Compose terminal query retention into the five-stage complex supplier

[SovereignSteak]

Result

This PR composes the pinned PR233 source-assisted flow with the retained PR244 five-stage complex supplier by aligning each terminal center query with one retiring dirty coordinate.

The resulting complex profile has

m = 110, W = 14,692, calls = 358,975
rank mass = 1,613,040, deficit = 3,080, max child = 46

Its moment certifies the conditional complex saving 754736418878859/10^18 = 0.000754736418878859, compared with 747454944651775/10^18 = 0.000747454944651775 for the retained five-stage baseline (about 0.97417% greater complex-supplier saving).

Construction

There are 22 terminal center queries, each the sum of nine independent physical coordinates. Eight additions replace one row of the identity by that query. The row replacement is invertible on arbitrary dirty data. Retain the pivot at rank 20 until the ordinary center cut, copy/read it, then execute its existing rank-2 final climb. Reverse the eight additions in cleanup.

This costs 176 forward additions and 176 inverse-cleanup subtractions. It adds no dirty roles, recursive children, or coefficient denominators. The complete five-stage ledger and the finite bill still include all center copies, source-K operations, ordinary target reads, dirty-response subtraction and inverse cleanup, routers, bridges, and endpoint operations.

Claim boundary

This is a complex-supplier improvement only. The bit supplier still binds, so this PR claims no improvement to assembled multiplication κ. It also does not claim that the repository's current add-only parser or pinned Lean theorem checks the new scalar word. The construction is justified compositionally under the inherited exact frame, compiler, precision, and analytic interfaces. A monolithic global scalar transcript and new Lean admission are not included.

Checks

The patch's portable commands are:

python3 -B research/terminal-query-retention/verify.py
python3 -B research/terminal-query-retention/verify_query_retention.py
python3 -B research/terminal-query-retention/two_port_screen.py

The first verifies the 22 selected sparse input/query identities, all 198 local dirty columns, the literal pivot operations, and the strict rational moment bound. verify.py --flow PATH additionally binds those rows to a full regenerated PR233 flow witness. The exact construction argument, independent critic review, profile, and receipts are included. The composition research log preserves the command chain for regenerating the original flow and rebuilding the allocator, source-K splice, finite bill, and profile; the full regenerated working tree is not vendored in this PR.

The baseline PR233 checks were rerun at 109a857a329d18ed5552d5573f17ddfa886ae57f; the retained five-stage complex baseline is pinned to a568d94f941929232ab393c7d33dc5a30e017892. Main at the time of the experiment was 3b6b66891c0ac888521cf591fe306c6286601d4f.

Provenance

The PR233 source-assisted flow and the PR234/244 five-stage geometry retain their original attributions and notices. The new terminal-query composition and independent checks were prepared for SovereignSteak with substantial OpenAI Codex assistance. This PR makes no exclusive priority or publication-novelty claim.

[chafreaky]

For the record: pricing #233's certified three-stage profile through the five-stage ledger stated here (H5 = 5·H_inv + 2v·(e42 + e21 + e46 + e4), m = 110, W = 14,692) gives a = 7547/10⁷ with exact rational bounds (7548/10⁷ rejected), i.e. the pairing alone accounts for essentially all of the 7.54736·10⁻⁴ priced here, with the terminal-query step contributing within the 10⁻⁷ grid. Same formula recovers 7474/10⁷ on #194's profile (Sussman's Lean figure). Recorded in #225 as Proposition E, crediting this PR for the ledger statement and the first composition.

[chafreaky]

Follow-up to the priced figure above: the helper interface is now admitted in Jacob Sussman's own framework. #256 exports #233's word as one explicit gcert/1 program (12,052 registers, N = 262,944; his reference checker gx.check1 accepts it, and the same emitter reproduces his published histogram of #193 exactly), and jacobalansussman/wht-power-saving-lean#2 carries the Lean kernel checks: wht_main_block_B2Gp233x at 1 − 7547361/10¹⁰ (his mirror: 7547364 holds, 7547365 fails) and the Fourier transform of every length at 1 − 7547360/10¹⁰, tools/Compare.lean passing for both. So the 7.547·10⁻⁴ complex figure this PR composes is no longer prospective on the helper side; what remains for κ is the bit supplier, which binds.