Independent verification: every child record and endpoint adapter of the selected frontier1094 CLIFFORD-RECIPES exact with global phase (no new kappa)

[thakrarsagar]

Independent verification: no new κ, and the selected record is unchanged.

Every child record and endpoint adapter stored in the selected frontier1094 gauge44 word's CLIFFORD-RECIPES.json equals what Lemma G assumes (T_B T_A⁻¹, or H6 for adapters), on all 512 columns with global phase. The check uses a kernel written from scratch.

• Track: independent verification, seed 76.
• Card: independent-moment, with the scope refined: one selected assembly premise is checked by a genuinely independent exact implementation.
• Base: 0b1cccf8.
• Package: research/frontier1094-recipes-exact-seed76/.

Why this is needed

Lemma G's RecipesExact (research/e8-lemma-g-lean/LemmaG/Stream.lean:110-112) is a hypothesis of every Lemma G/A/HPE theorem. It says every relabel A → B executes T_B ∘ T_A⁻¹. Every climb that the selected complex profile prices as a rank-r child relies on its stored recipe L ∘ (C_[r] ⊗ I) ∘ R meeting it exactly.

A phase or input-character error in a recipe would leave ranks, histograms and the paid profile unchanged, so rank-level checks cannot see it.

Before this PR:

• The producer's own check is complete, but not independent. phases_full.py/lower_child (icekylinx) asserts equality of the signed Z4 tableau and of column 0, which pins each operator exactly, global phase included. But it ran in the producer's own code, at generation time.
• The Lemma G package (e8-lemma-g-lean, DreamingOfClouds) ran independent all-512-column checks of these premises (Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484's I-tr for H2, check_adapters.py for Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433's H6 identities) on four other words, not on the selected word.
• Seed80 (research/complex-frame-distance-seed80) checks the ranks of the same 1,004 frames and 2,896 edges, and makes no phase claim.
• Our Independent verification: the selected frontier1094 complex rank ledger, rebuilt from its emitted program (no new kappa) #1262 rebuilt the rank ledger, not the phases.

So this PR is a second, independent, byte-bound check of the selected word's stored recipes. It is not the closing of a known gap.

Result

PASS_FRONTIER1094_RECIPES_EXACT:

• 2,896 / 2,896 child recipes satisfy L ∘ F_r ∘ R ∘ T_old = T_new, which is equivalent to L F_r R = T_new T_old⁻¹.
• 224 / 224 endpoint adapters satisfy Lemma G's H6:
  • source: M ∘ C_q = T_start;
  • target: M ∘ F_9 ∘ C_q⁻¹ = T_final.

Both hold exactly on all 512 columns of ℂ^(2^9), with global phase included.

The K histogram (C gates per identity) is {1:120, 2:400, 3:480, 4:254, 5:64, 6:432, 7:416, 8:476, 9:246, 16:8}. The run takes about 33 s of CPU on one core, including calibration and controls.

How

• Binding.
  • The chain runs: selected record → frontier1094 certificate (1122cb3a…) → capsule selected-replay.tar.gz (f1da8061…, pinned in batch1099's integration record) → template and owner audit → the gauge44 files.
  • The gauge44 files are bound by the owner audit's raw digests:
    • CANONICAL-WORD 16bc0ebb…, whose payload digest is 4ddb29fb…;
    • CLIFFORD-RECIPES d0768f21…;
    • CLIFFORD-REVIEW cb0e10a8…;
    • LOCAL-PROGRAMS 241fde27….
  • The template's provider entry and SLOT-PINS-k8 bind the same files.
  • The checker parses exactly the bytes it hashed and resolves members by full path. The split-centres decoys share the same basenames and are rejected by digest.
• Inventory.
  • The 2,896 child records are exactly the word's directed edges, which include both centre directions.
  • They are also exactly the climb and centre relabel keys of both emitted orientations (3,486 climbs and 8 centres each).
  • The ranks and nesting are checked, and so are the 224 adapters, with their ports and frames, and all 6,016 monomial records.
• Kernel.
  • clifford.py uses the standard library only and imports no repository code. It was written from the Lean gate definitions (HyperplaneEnd/Clifford.lean, Exact.lean); the producer's code was read only as a specification.
  • Each side is run on the packed identity (row y = Σ_x N[y,x]·2^{βx}) with exact integers, and the two sides are compared after scaling to a common 2^K.
  • The comparison is sound at β = 2K + 2, Lean's check radix. A C gate at most quadruples a component, so scaled digit differences stay below 2^β, and a zero signed-digit expansion then forces every digit to zero.
• Calibration before any record is judged:
  • the Exact.lean literals (pinned): canon(E), canon(U), L.gates and R.gates equal fE/fU/wL/wR for the three pairs, and their rank-7 identities hold;
  • Independent audit: semantic binding of three Lean HPE Clifford pairs (no new kappa) #1415's three operator digests of T_U ∘ T_E⁻¹;
  • Research audit: verify all selected cold-wrapper amplitudes (no new kappa) #702's 14 frame-kernel digests, all of which are frames of this word;
  • hand values;
  • the frame-0 and frame-1 shortcuts;
  • basis dependence: reordered rows give the same T, while another basis of the same span gives a different T.

Controls

Twelve semantic mutations, each rejected on every sample record it applies to:

Group	Mutation
Record	global phase +1
Record	input character (linear_Z4 += 2)
Record	CZ cross term
Record	offset translation
Reading	L and R swapped
Reading	direction reversed
Reading	monomial gate order
Reading	F_r / C_q sign
Reading	C_[r] read as one gate
Adapter	port mask
Adapter	role
Frame	other basis of the same span (the reordered-rows positive control passes)

The gate-order mutation is used on children only. All 224 endpoint monomials satisfy q(Gx) = q(x), so on adapters it is an exact equivalence; the order is pinned by the children and by FX1's Lean Mono.gates literals.

Comparator controls. These check this package's own comparator; they make no claim about the producer's check.

• A projective comparator would accept the global-phase mutant.
• A column-0-only comparator would accept the input-character mutant.
• An unsound radix raises an error, and β = 2K is shown to admit a collision.

Binding controls: the decoy recipes, the decoy word, one phase digit changed in the recipe bytes, a duplicate JSON key, a flipped archive byte and unsafe archive members are all rejected.

test_package.py has 26 tests. They include:

• an AST scan for standard-library-only imports;
• mutated child and adapter records rejected by evaluate();
• receipt coverage;
• I5, I6 and I7 negatives;
• a fixture-pin negative;
• the measured digit bound on the 16-gate identities.

Scope: what this does not show

• The executor bridge. It does not show that the emitted or hosted program applies these records with exactly these semantics, i.e. that Lean's rec(A, B) equals the record's circuit operator (H1 and check_extended_labels).
• The other recipes. It does not check the 36 residual wrapper recipes (RESIDUAL-ADAPTERS.json) or their 480 residual events per orientation (Lemma A), or the 866 identity adapters per orientation (352 entries, 514 exits). It is a record-level check of CLIFFORD-RECIPES.json, not of every relabel in the stream.
• Other hypotheses. It does not cover scalar events, hosting and charts (Research audit: exact phase criterion for selected PR1094 residual charts #1255), WellLabelled/hS, the compiler or precision.
• Lean and κ. There is no Lean proof of this instance and no new κ.

Checks run

• verify.py: PASS_FRONTIER1094_RECIPES_EXACT, and RESULT.json is reproduced byte for byte.
• test_package.py: 26 tests pass.
• research_package.py --check-only passes.
• The registered python3.12 replay research_package.py passes: PASS_REGISTERED_RESEARCH_PACKAGE, 36 s.
• These were run on Python 3.12.15 and 3.14.8 (macOS 26.5, arm64).
• CI: a red verify (…, tests) job is pre-existing on main (stale spectrum-audit pin) and is not caused by this package; the repair is CI repair: refresh the single-intersection spectrum audit pin after #778 (tests job red on main) #1752.

Reproduce

python3 -I -B research/frontier1094-recipes-exact-seed76/verify.py        # about 33 s; PASS_FRONTIER1094_RECIPES_EXACT
python3 -I -B -m unittest discover -s research/frontier1094-recipes-exact-seed76 -p test_package.py
python3.12 scripts/research_package.py --package research/frontier1094-recipes-exact-seed76

Overlap and credit

• Lemma G (e8-lemma-g-lean, DreamingOfClouds, Lemma G of #484: clean proof and Lean 4 formalisation of its core #509 from Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484): it states RecipesExact and H6, and its I-tr and check_adapters.py checked them on four other words. Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433 (icekylinx) is the source of the H6 identities.
• HyperplaneEnd/Clifford.lean and Exact.lean (jeremykothe2, [Lean] Hyperplane-ended helpers: Lemma A with an arbitrary terminal frame (no κ claim) #593): the gate semantics, the literal pairs and the packed check with radix 4^(K+1), which is β = 2K+2.
• The producer: phases_full.py/clifford_exact.py (icekylinx), adapting PR425's exact phase lowering (jacklightChen).
• Seed80 (woklerx): ranks only.
• Independent verification: the selected frontier1094 complex rank ledger, rebuilt from its emitted program (no new kappa) #1262 (ours): the rank ledger.
• Independent audit: semantic binding of three Lean HPE Clifford pairs (no new kappa) #1415 (commdata2338) and Research audit: verify all selected cold-wrapper amplitudes (no new kappa) #702 (BigCactusLabs): their digests calibrate the kernel. Also related: Independent verification: quadratic-phase certificate for a selected cold wrapper #712 (jsnider3).
• Open Independent verification: bind all 511 cold hyperplane operators with phase and spectator #1697 (navinor), the cold hyperplane operators, and open [Lean] Prove the exact canonical identity for selected Clifford child 0→9 #581 (jamesyc), one child in Lean.
• Open Tooling: exact sparse phase recipes reproduce the three frontier1042 phases pins, 12x on a shared host (no new kappa) #1646 (JosieElliston), on the Tooling: sparse exact U8 phase compilation with identical recipes #1029 (aliromman) and Tooling: accelerate exact Clifford helper checks with identical receipts #662 (cbethin) engines, and selected-replay-fastpath: these re-run the producer's complete check while reproducing the bytes. That is semantic, but not independent. Our Tooling: opt-in parallel exact U8 phase recipes, byte-identical; 5.7x alone, 28.8x with merged PR662 evaluator (no new kappa) #1041 is a parallel driver.
• Tooling: exact Clifford state reuse with independent controls (no new kappa) #1092 (ToikY) and Research audit: exact phase criterion for selected PR1094 residual charts #1255 (bitplane).

find_overlap.py found no independent phase-exact check of this word's recipes.

Disclosure

Prepared by Sagar Thakrar (thakrarsagar) with substantial AI assistance from Claude (Anthropic) via Claude Code.

• Parallel read-only scout and judge subagents selected the question; both judges ranked it first.
• Reader subagents and a synthesizer extracted the specification from the Lean files, the capsule and the producer code (read as specification only).
• The kernel and verifier were then written fresh and checked by the calibration fixtures and controls.
• A post-PR adversarial review corrected the description of the producer's check, the headline scope, the identity-adapter count and the credits, and added evaluator-level and inventory negative tests (second commit).

No claim was posted to Discussions. New material is Apache-2.0.

[Mister-Meeseeks]

Batch review at dafbaadeb423b3bc80fbf6fcd6f415400dc0ffbf.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent exact Gaussian-integer packed evaluation checks all2896 stored selected child records and224 endpoint adapters on512 columns including global phase. Source bindings, complete inventory and sound radix bound reviewed;26 controls/tests pass. Executor bridge,36 residual wrappers, identity adapters and full theorem remain separate obligations.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.

[ywz65]

DONE — published #2638 at 161014fe7e603135f149c680dde424005b294c23. UTC 2026-10-15T16:36:49.466248+00:00.

The opt-in packed-checker adapter preserves the full 2,896-child/224-adapter/512-column replay, exact legacy result and receipt bytes, and independently audits all 4,536,832 actual table entries. The source snapshot, executed-kernel companion receipt, eight source/cache/fault controls and Git-free replay passed; separate AI review found no material issue. Four serial fresh processes measured a 2.44x median wall-time ratio on the shared Windows host, with individual observations and limitations retained. Existing PR662 algorithms and PR2329 production integration are credited. No new certificate, supplier, exponent or portable speed guarantee is claimed.

Original advance claim retained below.

---

CLAIM — LOCAL-ONLY — opt-in table integration for this independent packed all-column checker.

Owner: ywz65, with OpenAI Codex assistance. Started 2026-10-15T16:14:55.655474+00:00; expires 2026-10-15T19:14:55.655474+00:00 unless updated. Base: canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Source: this PR at dafbaadeb423b3bc80fbf6fcd6f415400dc0ffbf, retained research/frontier1094-recipes-exact-seed76/clifford.py SHA-256 d5e42ddabd141b7bfbd70fe13908f3c3a06aeccebeab90623596bfb1988b97fb.

Bounded scope: reuse Charles Bethin's existing #662 permutation/phase table builders in the packed checker's gate loop through an authenticated opt-in adapter. Preserve all 2,896 child checks, 224 adapters, all 512 columns, global phase, calibrations, semantic controls and exact receipts; leave frozen source files unchanged. Check all actual table entries independently, cache invalidation, source refusal and useful faults. Run alternating fresh-process baseline/candidate full-checker benchmarks. No new table algorithm, certificate claim, selected result or exponent is proposed. #2329 already integrates these tables into production clifford_exact.zero_state; this scope is its independently authored packed-integer checker counterpart, with no producer import or acceptance-result reuse.

Initial LOCAL-ONLY full-checker probes pass in both modes; a first serial pair was about 72 s baseline and 39 s candidate, not yet a controlled performance result. Overlap: complete cached Discussions snapshot at 2026-10-15 12:29:05 UTC, supplemented by current recent-100 open PRs and #1781/#662/#2329 REST heads/comments. Newer complete Discussion coverage remains unavailable; no claim of exhaustive novelty.