Conditional kappa 0.001016469657190768: shared-donor chains with target re-synthesis

[rohanarun]

Transfer PR402 target re-synthesis onto PR404 shared-donor chains: conditional κ = 0.001016469657190768 (63529353574423/62500000000000000), +0.00465719% over #404 (0.001016422320428301).

The two target paths 177 and 220 change (3,5) to (6,2). Each delivery is relocated using its unique complete predecessor gate after #404's changed entrance and prefix chronology. The full raw operator remains identical on all 1021 columns, including all helper dirt. #404's 194 gauges, shared-donor chains, overlapping 124/125/172 target recovery and credited #376 target201 frame improvement are preserved.

We retain #404's original old-response/full-cleanup bracket and its eight-replica packing (738 banks per stage, 394 rank-one paddings). #403's packing gain is not added: #404 already attains the fixed residual-pattern packing bound. All newly needed Gaussian phases, both formal dirty orientations, exact chronological target-matrix identity, inverse routes, padding and scalar costs are freshly checked.

Complex lower: 203500783810111213217/200000000000000000000000. Bit lower: 255384852701747/250000000000000000. Live stock 14322, physical stock 15113, mass 1043010, deficit 2496. Recomputed local bound 7779885932526, per-vertex bound 622357056395634, row 15445 < 20161.

Verification at draft submission

• Full fresh research: shared-donor chains and overlapping target recovery, conditional kappa = 1.016422320428301e-3 #404 complex verifier: PASS, including every reconstruction, 194-gauge local replay, phases, original banks and outer assembly.
• Changed packaged pipeline: PASS. Independent raw-operator interpreter and mutation controls; both dirty formal orientations and chronological 120-column target identity; new/reflected exact Gaussian edges; all 37 residual normalizations; full emitted bank program; independent decoder and eight adverse controls; regenerated invoice and finite bridge; two exact moments, fallback, six bootstrap levels and all 47 strict inequalities.
• Fresh bit replay at the changed complex bound: PASS.
• Full clean wrapper locally: PASS_FULL_SHARED_DONOR_RESYNTH_AND_FRESH_BIT_COMPOSITION at the unchanged published head. Fresh baseline 58.77s, full changed pipeline 55.91s, fresh bit replay 15.21s; manifests match before and after.
• Full clean wrapper CI, Python 3.11 and 3.14: queued, run 38128381678. Submitted as a draft before CI as requested; outputs are retained on failure.

Run python -B research/e8-shared-donor-resynth/verify.py /tmp/shared-donor-resynth. It freshly executes the entire immutable #404 supplier, then all changed checks and mandatory fresh bit replay. No supplier code is modified. All 154 original #404 files are included byte-for-byte under research/e8-shared-donor-chains, with raw Git-blob pins and byte-preserving attributes. #402 reconstruction bytes/designs are pinned in the inherited e8-response-resynth-bank64/vendor402 package.

Scope and credits

Finite conditional construction only. Inherited all-size window, arbitrary correlated-bank, recursive compiler, ordinary-call/fixed-tape, restored-row, common-grid, precision and analytic contracts remain assumptions. No unconditional multiplication exponent, global optimality or formal Lean proof is claimed.

Credit Dugongue for #404's shared-donor construction, chronological recovery and complete local/bank framework; chafreaky / Chafik Boukhalfa for #402's exact target re-synthesis; applecrusher #376 for the public frame improvement retained by #404; all source notices and earlier lineage are preserved. The structural transfer, independent replay and freshly checked composition are by Rohan Arun with substantial OpenAI Codex assistance, Apache-2.0.

Pins: #404 12f488264cdd74a3b60d0fb534f4955792384f5c; #402 7883c63ec724999b921c2304b66648cbb9e7a112. Parent #405 preserves prior work; its distinct bank64 result is not added here.

Legacy-checker compatibility audit

After #407 reported legacy-checker rejections, we reproduced them independently. This word does not pass the unchanged gx.check1/gxcore pipeline: E4 rejects the inherited overlapping target dependency, and the fixed-sixths dirty replay rejects an intermediate quarter coefficient. The exact x-content and gauged-response checks pass separately. An independent rational replay over all1021 raw input columns finds denominator powers at most 2² and 3¹ (a common denominator12), with maximum absolute coefficient4; this observation covers the raw main word, not an all-size compiler theorem.

Our finite admission deliberately uses the exact chronological120-column target identity in place of the disjoint-role E4 sufficient condition, and charges literal HALVE/DIVIDE3 operations in the dyadic/divisor3 framework (odd_grid = 2^(-P)3^(-G(D+1))). Both full formal dirty orientations are checked directly. These facts do not turn the result into a legacy gx/Lean certificate: the already stated all-size compiler, common-grid and precision interfaces remain conditional. Comparisons with #407's checker-clean construction must retain this distinction.