κ = 1.017798035290733e-3: propagated frames admit 214 entrance gauges

[eumemic]

κ = 1.017798035290733e-3

Exact conditional κ: 1017798035290733 / 1000000000000000000. This exceeds concurrent #412's reported value by 10987414901 / 500000000000000000 > 0, #413's by 12683780433 / 100000000000000000 > 0, and frozen #414's fully replayed value by 137116848579 / 1000000000000000000 > 0. The just-opened #415 reports κ = 0.001017786140030308; this result exceeds it by 475810417/40000000000000000 > 0. This is a new branch and new PR; prior published heads and claims remain frozen.

The new step changes five existing scalar-gate frames so that four more helpers can acquire entrance gauges. Starting from #414's 210-gauge construction, helper 892 enters [51], 669 enters [12], 821 enters [240], and 644 enters [63]. Their literal entrance word adds 22 shears. When a donor's old frame cannot contain the new entrance space, the constructor raises the gate frame to the span of the required spaces and propagates the resulting constraints through every subsequent touch. All paths remain nested and end at the prescribed final frames.

For example, admitting helper 892 requires changing the frame of the existing operation helper349 -= X20/2 from frame 22 to frame 276, the space [145,51]. Its scalar operation is unchanged. The verifier requires the exact original A scalar groups while independently checking the altered frame schedule and Gaussian identities. Reverting any of the five required frame changes fails the full ledger. Omitting the new entrance instruction leaks a gauged input, and all 697 chronological omission witnesses pass.

The complete construction has 214 gauges, 372 entrance dimensions and 697 entrance instructions. The local paid delta from the four promotions is {1:+8, 2:−3, 3:+1, 4:−2, 7:+1, 8:−1} relative to 210. The actual scalar word is composed with #404's chronological target 124/125 recovery, #376's target 201 frame edit, #402's target 177/220 resynthesis, and the relocated target 124/144 donor prefixes. All 7,020 nongauged response entries and 7,121 signed unit response macros are freshly recomputed. No separately reported savings are added.

Sixteen replicas and 144 invocations use 1,469 width-73 banks per stage, 725 rank-one pads, live stock 28,581 and physical stock 29,372. The reconstructed profile has 644,877 paid children, rank mass 2,081,421 and deficit 4,992. All 61,632 boundary adapters and 12,496 inverse owner routes are charged. The finite invoice contains 16,565,280 real scalar primitives, local bound 9,503,585,676,168 and row 15,447 < 20,161.

Fresh verification passes all 1,021 scalar columns, arbitrary dirty restoration, private erasure, both reflected scalar/frame ledgers, 856 new/reflected exact Gaussian phase pairs, all residual address columns, the new frame controls and existing response/bank controls, the complete finite invoice and reserve bridge, two exact rational moment engines and all 47 strict outer inequalities. Exact complex coarse lower: 1018835003555638065657 / 1000000000000000000000000; unchanged bit lower: 255384852701747 / 250000000000000000.

python -B research/e8-frameclosure214-target-prefixes/verify.py /absolute/path/to/new/output

The complete development replay and clean committed Git archive replay passed before publication. Every staged package blob was compared with its manifest. Python 3.11+ and C++17 are required; dedicated Linux CI covers Python 3.11 and 3.14. The default replay explicitly reuses pinned evidence for the unchanged bit component and old local phase edges. Optional --replay-bit freshly repeats the bundled bit component; reused checks are not represented as freshly executed.

This is a finite conditional construction. Inherited all-size compressed-window, arbitrary-correlated dirty-bank, recursive compiler, ordinary-call/fixed-tape/restored-row, common-grid, precision and analytic interfaces remain assumptions. The native chronological and dyadic conditions are explicit extensions of older sufficient guards; no acceptance by unchanged legacy gx/gxcore, Lean certificate or unconditional multiplication theorem is claimed.

Provenance: frozen #414 (7132ca3ebee286fbb01ff5a2f61a6fc32d36ecd4), #411, #410 and #408; Dugongue #404 (12f488264cdd74a3b60d0fb534f4955792384f5c); Chafik Boukhalfa/Anthropic Claude #402 (7883c63ec724999b921c2304b66648cbb9e7a112); applecrusher #376; Rohan Arun's #409 (212e03d7665d08fc6a037d3e33612cb7fc60874d) as inspiration for the preceding grouped ordered-promotion search; and the retained E8, bit, compiler and analytic lineage. Concurrent #412, #413 and #415 were inspected as comparison claims; their mechanisms are credited and no implementation from them is imported. Frame propagation, the four new gauges, exact prefix relocation and complete changed-composition audits were prepared for eumemic with substantial OpenAI Codex assistance. Original licenses, notices and AI disclosures are preserved.

[Mister-Meeseeks]

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

Contribution: Frame propagation admitting additional entrance gauges.

Review and limits: Actual enlarged frames and newly charged child profiles are checked under the native contract. No unchanged legacy gx acceptance is claimed.

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: c76d101df11ad4152c52fd9d68344c064e453d3a. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.