Conditional kappa 0.001017250500928266: ordered sequential entrance gauges

[rohanarun]

Promote ten existing entrance donors to pivots using an ordered two-layer construction: conditional κ = 0.001017250500928266 (508625250464133/500000000000000000), +0.07681919% over #406.

The new mechanism goes beyond #404's pivot/donor disjointness. Prepend 51 literal entrance shears to #406; every source is read before it is written by a later entrance gate. The resulting prefix is S = I + N with N² nonzero (148 entries), N³ = 0, and explicit inverse I - N + N², realized by the actual reversed elementary word. Reversing the entrance layers fails an exact gauged-dirt control.

Gauge count increases 194 → 204. All 1021 raw columns, retained totals, actual nested paths and all 204 zero response columns are checked exactly. Local paid delta is {3:+9,4:-8,5:-1}, reducing local rank mass by ten. The original #404 shared-donor construction, overlapping target recovery, credited #376 frame edit and #402/#406 target re-synthesis remain included.

Repack the changed residual inventory over 32 replicas: 2947 banks per stage, 1531 rank-one paddings; live 57243, physical58034. All 288 invocations and 117504 boundary adapters are charged. Fresh invoice: local bound 7845447935020, per-vertex bound 2509741657493211, row 15449 < 20161.

Complex lower: 101828635323117962043/100000000000000000000000. Bit lower: 255384852701747/250000000000000000.

Evidence at draft submission

PASS locally: exact ordered reconstruction and reversed-layer/omitted-gate controls; both independent formal entrance-chart orientations; exact chronological target matrix; full scalar expansion and private erasure; every entrance-gate omission; 814 new/reflected Gaussian phase pairs; all37 two-sided residuals; expanded global schedule; independent actual inverse-owner/padding decoder with eight mutations; three replica-expansion mutations; full regenerated finite invoice and bridge; two exact moment engines, fallback, six bootstrap levels and all47 strict outer inequalities.

Fresh bit replay now PASS locally: the unchanged bundled bit implementation was rerun at this exact new complex lower, including all 1782 formal columns, 822 independent dirty registers, 18 column controls, six permanent mutated-record rejections, geometry, banks, pricing and the finite reserve check. The receipt reports PASS_NEW_PR376_R822_PR381_B4_COMPOSITION, with bit lower 255384852701747/250000000000000000. All five pinned package manifests were independently rechecked afterward.

Full local wrapper attempt: the fresh complete #406 baseline passed (132.66 s), followed by the entire new packaged constructor/local/phases/global/invoice/outer build (108.82 s). The final bit replay stopped while linking legality-r822: errno=28 (No space left on device). This failed run and its logs are retained. The separate fresh bit run above passed at the identical complex bound.

Still pending: one uninterrupted complete wrapper pass and the Python3.11/3.14 CI matrix; GitHub jobs are queued. Separate local component passes do not establish that end-to-end wrapper result. Draft-first submission as requested. CI retains failed outputs.

Run python -B research/e8-sequential-gauges/verify.py /tmp/sequential-gauges. The wrapper first freshly executes the entire #406 wrapper (including full #404), then reconstructs and checks this extension, then freshly replays bit composition. All source and witness manifests are checked before and after.

The only local-admission relaxation replaces the global disjoint-source/target assertion with the exact chronological read-before-write premise. All scalar, symbolic, phase, lifecycle, source-pin and omission checks remain. LOCAL-ADAPTATION.json records the change; PROOF.md proves why the omission formula remains valid. The immutable #403 bank emitter/independent decoder/bridge are rerun with the new replica count and witness.

Discovery screened 53440 weighted bases, exactly admitted four groups, then screened 51200 more on the extended word with no additional positive nomination. Accepted coefficients and full costs are exact; discovery scores and bounded negative screens are not global optimality claims.

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 interfaces remain assumptions. No unconditional multiplication exponent or formal Lean theorem.

New ordered donor-to-pivot promotion, replica packing and exact integration by Rohan Arun with substantial OpenAI Codex assistance. Credit Dugongue for #404 shared-donor chains, #401 normalization and the exact local framework; chafreaky / Chafik Boukhalfa for #402 re-synthesis; applecrusher #376 and all earlier source lineage. Apache-2.0; original notices retained. Parent #406 is pinned at 5d0d8dff39db99f922ead6d11963aa643511e3ee.

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.