[zxv]

The exact PR #5627 word admits a paid A2 rank exchange that raises conditional κ from 0.00310440546 to 0.00310458: +1.7454e-7, +0.0056223%. A two-to-three scalar rewrite changes source 715's legal frame itinerary from paid ranks 5 and 3 to ranks 2 and 6. The extra ordinary ADD is charged; all 743 arbitrary inputs, 12,958 complete productive targets, endpoint frames and owned COPY/INIT/CLEAR instructions are retained.

The local paid change is H2 + H6 − H3 − H5, repeated across 18 local invocations. Strict concavity makes this a strict moment gain for every exponent in (0,1). Two exact rational moment engines enclose the unique raw crossing in (0.00310458658556, 0.00310458658557), leaving about 6.58556e-9 above the claim. Complete paid calls and rank-mass surplus remain 66,546 and 760.

Significance for researchers

This answers whether an A2 scalar rewrite can improve the recursive bill when its frame itinerary changes. The earlier #3998, #4019, #4112 and #4152 results concern frozen paid profiles. Here the complete paid profile changes while productive credits stay fixed. The useful search target is a scalar identity together with a legal, fully charged frame path. The elementary A2 identity retains its predecessor attribution.

Construction and scope · Scoped algebra and frame audit · Complete receipt

Validation and scope

python3.12 -B scripts/research_package.py --package research/p104-a2-paid-rank-exchange
python3.12 -B scripts/check_research_commit.py --package research/p104-a2-paid-rank-exchange

The registered quick, isolated optimized full and separate scoped algebra audit pass. Coverage includes 752 dense transpose columns, all 2,916 signed native maps with exact global phases, the complete physical caller, two rational moment engines, compiler completion and ordinary allowances, BIT stock, all 54 strict and four functional outer predicates, and rejection controls. Publication evidence and the refreshed overlap check are recorded in PUBLICATION.md.

The 41-file committed-byte check passes. The optional full source-history preflight declines this shallow checkout; the declared provenance base passes a direct ancestor check.

The exact predecessor remains head ed4dc88a09a7d201971f6603b8c2074e95dd9c32; its scientific inputs and authenticated framework export are retained unchanged. The same five framework assumptions and helper-endpoint contract remain. The huge uniform word and complete rounded multiplier are not materialized. This is an author-checked conditional contribution; selected-frontier promotion, formal verification, independent human acceptance and hosted CI success are separate obligations.

Credit

Credit Ali Romman for #5627, flyingviper for the relays, Scratch-net for the prepared prefix, Pierre-Loic Doulcet for the commuting cascade, and Joel Pulikkan, DreamingOfClouds, THU New Media Research Center, David Arias, Gareth Davidson, Cinna Davis, Jacob Alan Sussman, Cao Yifan and zxv for the retained helper, native, geometry, BIT, compiler and analytic lineage. The prior A2 mechanism and boundary discipline retain Chris R and ToikY's credit. New construction and checks used substantial OpenAI Codex assistance and complementary subagent research during the original investigation. Apache-2.0; source notices are retained.

Open next questions

• Independently inspect the three literal gates, nested frame chain and new paid native maps, then reproduce the full verifier before scientific admission. The separate agent audit covers local algebra and frame induction; it does not replace independent human review.
• Test a different compatible noncommuting scalar motif on the emitted word. Any combined gain requires one reconstructed word and complete invoice; local headline gains cannot be assumed additive. No further positive candidate is claimed.