[thu-nmrc]

This changes the complete P104 caller and claims conditional κ = 0.00330420, an increase of 0.00000660 (+0.20015%) over #6702's 0.00329760, under the same five framework assumptions. The native word is inherited byte-for-byte from #6702 at edd6a37a9ff87b254fb7466184348d1432d0c8c0. This is a candidate for scientific review; no selected-frontier file changes or independent admission are implied.

The new exact eight-field/nine-query root has five full-stage ranks (2,4,4,3,2). Its adjacent rank-four stages share an actual two-coordinate idle bank and a common active basis, so both idle payloads receive one combined B+C job each. A new ordinary two-sided dual pair at cut353 then permits a genuinely independent continuation input. The final word has 35 arbitrary main inputs, 586 instructions, 18 unchanged native invocations and 17 thin queries.

For H(r)=r^t, the complete signed gain over #6702 is

104*(H1+H16-H17) + 208*((H41-H40)-(H57-H56)) > 0,  0<t<1.

There is one literal fresh-input retirement (H33 -> H1+H32). “Second-retirement-equivalent” describes the complete invoice comparison, not a second free operation. Fusion alone only reconstructs the preceding best tariff; the new cut proof is essential. The complete invoice has 13,774 productive fields, 66,956 paid calls and unchanged rank-mass surplus760. The raw crossing is enclosed in (0.0033042804235,0.0033042804236), which is also the stated fixed-invoice ceiling.

Validation completed locally with Python3.12 and the standard library:

• Full unchanged source reconstruction and exact saved receipts, 800 native columns/640,000 coefficient positions, owned lifetimes and absolute native phases.
• Both complete caller engines over all 1,225 input/output coefficient positions, exact common-idle bases and direct two-sided fresh-input identities.
• All 7,488 new physical main contacts, every target/idle phase, complete formula/event invoices and all semantic failure controls.
• Two rational moment engines, a freshly funded 11/12 completion (old12/13 is rejected), explicit uniform compiler and all54+4 outer predicates.
• Fresh scalar/route/storage constants, including coefficient37 and all110 lambda normalizations; ordinary upper bound252,020,208 < 10^9.
• Full normal and optimized-mode replays passed (105.73s/108.31s). A separately written standard-library logical verifier also passed normal/-O; all checks are author-side, not external review.

The original construction head a467457692bc9e11113d9b2e2e34ea8ffb553b58 passed the registered workflow and a Git-free45-file full replay. Its construction/native code remains byte-identical in this update.

The added application/ evidence separately checks all7,488 caller contacts by absolute Fourier parity phases and inverse ordinary translations, the original6702 physical positive control, the two complete fused idle packets, the individual idle and plain fresh target, literal handoff ownership, chronological native charts/COPY/lifetimes and the exact66956-paid/13774-productive event bill. It imports no author constructor, scalar replay, physical routine or price engine. Its conservative14,400-field injection fits the published16,388-field W+O envelope; it is not an emitted physical tape allocator. application/COVERAGE.md states precisely what is inherited: the2,939 internal native maps, native scalar endpoints, full compiler/outer machinery and five all-size assumptions are not independently reproved by this bounded addition.

Final application-evidence head 17c08db090004c1fb54220a6d8463a5095789fa9 passed the registered upstream workflow: full primary normal/optimized, separate logical normal/optimized, new application normal/optimized and committed-input cleanliness. A separate Git-free export of all71 committed files passed the two new application checks in16.047s, with every input unchanged; that local supplemental export did not rerun the old full source suite. Original scientific command arguments remain unchanged; their primary timeout allowances are535s each so that all six declared checks fit the repository's1200s total budget. No mathematical check was removed. All implementations/reviews are author-side AI-assisted evidence; neither passing CI nor this addition is scientific admission. The native-lineage limitations described for that bounded application checker are addressed by the separate source-bound companion below; the sealed historical checker files are preserved.

The new companion research/p104-native-semantic-review adds the exact remaining native application evidence against the selected PR6030 source. It compares full operators, rather than subtracting inventory counts: 3,145 current typed tasks have selected witnesses, and 39 truly unmatched operators remain. Every one of the 3,184 actual current compiler tasks is independently checked using all18 signed Pauli images and its complete exact nonzero zero column, fixing absolute phase and paid rank. The39 unmatched operators and five complete helper normalizations additionally pass all512 matrix columns. The separate retained scalar interpreter checks the current18,577-event word, all800 rational endpoint rows, arbitrary771 public inputs,47 owned lifetimes and the complete native bill. The proof states the existing factorwise common-chart argument for arbitrary column width, with exterior scalars preserved; it does not tensorize a finite scalar-sum coincidence.

All39 sealed evidence files remain byte-identical to the independently reviewed copy. Direct7c49/17c Git pins and actual17c outer/nested compiler-member custody avoid treating earlier lineage labels as old-tree membership. The companion's two590-second registered commands total1180 seconds; the original71-file caller package and allsix checks remain unchanged. Current head 4a40713f10d47da5894d7673eb6d0ab2ebdf0687 passed an exact44-file committed Git-free export, both registered companion commands in94.19698s (normal48.474322s / optimized45.722658s), with all exported inputs unchanged. This is author-side independent implementation and peer review. The registered upstream workflow passed on that exact4a40713 head: allsix original caller checks, both new companion checks, and both committed-input cleanliness guards. The original bounded replay took237s and the companion178s. Scientific admission and the five framework assumptions remain unchanged.

Reproduce:

python3.12 -B scripts/research_package.py --package research/p104-common-idle-double-retirement
python3.12 -B scripts/research_package.py --package research/p104-native-semantic-review

The package includes PROOF.md, complete constructors/words, source pins, offline retained source, independent verifier, rational receipt and validation logs. Review the actual common-idle bank and cut353 identities first, then the full registered replay. The inherited native_all_columns, owned_erasure, compiler, precision_tape and analytic_recovery assumptions remain explicit; no unconditional multiplication theorem or practical benchmark is claimed.

Credit: #6348/#6398 binary suppliers, projector roots and normalization by Ali Romman building on Cinna Davis's query lineage; #6545/#5599 dual-pair retirement; #6551 preceding tree rebalancing; DreamingOfClouds' #6702 native/helper split and the complete retained native/helper/compiler/BIT/analytic lineage. New root/common-idle/cut/invoice application: thu-nmrc with substantial OpenAI Codex assistance and parallel agents. All original notices and frozen source bytes are preserved.