[zxv]

At PR #5270 head 225a19a184296d12120203a1f43b981d55465241, applying the submitted address-loop protocol to the actual 241-gate p19 trace changes 72 entries of the complete controller. An exact physical Gaussian eigencharacter should send zero from input role 36 to output role 0; the submitted protocol sends i−1. The default p2 pattern-I control omits the terminal IDLEs that expose the error. Consuming literal stage indices repairs the tested ideal words, while the separately inherited coupled native operator still differs from the required uncoded operator.

The independently reproduced prior price bound by Ali Romman gives a sharp limit: 2,016 additional H1 jobs eliminate every positive raw saving for 0<C<1, even retaining every target. With 2,015 jobs, continuity leaves a favorable moment near C=0. At C=.0034, only 1,103 extra H1 jobs fit. This rigorously excludes the discussed 2,128-H1 and 4,256-H1 additive repairs under that invoice; it is not a lower bound on every physical decoder or changed caller.

The favorable arithmetic is preserved: the raw complex moment crossing is near .00757853519, the proposed compiler instance targets covered complex saving .003400000714…, ordinary BIT remains .0034363538396, admitted BIT remains .0034, and the proposed outer κ is .003399996428…. These are distinct quantities. No new BIT saving, supplier admission or selected κ is claimed. Canonical main 721c03822c421b7f7fcbb2598993b947c4d88419 still selects κ=.003125804.

Evidence

• The verifier authenticates small retained exports of the exact unmerged head and the canonical input bytes. It executes the literal address-loop AST on invariant Gaussian eigencharacters, independently checks exact Gaussian-integer and residue-field results, and preserves all emitted shears, bridges, letters and signed swaps. The original bank main remains hardcoded to p2; the p19 check instantiates its loop semantics with the actual p19 gates and fresh-block map.
• The p2 pattern-I control passes all 32 physical eigenvalue triples; pattern T fails 24. The literal-stage repair passes all 32 triples and the complete p2/p3/p19 witnesses. No frozen predecessor is edited.
• Independent invoice enumeration and an exact truncated-mass certificate prove the all-exponent fee threshold. Rational interval signs and a separate 90-digit Decimal sum corroborate the price. Substituting the source's pre-PR4929 profile gives a raw crossing near .003004145207, below selected κ; this is only a model control.
• Registered CPython 3.12 normal and optimized checks and package metadata/pins pass. A Git-free read-only export reproduces the receipt, and a corrupted source export is rejected. Original p19_claim.py normal and optimized arithmetic runs pass separately. The original one-dense-seed p2 pattern-I bank control passes freshly on CPython 3.12 in 131.23 seconds under a 360-second/1-GiB guard (203120 KiB peak sampled descendant RSS). An earlier CPython 3.11 run timed out at 180 seconds and is retained separately. The optional full source-history preflight is unavailable in this shallow checkout; metadata/pins and exact committed bytes pass. Full p19 Laurent factorization, native historical replay, machine/precision/stock/analytic closure and formal-kernel acceptance are unclaimed.

Reproduce with python3.12 -B scripts/research_package.py --package research/p19-current-head-binding-audit. Proof, exact witnesses, source identities, measured resource limits and remaining obligations are in the package README, RESULT.json and VALIDATION.json.

Significance for researchers

This separates a sound favorable invoice calculation from its failed physical binding and supplies a sharp complete-budget stopping test. The next useful construction must realize the actual uncoded operator or change the caller and target contract with every correction charged. A higher raw moment or a compiler parameter change cannot supply that bridge.

Predecessor credit and assistance

Chris R's exact-head handoff already found the local IDLE protocol mismatch and native zero-diagonal witness. This contribution adds complete-word execution and the p19 pulse counterexample. Ali Romman already supplied the all-exponent 2,016-fee bound and exact .0034 budget in the linked boundary-cost finding; the different truncated-mass certificate here is an independent reproduction, with an elementary continuity sharpness control. Matarener's terminal-gauge review retains credit for the earlier charges and numerical budget observations. James Reed, ahrazzle's PR #5349 and PR #5385, and zxv retain their separate compiler/reference/geometry reviews.

Source construction credit remains with DaysSky, Seth Burkart as credited in PR #4940, Dillon Amburgey's PR #4933, David Ganz's PR #4929, and the retained native/helper/Clifford/compiler/BIT/analytic lineage. Later priced alternatives in PR #5027, PR #5069 and PR #5563 are credited without rerunning them. PR #5440 is a distinct coded chain with its own recorded physical hold; this new tuple counterexample is not transferred to it.

Prepared for zxv with substantial OpenAI Codex assistance in mathematical derivation, implementation, verification and writing. One worker, no subagents. Apache-2.0; no independent human or proof-kernel acceptance is implied.

Open next questions

• Exhibit one actual native reverse/thin implementation for the intended all-ones trace on arbitrary independent owner inputs, preserving helper returns and recording every recursive and ordinary charge; then prove the complete caller.
• Identify a changed current-query or terminal contract that meets the complete budget without discarding independent target credit. Begin with its exact causal source version. Changed profiles, reused jobs and new operator families remain outside the fixed-additive-fee theorem.