species the current bank construction +absorbs: it is frame-transition increments. Non-gauge chains already bank their +residual projectors and keep every increment child, so the published mechanism +cannot absorb this family — this is exactly the "genuinely different residual type" +the suppliers' crossover notes reserve. A completed finite witness must add: + +* R1: the residual-type definition, block shapes and per-occurrence block + assignment (schedule.py supplies the admissible tilings); +* R2: formal-column replay of the modified word (F2 identity and defining-integer + decoder) under bank re-assignment at the enumerated transitions; +* R3: exact charts, incidence colouring and prime witnesses for the new blocks; +* R4: moment-envelope parity (any completion child R1 introduces must be added to + the ledger and the kappa recomputed). + +Until then the claim is an accounting construction and certified target, in the +same sense every repository witness is conditional on its stated interfaces — and +strictly more limited than the published witnesses, which have their physical +realizations built and replayed. + +## Inherited conditions + +The retained analytic, uniform-recursion, fixed-tape, all-size compiler, selector, +routing, precision and finite-bridge hypotheses of the PR184/PR186/PR193/PR200 +lineage are inherited, not proved. This is not an unconditional multiplication +theorem, a formal verification of the algorithm, or a runtime benchmark. diff --git a/research/residual-bank-run1/README.md b/research/residual-bank-run1/README.md new file mode 100644 index 0000000000..ab1664287a --- /dev/null +++ b/research/residual-bank-run1/README.md @@ -0,0 +1,90 @@ +# Building PR208's priced target: rank-22 residual bank absorption + +This package **builds the accounting construction** that PR #208 priced and left +unbuilt — the first certified-shape rung of its bank-absorption ladder: absorb the +bit word's **rank-22 residual family** into the banks — and states precisely what a +physical realization must still supply. + +Under the retained multiplication interfaces, the certified accounting target is + +$$ +T(n)=O\left(n(\log n)^{1-\kappa}\right),\qquad +\kappa=\frac{700427501305159}{10^{18}}=0.000700427501305159, +$$ + +**conditional on the physical realization obligations R1–R4** in +[obligations.json](obligations.json). The binding branch is the unchanged complex +supplier: the absorbed bit word clears the complex cap, so κ sits at the complex +side's own value, exactly as PR #208's rung table predicts (`7004273/10^10` on its +10^-10 pricing grid; this package certifies the finer 10^-18 grid point). + +| | κ | status | +| --- | --- | --- | +| main reviewed (#186) | 6.61885549259598e-4 | published | +| #205 packed diagonal bit | 6.83061299399923e-4 | verified this queue | +| #210 shared entrance gauges | 6.83883297459132e-4 | verified this queue | +| **this package, rank-22 absorption** | **7.00427501305159e-4** | **accounting certified; R1–R4 open** | +| #208's priced rung-1 target | 7.004273e-4 | model price (superseded by the exact grid above) | + +That is **+2.42% over #210's frontier** (+2.52% over the #207 row #208 priced) and +**+5.82% over main** — the complex +supplier's own cap, with no complex-side work, exactly the move #208 priced. + +## What is new and machine-checked + +1. **The absorbed family, with provenance.** The rank-22 ledger bin is enumerated + occurrence by occurrence from the pinned PR200 word + ([inputs/absorbed-occurrences.json](inputs/absorbed-occurrences.json)): + 1,320 physical-chain frame jumps, 24 copied-centre children and 880 source-chain + frame jumps per vertex — 2,224 × 3 = 6,672 ledger children. This is not the + banked gauge-exterior species: non-gauge chains already bank their residual + projectors and keep every increment child, so this family is the *"future + genuinely different residual type"* PR #207's crossover notes reserve. +2. **The whole-bank schedule.** Dirt volume `22 × 20,016 = 440,352 = 72 × 6,116` + fills whole banks; the stock drop equals the bank count exactly; the retained + ledger (857,622 children, largest 21) satisfies the row identity + `72·50,286 − 3,614,784 = 5,808` with the deficit unchanged + ([schedule.py](schedule.py)). +3. **Exact arithmetic to the κ.** Both rational interval moment engines, the + three-level finite ordinary composition and the unchanged 47-constraint + balanced assembly, with the adjacent 10^-18 grid point **excluded** + ([arithmetic.py](arithmetic.py)). The engine reproduces PR #205's certified + packed coarse saving to the digit before the absorption is applied — the + pipeline is validated against a published certificate, not just self-consistent. + +## What is not built here + +The physical realization of the new residual type: the banked word's formal +columns (F2 identity and defining-integer decoder) under the modified transitions, +the block assignment, charts, incidence colouring and prime witnesses. These are +stated one-to-one against the gauge-family precedent in +[obligations.json](obligations.json) (R1–R4, all OPEN). Until they verify, this is +an **accounting construction and a certified target**, not a completed finite +witness — the same distinction PR #208 draws ("priced target, not built"), moved +one full step forward: the target is now certified to the grid point, the family is +enumerated, and the remaining work is a closed checklist. + +As every result in this repository: conditional on the retained analytic, +uniform-recursion, fixed-tape and finite-bridge interfaces; never an unconditional +multiplication theorem. + +## Reproduce + +```sh +python3 -B verify.py # read-only replay, ~1 minute +python3 -B verify.py --write # authoring only +``` + +Python 3.11+, assertions enabled. No network, no git, no scratch space. + +## Credits + +The absorbed word and its checkers: Chafik Boukhalfa (#200). Complex supplier: +ikeboy (#193/#202 lineage). Bank mechanism: Evan McKinney (#197), realized on this +word by rohanarun (#205); completed entrance banks: PR #186/#207 (Dugongue) and the +BANK-PROOF-PR200.md argument. The pricing model this builds: maxime-fleury (#204, +#208), whose rung-1 target is reproduced and sharpened here. Frame/ceiling context: +rohanarun (#211/#213), eumemic (#210), DaysSky (#192/#201/#212). All retained +upstream attributions of the PR168/PR184 lineage stand. + +Prepared with OpenAI Codex assistance. Apache-2.0. diff --git a/research/residual-bank-run1/SOURCE.json b/research/residual-bank-run1/SOURCE.json new file mode 100644 index 0000000000..db23ea92f3 --- /dev/null +++ b/research/residual-bank-run1/SOURCE.json @@ -0,0 +1,12 @@ +{ + "files": { + "banks.py": "0548a1c15bd6f6dea4505f5fd2ca1bb4ecbe914c8c90769b8cd8beeef428d0cf", + "inputs/absorbed-occurrences.json": "1aedd8640818afe63eb7797f0332b915ed64ebeea3e9f210aaf40a06a02478a7", + "interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", + "obligations.json": "0268fc3628421bb930e9f56a23469a45f3b2bfae8888f6030622c2a51ce6a511", + "paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "references/pr193-source-assisted-v4.certificate.json": "d84406d2fcc6990deba2b135509e6d86600e57123d88f9b21f7b7240e1aeb513", + "references/pr200-bit.certificate.json": "853afa75980e11ce16b333c28311c4f635e84065867c049fda9916c2419091ed", + "references/pr205-packed.certificate.json": "c11fbb9aaa99594afc8d21e33761dc6d1d6c76ce3dbc36d5b64cae872c242f5a" + } +} diff --git a/research/residual-bank-run1/arithmetic.py b/research/residual-bank-run1/arithmetic.py new file mode 100644 index 0000000000..7de1b126bd --- /dev/null +++ b/research/residual-bank-run1/arithmetic.py @@ -0,0 +1,148 @@ +#!/usr/bin/env python3 +"""Exact paid moments, finite ordinary-leaf composition and the balanced assembly +for the rank-22-absorbed profile. + +Inherited machinery (vendored byte-identically): + interval_moment.py - PR200's exact rational interval moment engine + paired_cube_assembly.py - PR184/PR168-v4's unchanged 47-constraint balanced assembly +Profiles come from the pinned certificates and schedule.py's retained ledger. +""" +import importlib.util +import json +import sys +from fractions import Fraction as Q +from pathlib import Path + +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 load(name, path): + s = importlib.util.spec_from_file_location(name, path) + m = importlib.util.module_from_spec(s) + s.loader.exec_module(m) + return m + + +def profile(m, W, H, delta): + H = {int(r): int(n) for r, n in H.items()} + return dict(m=m, W=W, child_multiplicities=H, N=delta, L=0, + total_rank=sum(r * n for r, n in H.items()), maxchild=max(H)) + + +def paid(im, row, a, bit): + result = 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']) + result.update(lower=result['lower'] + w * e, upper=result['upper'] + w * f) + return result + + +def certify(im, row, bit): + den = 10 ** 18 + lo = 0 + hi = den // 100 + assert paid(im, row, Q(lo, den), bit)['upper'] < 1 < paid(im, row, Q(hi, den), bit)['lower'] + while hi - lo > 1: + mid = (lo + hi) // 2 + v = paid(im, row, Q(mid, den), bit) + if v['upper'] < 1: + lo = mid + elif v['lower'] > 1: + hi = mid + else: + raise AssertionError('Interval inconclusive') + a = Q(lo, den) + b = Q(hi, den) + return dict(saving=a, accepted=paid(im, row, a, bit), next_excluded=paid(im, row, b, bit)) + + +def build(schedule): + im = load('interval_moment', HERE / 'interval_moment.py') + assembly = load('frontier_assembly', HERE / 'paired_cube_assembly.py') + c191 = json.loads((HERE / 'references/pr193-source-assisted-v4.certificate.json').read_text()) + b200 = json.loads((HERE / 'references/pr200-bit.certificate.json').read_text())['bit'] + pack = json.loads((HERE / 'references/pr205-packed.certificate.json').read_text())['physical'] + + cp_raw = c191['complex_profile'] + cp = profile(cp_raw['m'], cp_raw['W_per_vertex'], cp_raw['child_histogram'], cp_raw['deficit_per_vertex']) + packed = profile(72, pack['W'], pack['child_histogram'], pack['deficit']) + + kept = schedule['retained_profile'] + absorbed = profile(72, kept['W_after'], kept['histogram'], kept['deficit']) + assert absorbed['total_rank'] == kept['rank_mass_after'] + assert absorbed['maxchild'] == kept['maxchild'] + + complex_cert = certify(im, cp, False) + before = certify(im, packed, True) + after = certify(im, absorbed, True) + # The engine must reproduce PR205's certified packed coarse saving exactly. + certified_packed_saving = Q(json.loads((HERE / 'references/pr205-packed.certificate.json').read_text()) + ['arithmetic']['bit_after']['saving']) + assert before['saving'] == certified_packed_saving, 'engine drift: packed row not reproduced' + + old = Q(b200['coarse']['ordinary_saving']) + coarse = after['saving'] + chain = [old] + for _ in range(3): + a = (1 - coarse) * coarse + coarse * chain[-1] + assert chain[-1] < a < coarse < 1 - a + chain.append(a) + leaf = chain[-1] + + bridge = c191['assembly']['finite_bridge'] + bridge['rows']['degree_gap'] = Q(bridge['rows']['degree_gap']) + beta = eta = Q(1, 10 ** 24) + weak = Q(1, 10 ** 30) + den = 10 ** 18 + + def assemble(bit_saving): + b = complex_cert['saving'] + a = min(bit_saving, (1 - beta) * b - weak) + q = a * (1 - 2 * eta) + bound = (1 - eta) * q / (1 + q) + z = bound * den + k = Q((z.numerator - 1) // z.denominator, den) + out = assembly.assembly(a, b, bridge, k, eta=eta, beta=beta) + assert len(out['strict_constraints']) == 47 and len(out['margins']) == 7 + try: + assembly.assembly(a, b, bridge, k + Q(1, den), eta=eta, beta=beta) + except AssertionError: + pass + else: + raise AssertionError('Next final grid accepted') + constraints = out.pop('strict_constraints') + return dict(kappa=k, assembly=dict(out, strict_constraint_count=len(constraints), + minimum_constraint=min(constraints.values())), + binding='complex' if a == (1 - beta) * b - weak else 'bit') + + before_assembly = assemble(chain[0]) + after_assembly = assemble(leaf) + assert before_assembly['kappa'] < after_assembly['kappa'] + assert after_assembly['binding'] == 'complex', 'rank-22 absorption must clear the complex cap' + + return dict( + complex_coarse=complex_cert['saving'], + bit_coarse_before=before['saving'], + bit_coarse_after=after['saving'], + bit_before_next_excluded=before['next_excluded'], + bit_after_next_excluded=after['next_excluded'], + ordinary_seed=old, ordinary_chain=chain, ordinary_leaf=leaf, + before_assembly=before_assembly, after_assembly=after_assembly, + kappa_gain=after_assembly['kappa'] - before_assembly['kappa'], + ) + + +if __name__ == '__main__': + sys.path.insert(0, str(HERE)) + import schedule as sched + out = build(sched.build()) + for k, v in out.items(): + if isinstance(v, Q): + print(k, '=', v, float(v)) + elif isinstance(v, dict) and 'kappa' in v: + print(k, 'kappa =', v['kappa'], float(v['kappa']), 'binding', v['binding']) diff --git a/research/residual-bank-run1/banks.py b/research/residual-bank-run1/banks.py new file mode 100644 index 0000000000..6505ebd37e --- /dev/null +++ b/research/residual-bank-run1/banks.py @@ -0,0 +1,104 @@ +"""PR197 chart inversion and bank colouring helpers (byte-identical extract of packing.py up to build()). + +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<=1,'log interval domain') + base=Q(4,3);k=0 + while x>base:x/=base;k+=1 + def short(y): + z=(y-1)/(y+1);power=z;s=Q(0) + for j in range(LOG_TERMS):s+=power/Q(2*j+1);power*=z*z + lo=2*s;tail=2*power/(Q(2*LOG_TERMS+1)*(1-z*z)) + return lo,lo+tail + lo,hi=short(x);blo,bhi=short(base) + return lower(k*blo+lo),upper(k*bhi+hi) + +def exp_interval(lo,hi): + require(0<=lo<=hi1 and W>0,'profile dimensions') + raw=profile['child_multiplicities'];hist={int(t):n for t,n in raw.items()} + require(len(hist)==len(raw),'aliased histogram keys') + require(all(00 for t,n in hist.items()),'invalid child or multiplicity') + mass=sum(t*n for t,n in hist.items());require(mass==profile['total_rank']==W*m-profile['N']+profile['L'],'rank mass') + require(max(hist)==profile['maxchild'],'maximum child') + require(0=0,'nonnegative saving');lo=hi=Q(0);rows=[] + for t,n,L,U in prepare(profile): + E,F=exp_interval(a*L,a*U);w=Q(t*n,profile['m']*profile['W']);lo+=w*E;hi+=w*F + if details:rows.append(dict(child=t,multiplicity=n,log_lower=L,log_upper=U,exp_lower=E,exp_upper=F,contribution_lower=w*E,contribution_upper=w*F)) + result=dict(saving=a,lower=lo,upper=hi,strict_gap_lower=1-hi) + if details:result['terms']=rows + return result + +def saving_grid(profile,denominator=10**24): + require(type(denominator) is int and denominator>0,'positive saving grid') + prepare(profile);lo=0;hi=denominator//32;iterations=0 + require(moment(profile,Q(lo,denominator))['upper']<1,'initial contraction') + require(moment(profile,Q(hi,denominator))['lower']>1,'initial exclusion') + while hi-lo>1: + mid=(hi+lo)//2;m=moment(profile,Q(mid,denominator));iterations+=1 + if m['upper']<1:lo=mid + elif m['lower']>1:hi=mid + else:raise ValueError('Moment interval overlaps one; increase enclosure precision') + accepted=moment(profile,Q(lo,denominator),True);rejected=moment(profile,Q(hi,denominator),True) + require(accepted['upper']<1 bank, offset) generated and hashed.", + "reference_precedent": "PR205 packing.py: 'For each role, the inherited fixed normalizer sends its true residual projector to its assigned block'; BANK-PROOF-PR200.md block allocation with 9-edge-colouring of 462,078 role-copy uses.", + "status": "OPEN" + }, + { + "id": "R2", + "name": "formal columns of the modified word", + "statement": "Re-run the complete formal-column checks on the modified word: every source, target and dirty-register column over F2 and over the defining integers (residual bound and packed digits as in PR200's terminal-modified replay), with the rank-22 transitions realized by bank re-assignment instead of paid children. The F2 identity and the defining-integer decoder must both hold.", + "reference_precedent": "PR200 paired-cube-diagonal-bit-168 verify.py: 'all formal source/target/dirty columns, complete target chronology... F2 identity and its defining integer decoder'.", + "status": "OPEN" + }, + { + "id": "R3", + "name": "charts, routing and prime witnesses", + "statement": "Exact charts (integer kernel bases with fraction-free inverses and replayed elementary factors) for every new block frame, the incidence colouring of the new bank incidences, and distinct integer Gram/prime witnesses for every frame the new blocks use, with residual factors below the retained q bound.", + "reference_precedent": "PR205 packing.py chart digest and colouring checks; 'All 24,401 used bit frame IDs... distinct integer Gram witnesses'.", + "status": "OPEN" + }, + { + "id": "R4", + "name": "moment envelope parity", + "statement": "Confirm that the paid moment envelope for the modified word is exactly the one arithmetic.py prices: retained child histogram as in schedule.py, stock 50,286 (three-copy normalization), deficit 5,808, worst-case bad fraction 1e-16 and fallback 32*72^2 per retained child, strict adapter and internally borrowed-row tolls paid. Any additional completion child introduced by R1 must be added to the ledger and the kappa recomputed.", + "reference_precedent": "BANK-PROOF-PR200.md 'Fully charged child inventory and exact price'; PR205 arithmetic.py paid() wrapper.", + "status": "OPEN" + } + ], + "claim_scope": "verify.py certifies: enumeration provenance, whole-bank volume condition, retained ledger and row identity, both interval moment engines, three-level ordinary composition, the 47-constraint balanced assembly and the exclusion of the adjacent kappa grid point. The resulting kappa is conditional on R1-R4 exactly as every published witness in this repository is conditional on its stated finite bridge and all-size interfaces; it is not a completed finite witness until R1-R4 verify, and it is not an unconditional multiplication theorem in any case." +} diff --git a/research/residual-bank-run1/paired_cube_assembly.py b/research/residual-bank-run1/paired_cube_assembly.py new file mode 100644 index 0000000000..43007488ad --- /dev/null +++ b/research/residual-bank-run1/paired_cube_assembly.py @@ -0,0 +1,58 @@ +#!/usr/bin/env python3 +"""Exact semantic assembly with the balanced prefix, for the paired-cube network. + +Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and +the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao +Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in +references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of +1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa. +The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in +research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from +structured_bulk_assembly.assembly. +""" +from fractions import Fraction as Q + + +def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)): + a,b=bit_saving,complex_saving + tau,sigma=1-a,1-b + q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2 + c=q+eta/4; eps=(1-eta)/(1+q) + minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8 + internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma) + margins=dict(balanced_prefix=1-eps,coordinate_movement=a, + compact_phase_layer=minimum,bulk_exposure=a, + Gaussian_arithmetic=min(1-eps-delta,r-delta), + scalar_work=1-eps-delta,dimension=eps) + slacks=dict(bit_positive=a,complex_above_bit=b-a, + complex_below_one_over32=Q(1,32)-b,beta_positive=beta, + beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a, + q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q, + c_positive=c,c_below_one=1-c,q_below_reservations=c-q, + lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf,compact_reservations=lp-(1-c), + lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps, + guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c, + record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta, + gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a, + small_field_exposure=1-eps-minimum, + artificial_boundary=8-eps+r-delta-minimum, + literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']), + row_product_gap=bridge['rows']['degree_gap']) + slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()}) + assert len(slacks)==47 and len(margins)==7 + assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/residual-bank-run1/references/pr193-source-assisted-v4.certificate.json b/research/residual-bank-run1/references/pr193-source-assisted-v4.certificate.json new file mode 100644 index 0000000000..1bf00cdb84 --- /dev/null +++ b/research/residual-bank-run1/references/pr193-source-assisted-v4.certificate.json @@ -0,0 +1,599 @@ +{ + "assembly": { + "arithmetic": "32-term rational logarithm enclosure; rational exponential majorant; upward 2^120 rounding", 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+ "next_lower": "1664335862527366085285815072313660921079442613294059590682498373/1664335862527366084446476550826973504231042931966971966887297024", + "next_upper": "72362428805537655881991959665811344394758374491046069160122671/72362428805537655845498980470737978444827953563781389864665088" + } + }, + "status": "PASS" + }, + "physical": { + "W": 56402, + "banks": 45842, + "chart_sha256": "22662b8580d62f26f50a7773ac45a40d4ffa8352bba5317ec3b2c0ce5897a810", + "child_histogram": { + "1": 377316, + "10": 6066, + "11": 3636, + "12": 12186, + "13": 4878, + "14": 11016, + "15": 2592, + "16": 8964, + "17": 4068, + "18": 4842, + "19": 1944, + "2": 175962, + "20": 15840, + "21": 45054, + "22": 20016, + "3": 92790, + "4": 28764, + "5": 24210, + "6": 12456, + "7": 12240, + "8": 7542, + "9": 5256 + }, + "color_stats": { + "longest_swapped_path": 11, + "swaps": 733 + }, + "conflicting_assignment_rejected": true, + "conservative_selector_calls": 5368513266, + "copies": 3, + "deficit": 5808, + "distinct_gauges": 220, + "gauge_roles": 2200, + "incidence_sha256": "76bff256b747bd188fdfa679059c8340cab7d8e1208db4b818d770ea08711117", + "incidences": 154026, + "interior_splices": 1760, + "m": 72, + "max_chart_factors": 171, + "max_den": 18, + "max_num": 5, + "maxchild": 22, + "patterns": [ + { + "count": 3300, + "rank24": 2, + "rank4": 6 + }, + { + "count": 42542, + "rank24": 3, + "rank4": 0 + } + ], + "physical_roles": 17114, + "rank_mass": 4055136, + "source_package": "research/paired-cube-diagonal-bit-168", + "status": "PASS exact actual-chain chart and incidence checks", + "terminal_sinks": 34, + "word_sha256": "0728ed1c7320430a87709b1034485cbabefec85d532b48897f74136cf3954218" + }, + "pinned_bit_files": 2242 +} diff --git a/research/residual-bank-run1/schedule.py b/research/residual-bank-run1/schedule.py new file mode 100644 index 0000000000..70c03e7964 --- /dev/null +++ b/research/residual-bank-run1/schedule.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python3 +"""Bank-absorption schedule for the rank-22 residual family on the PR200/PR205 bit word. + +Everything here is exact integer / rational arithmetic on pinned inputs: +the enumerated rank-22 increment occurrences (inputs/absorbed-occurrences.json), +PR200's bit certificate (references/pr200-bit.certificate.json) and PR205's packed +certificate (references/pr205-packed.certificate.json). + +What this builds (all machine-checked here): + * the absorbed family's exact inventory, with chain/frame provenance; + * the whole-bank volume condition and the bank count it implies; + * the retained child ledger and the row identity W*m - mass = D; + * candidate block tilings of width m=72 mixing the word's residual families + (4 and 24) with the new 22-blocks, and the divisibility of their patterns. + +What this does NOT build: the physical realization of the new residual type +(formal columns, charts, normalizers, routing, prime witnesses). See +obligations.json and PROOF.md. +""" +import json +import sys +from pathlib import Path + +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) + +M = 72 +NEW_RANK = 22 + + +def _int(x): + assert isinstance(x, int) + return x + + +def build(): + occ = json.loads((HERE / 'inputs/absorbed-occurrences.json').read_text()) + bit = json.loads((HERE / 'references/pr200-bit.certificate.json').read_text())['bit'] + pack = json.loads((HERE / 'references/pr205-packed.certificate.json').read_text())['physical'] + + # --- 1. inventory of the absorbed family ----------------------------------- + per_vertex = occ['counts_per_vertex'] + counts = { + 'physical_internal_chain_jumps': len(occ['occurrences_per_vertex']['H']), + 'copied_centre_children': len(occ['occurrences_per_vertex']['H_center']), + 'physical_target_jumps': len(occ['occurrences_per_vertex']['Y']), + 'source_chain_jumps': len(occ['occurrences_per_vertex']['src']), + } + listed = sum(counts.values()) + assert listed == per_vertex['physical_internal_H'] + per_vertex['physical_target_Y'] \ + + per_vertex['source_chain_src'] == 2224, counts + hist = {int(r): int(n) for r, n in bit['profile']['child_histogram'].items()} + assert hist[NEW_RANK] == per_vertex['ledger_bin_22_per_vertex'] == 3 * listed, hist[NEW_RANK] + normalization = 3 + occurrences = normalization * hist[NEW_RANK] # 20,016 three-copy normalization + volume = NEW_RANK * occurrences # 440,352 registers of dirt + + # --- 2. whole-bank volume condition --------------------------------------- + assert volume % M == 0, 'absorbed volume must fill whole banks' + banks = volume // M # 6,116 + assert banks == 6116 + + # --- 3. retained ledger and row identity ---------------------------------- + kept = {int(r): int(n) for r, n in pack['child_histogram'].items()} + assert kept[NEW_RANK] == occurrences + kept.pop(NEW_RANK) + mass_before = int(pack['rank_mass']) + assert sum(r * n for r, n in {int(r): int(n) for r, n in pack['child_histogram'].items()}.items()) == mass_before + mass = mass_before - volume + D = int(pack['deficit']) + W = int(pack['W']) + W_new = (mass + D) // M + assert M * W_new == mass + D, 'row identity after absorption' + assert W_new == W - banks == 50286 + assert sum(r * n for r, n in kept.items()) == mass + assert max(kept) == 21 + + # --- 4. block tilings of the bank width ----------------------------------- + # A bank is a coordinate-block partition of width 72. The word's own residual + # families are 4 and 24; the new type contributes 22-blocks. Every tiling of 72 + # over {4, 24, 22} using at least one 22-block: + patterns = [] + for c in range(1, 4): + for b in range(0, 4): + for a in range(0, 19): + if 4 * a + 24 * b + 22 * c == 72: + patterns.append(dict(rank4=a, rank24=b, rank22=c, blocks=a + b + c)) + patterns.sort(key=lambda p: (p['rank22'], p['rank4'], p['rank24'])) + assert patterns, 'no certified-shape tiling' + # Divisibility of the absorbed occurrence count under uniform 22-block banks: + uniform22 = [dict(pattern=p, exact_full_banks=(occurrences % p['rank22'] == 0), + banks_if_pattern=occurrences / p['rank22'] if occurrences % p['rank22'] == 0 else None) + for p in patterns] + fills = [u for u in uniform22 if u['exact_full_banks']] + assert fills, 'no pattern divides the absorbed occurrence count' + + schedule = { + 'status': 'bank-absorption schedule, accounting and tiling invariants; ' + 'no physical column, chart or prime witness is built here', + 'absorbed_family': { + 'rank': NEW_RANK, + 'provenance_counts_per_vertex': counts, + 'ledger_bin_per_vertex': hist[NEW_RANK], + 'normalization_factor': normalization, + 'occurrences_three_copies': occurrences, + 'dirt_volume_registers': volume, + }, + 'banks': dict(width=M, banks_from_volume=banks, volume=M * banks, + whole_bank_condition=True), + 'retained_profile': dict(m=M, W_before=W, W_after=W_new, deficit=D, + rank_mass_before=mass_before, rank_mass_after=mass, + children_before=int(pack['children']) if 'children' in pack else sum( + int(n) for n in pack['child_histogram'].values()), + children_after=sum(kept.values()), + maxchild=max(kept), + histogram={str(r): n for r, n in sorted(kept.items())}), + 'row_identity': dict(before=f'{M}*{W} - {mass_before} = {D}', + after=f'{M}*{W_new} - {mass} = {D}', stock_drop=W - W_new, + stock_drop_equals_banks=(W - W_new == banks)), + 'block_tilings': dict(patterns=patterns, uniform_22_block_banks=uniform22, + feasible_patterns=[u['pattern'] for u in fills]), + } + return schedule + + +if __name__ == '__main__': + out = build() + print(json.dumps(out, indent=1, sort_keys=True)) diff --git a/research/residual-bank-run1/verify.py b/research/residual-bank-run1/verify.py new file mode 100644 index 0000000000..88e150293f --- /dev/null +++ b/research/residual-bank-run1/verify.py @@ -0,0 +1,121 @@ +#!/usr/bin/env python3 +"""Offline verification of the rank-22 bank-absorption accounting construction. + +Read-only unless --write: pins every vendored input byte, rebuilds the absorption +schedule and the exact arithmetic from those inputs, and reproduces certificate.json. + + python3 -B verify.py # check + python3 -B verify.py --write # authoring: regenerate certificate.json and SOURCE.json + +The physical realization obligations (R1-R4, obligations.json) are checked for +presence and are NOT discharged here; the certificate's scope says so literally. +""" +import argparse +import json +import sys +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path + +HERE = Path(__file__).resolve().parent +sys.dont_write_bytecode = True +sys.path.insert(0, str(HERE)) +if hasattr(sys, 'set_int_max_str_digits'): + sys.set_int_max_str_digits(0) + +PINNED = [ + 'inputs/absorbed-occurrences.json', + 'references/pr193-source-assisted-v4.certificate.json', + 'references/pr200-bit.certificate.json', + 'references/pr205-packed.certificate.json', + 'interval_moment.py', + 'paired_cube_assembly.py', + 'banks.py', + 'obligations.json', +] + + +def digest(path): + return sha256(path.read_bytes()).hexdigest() + + +def pins(): + manifest = json.loads((HERE / 'SOURCE.json').read_text()) + actual = {name: digest(HERE / name) for name in PINNED} + assert actual == manifest['files'], 'Pinned input bytes changed' + return actual + + +def serial(value): + if isinstance(value, Q): + return str(value) + if isinstance(value, dict): + return {str(k): serial(v) for k, v in value.items()} + if isinstance(value, (list, tuple)): + return [serial(v) for v in value] + return value + + +def build(): + import schedule as sched + import arithmetic as arith + schedule = sched.build() + arith_result = arith.build(schedule) + obligations = json.loads((HERE / 'obligations.json').read_text()) + open_ids = [o['id'] for o in obligations['obligations']] + assert open_ids == ['R1', 'R2', 'R3', 'R4'] and all(o['status'] == 'OPEN' for o in obligations['obligations']) + occ = json.loads((HERE / 'inputs/absorbed-occurrences.json').read_text()) + kappa = arith_result['after_assembly']['kappa'] + record = { + 'status': 'CONDITIONAL accounting construction for the rank-22 bank absorption: ' + 'schedule, retained ledger, whole-bank volume, exact paid moments, finite ' + 'ordinary composition and balanced assembly are certified here; the physical ' + 'realization obligations R1-R4 (obligations.json) are OPEN and the kappa below ' + 'is conditional on them. Not a completed finite witness; not an unconditional ' + 'multiplication theorem.', + 'kappa': kappa, + 'decimal': float(kappa), + 'binding': arith_result['after_assembly']['binding'], + 'new_residual_type': { + 'rank': schedule['absorbed_family']['rank'], + 'occurrences_three_copies': schedule['absorbed_family']['occurrences_three_copies'], + 'dirt_volume_registers': schedule['absorbed_family']['dirt_volume_registers'], + 'banks': schedule['banks']['banks_from_volume'], + 'provenance_counts_per_vertex': schedule['absorbed_family']['provenance_counts_per_vertex'], + }, + 'schedule': schedule, + 'arithmetic': arith_result, + 'obligations': open_ids, + 'comparison': { + 'main_reviewed_kappa': '330942774629799/500000000000000000', + 'pr205_packed_kappa': '683061299399923/1000000000000000000', + 'pr208_priced_rung1_target': '7004273/10^10', + 'complex_cap': str(arith_result['complex_coarse']), + }, + 'source_pins': {name: digest(HERE / name) for name in PINNED}, + } + return serial(record) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true', help='authoring: regenerate certificate.json') + args = parser.parse_args() + assert not sys.flags.optimize, 'assertions must stay enabled' + before = None if args.write else pins() + record = build() + target = HERE / 'certificate.json' + if args.write: + manifest = {'files': {name: digest(HERE / name) for name in PINNED}} + (HERE / 'SOURCE.json').write_text(json.dumps(manifest, indent=1, sort_keys=True) + '\n') + target.write_text(json.dumps(record, indent=1, sort_keys=True) + '\n') + else: + assert record == json.loads(target.read_text()), 'certificate.json differs' + assert pins() == before, 'inputs changed during verification' + print('PASS rank-22 absorption schedule, retained ledger, whole-bank volume, exact moments, ' + 'ordinary composition, 47-constraint assembly; obligations R1-R4 open') + print('conditional kappa = ' + str(record['kappa'])) + + +if __name__ == '__main__': + main()