Conditional kappa 0.001002683712533373: R781 heterogeneous banks and padding fusion

[rohanarun]

Conditional κ = 0.001002683712533373 (1002683712533373/10^18), approximately 0.00225465% above #399.

This combines Dugongue's #398 R781 signed-prefix word, the two rank-eight residual helpers and heterogeneous bank construction from #390, and chafreaky's #394/#399 free sinks and padding fusion. #399 independently published the R781 padding combination while our matching local candidate was being checked; the additional gain here is its composition with the heterogeneous banks.

At 32 replicas, 64 rank-eight residuals fill eight mixed banks, each with one full rank-nine residual (8*8+9=73). The remaining full residuals occupy 3,115 ordinary banks, for 3,123 banks per stage. Three free sinks per replica absorb padding into their final rank-two climb, forming exact rank-three children. There are 864 fused occurrences and 27,171 remaining standalone paddings across nine stages. The exact local replay checks all 1,021 dirty columns in both orientations and private erasure.

The package explicitly constructs orthogonal bank placement matrices and inverse owner factors, compiles every ordinary Clifford edge, copied-centre direction, mixed child and endpoint with Gaussian phase, emits a global template, and recomputes the scalar/compiler/physical/precision invoice. Its mandatory full verifier first freshly reconstructs and admits #398, then rebuilds this changed construction and runs a new bit composition at the new complex bound. Two independent rational moment engines retain the full positive fallback, and the six-level bootstrap evaluates all 47 strict outer constraints.

Draft-first status: submitted first at b73a8b4f3d8b32676e7527005911a11a60a1c4fd. The complete changed-construction run now passes locally, including all 1,021 dirty columns in both orientations, all 3,139 ordinary Gaussian transitions, mixed/endpoint phases, literal bank routes, the global template, 13 mutation controls, finite invoice, both rational moment engines and the outer witness. The invoice counts 165,596 real-component primitives per local orientation, a per-vertex bound of 2,622,465,169,823,691, 55,296 additional fusion compiler groups, and a row coefficient of 15,449 < 20,161. The first run's bundled geometry path error is corrected and its failure log is retained.

Full isolated replay now PASSES on both Python 3.11 and 3.14 at unchanged head b73a8b4f3d8b32676e7527005911a11a60a1c4fd: CI run 38124830486. Each run freshly completed the full #398 supplier reconstruction/admission, the changed construction and invoice, and a new bit composition. Both final receipts report PASS_FULL_R781_HETEROFUSION_AND_FRESH_BIT_COMPOSITION. Downloaded artifacts 11696831932 (3.11) and 11696936717 (3.14), each containing 166 files, match the local profile, invoice and exact outer witness. The CI preserves complete logs and artifacts, including failure output when present. All 64 repository checks now pass, and the PR is ready for review.

python -m pip install -r research/e8-r781-signed-source/requirements.txt
python -B research/e8-r781-heterofusion/verify.py /absolute/new/output

C++17 and Boost headers are required. The immutable #398 package is renamed e8-r781-signed-source to avoid collision with our #395 package; its source bytes, manifest and licenses are preserved. Existing packages remain independently replayable.

Conditional scope: finite construction, not a Lean proof or unconditional integer-multiplication theorem. The inherited all-size local identity, arbitrary-dirty banking, compressed-window, orthogonal cover, compiler, tape, precision/recovery, restoration and analytic interfaces remain assumptions. Padding timing uses #394/#399's explicit operator-level replacement under the arbitrary-dirty property; unchanged intermediate exterior canonical labels are not asserted. The new invoice conservatively charges full coefficient expansions, endpoint adapters and an additional 64 compiler groups per fused occurrence.

Credits: Dugongue (#398/#390), applecrusher (#376), Chafik Boukhalfa / chafreaky (#378/#394/#399), jacklightChen (#377), Jacob Sussman, the DaysSky/utcorvusvolat-dotcom bit lineage, DreamingOfClouds (#315), and all retained suppliers; Rohan Arun (#387/#392 bootstrap, #395 exact mixed-phase/global-invoice combination, and this R781 heterogeneous composition), with OpenAI Codex assistance. Apache-2.0; original supplier notices remain intact.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: R781 heterogeneous banks with padding fusion.

Review and limits: Dedicated full wrapper checks changed suppliers and a fresh bit composition. Earlier bundled packages are covered separately by source identity and targeted reviews.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: b73a8b4f3d8b32676e7527005911a11a60a1c4fd. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.