Candidate conditional kappa 0.001017923290728024: propagated entrance frames

[rohanarun]

Conditional κ = 0.001017923290728024 (127240411341003/125000000000000000), 0.01230651% above #416. Subsequent #419 reports 0.001017962405296845, which is higher than this PR. #420 reports a value below this PR.

Apply #416's four frame-propagating gauge promotions to our #415 word, with exact relation transport. Three relations transfer directly. The relation for 892 initially fails on target coordinates 133 and 149 because 1010 is already gauged; substituting its explicit #409 relation repairs every rational response equation. Both the rejected transfer and corrected witness are retained.

The combined word has 208 gauges, 560 entrance instructions and five propagated original-A frame changes. Its local paid delta is {1:+8,2:-3,3:+1,4:-2,7:+1,8:-1}, reducing rank mass by four. Outside the 25 new entrance shears, original A scalar groups are preserved.

Validation on the published mathematical code (e4a8214d0c13ad5d7a436a848448f614a6ca9c79):

• All 1,021 full-word and pre-snapshot raw columns, literal shear multiplication, gauged zero-response columns, nested paths, final endpoints, five reverted-frame controls and an omitted-gate control passed.
• Both formal scalar orientations, private erasure, chronological target matrix, 7,057 recomputed dirty-response entries and 7,158 unit macros passed. All 854 new/reflected Gaussian phase pairs and 16 signed coefficient microchecks passed.
• Changed physical assembly, independent owner/padding decoder and eight structural controls, regenerated finite invoice, reserve bridge, two rational moment engines and 47 strict outer inequalities passed.
• Fresh bit composition passed at this exact complex bound. All eight package manifests passed.

Successful receipts and retained failures are committed with raw and compressed hashes. The first physical replay failed while serializing its template with OSError: [Errno 28] No space left on device. After lossless archival of completed local outputs, the unchanged code passed in a fresh output directory. No mathematical assertion was bypassed.

Still pending: uninterrupted replay of the complete parent/new wrapper and Python 3.11/3.14 CI. Separate component passes are not represented as a full wrapper pass. Draft-first publication was followed by the local checks above; the PR remains a draft.

32 replicas; 2,941 banks per stage; 57,189 live and 57,980 physical registers. The invoice charges 32,774,592 real primitives, local bound 9,400,678,229,684, 119,808 bank-boundary adapters and row reserve 15,449 < 20,161. Complex lower: 254740128591982906821/250000000000000000000000; unchanged bit lower: 255384852701747/250000000000000000.

Run python -B research/e8-propagated-entrances/verify.py /absolute/path/to/new/output. This freshly runs all of #415, this construction and fresh bit, checking all eight manifests before and after.

This uses the same broader chronological/dyadic framework as #415/#416. No unchanged legacy gx/gxcore E4/E5 acceptance, Lean theorem or unconditional multiplication exponent is claimed. All-size window, arbitrary dirty-bank, compiler, fixed-tape, restored-row, common-grid, precision and analytic interfaces remain conditional.

Prepared by Rohan Arun with substantial OpenAI Codex assistance. Credit eumemic #416 for frame propagation, gauge witnesses and the immutable constructor/local admission; #411 for prefixes and dyadic lowering; Rohan #415/#413/#409; chafreaky #402; Dugongue #404/#401; #403 banks; applecrusher #376 and Sussman's E8 lineage. Apache-2.0 and original notices are retained. Parent #415: 4ad1ef5c67e9943d21ee8c13325ca5705546ae28; #416: c76d101df11ad4152c52fd9d68344c064e453d3a.