[Matarener]

Requested by Mark · project thread

Change and mathematical scope

Audit, no new κ. Hypothesis (c) of #5561 ("free helper START and FINAL frames"), which also covers the mid-frame start of #5553, is the general helper-endpoint contract that the unmodified P104 local.py already implements. Chris R's independent #5550 audit checked that contract on the #5545 word.

• native() credits each helper with the rank of chart(initial)⁻¹·chart(final) for any nested pair of frames, and prices two normalizers per helper as ordinary routes. Independently verify the P104 forward caller and target bindings (no new κ) #5550 makes the mechanism explicit: each endpoint lowers to U = M_left·G_r·M_right. M_right⁻¹ is applied to the fresh helper input before LOCAL and M_left⁻¹ after it, so a helper from E to B delivers G_r, with r = dim B − dim E, on an arbitrary fresh input. Starting higher lowers the credited rank by exactly the removed climb. PROOF.md gives the chart-invariant argument.
• The Conditional κ = 0.00304117 (+6.0e-7 over #5544) #5545 word audited by Independently verify the P104 forward caller and target bindings (no new κ) #5550 already has 192 nonzero helper starts and 65 below-FULL finals (40 endpoint pairs). The P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561 headline word has fewer of both: 58 and 44.
• The canonical-start rule cited in P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561 belongs to the Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610/Complete coupled-output caller: conditional κ = 0.003027288235 (+5e-12 over #5400) #5413 neutral caller, whose helper adapters J are pure coordinate permutations. It is not a P104 predicate. The T74 lineage has the same wrapper mechanism (Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458 Lemma A entering helpers; Conditional κ = 0.001609915765452068: hyperplane-ended helpers on the PR588 witness #591 hyperplane-ended helpers).

Remaining obligations, not touched here: #5561's retime legality, pricing and strictification (its own verifier); its claim lines versus the certified endpoints .00308142 / .003076879 (as in the intake record); admission of the #5551 parent; inherited local native semantics; the five framework assumptions.

Task and overlap

Base 5e0052ca0aa3036a3afa8b0438927377c8d97d53. Source #5561 head 452d27dde67ee9f772dbbd3be129db97a8ecb9c1; its two words are byte copies in inputs/. Card scalar-to-moment, scope refined: an audit of the changed frame itinerary already proposed in #5561. The intake record lists free-frame admissibility as "a separate unverified hypothesis". Before starting, I checked open PRs through #5564 and main for an existing check and found none. Nearest work: #5550 (checker reused), #5548, #5557, #5561, #5553.

Validation

python3 -B scripts/research_package.py --package research/p104-free-endpoint-contract-audit

Result: PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed, Python 3.12, about 2 min 47 s, standard library only.

• Positive control. The patched Independently verify the P104 forward caller and target bindings (no new κ) #5550 checker, with four literal input lines swapped in a temporary copy (the canonical capsule is untouched), runs on the Conditional κ = 0.00304117 (+6.0e-7 over #5544) #5545 word and invoice. It reproduces Independently verify the P104 forward caller and target bindings (no new κ) #5550's complete frozen output b51a7d19c10faea7d569a48e9536db8ba1e7418f8dd8dfb25646cc87cc9c4009 byte for byte.
• P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561 headline word: PASS.
  • 527 helper endpoints, 272 exact signed-Pauli and phase-anchor checks.
  • Invoice recounted as 66,852 paid / 12,814 productive.
  • Ordinary passes 124,232,680 ≤ 184,647,552.
• P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561 starts-only word: PASS. 278 exact checks, 67,374 / 12,814, ordinary passes 124,754,680.
• Negative controls.
  • A changed helper endpoint is rejected.
  • A changed invoice is rejected.
  • All ten Independently verify the P104 forward caller and target bindings (no new κ) #5550 controls reject on each word.
• Also run, outside the package. P104 free helper endpoints: conditional κ .0030814243 (retime of #5551's word) #5561's own verify.py was re-run unchanged and passed on both parts (raw crossings as stated there).

Credit

Chris R / Clear1nsight (#5550 checker, used unchanged except four input lines). DreamingOfClouds (#5561, #5553). thu-nmrc (#5551). Ali Romman (#5544/#5545, P104 caller). chafreaky (#458). The P104 lineage (#2305/#2152/#2219) and all retained contributors are credited in the cited packages. Prepared with Claude (Anthropic) via Claude Code.

Open next questions

The #5551 admission. Correction of #5561's claim lines to its certified endpoints. A deterministic generator for the #5561 retime. Details are in the README and TASK.json.

🤖 Generated with Claude Code

https://claude.ai/code/session_01NGucs6E49BNE3ev5xk8Afu