κ = 1.017660918442154e-3: grouped 210-gauge entrances with exact prefixes

[eumemic]

κ = 1.017660918442154e-3

Exact conditional κ: 508830459221077 / 500000000000000000. This improves frozen #411 by 31460377381 / 1000000000000000000 > 0. It is a new branch and new PR; previously published heads and claims remain frozen.

Concurrent frontier: #412 reports κ = 0.001017776060460931 and #413 reports κ = 0.001017671197486403, both numerically above this result. Their current descriptions explicitly retain open changed-phase, fused-routing or complete physical-assembly/invoice obligations. This PR publishes a complete finite replay improving #411; it is not advertised as the highest current numerical claim. Those newer sources were read as context, with no implementation imported here.

Four former entrance donors become pivots together in the rank-one space [48]: helpers 766, 917, 627 and 948. Their shared nine-donor solution uses 23 explicit elementary shears. The completed construction has 210 gauges, 368 entrance dimensions and 675 entrance instructions. The ordered dependency graph and exact chronological omission certificate permit pivot/donor overlap; the constructor checks all 1,021 columns of both the full raw operator and the retained snapshot against the literal prepended word.

The grouping was missed by a preliminary local-cost screen. Charging the complete residual-bank normalization showed the saving, and the final verifier rebuilds the entire profile. The original screen and its corrected bank pricing are preserved as discovery evidence; neither is a proof of global optimality.

The exact composition retains #404's chronological target 124/125 recovery, #376's target 201 frame edit, #402's target 177/220 resynthesis, and #411's target 124/144 donor prefixes. Those prefixes are relocated onto the new scalar word. All 7,042 nongauged response entries and 7,143 signed unit response macros are freshly recomputed. Quarter/eighth additions use explicit paid copy, halving, accumulation and clear words; no unchanged sixth-grid/gx E5 acceptance is claimed.

Sixteen replicas and 144 invocations use 1,470 width-73 banks per stage and 734 rank-one pads. Live stock is 28,590, physical stock 29,381, paid children 644,382, rank mass 2,082,078 and deficit 4,992. All 60,480 bank-boundary adapters and 12,496 inverse owner routes are charged. The finite invoice contains 16,551,456 real scalar primitives, local bound 9,491,967,093,544 and row 15,447 < 20,161.

Fresh verification passes arbitrary dirty restoration and private erasure, both reflected scalar/frame ledgers, every entrance omission witness, 842 new/reflected exact Gaussian phase pairs, all residual address columns, bank ownership and adverse controls, the complete finite invoice and reserve bridge, two exact rational moment engines and all 47 strict outer inequalities. The exact complex coarse lower is 203739521436939321933 / 200000000000000000000000; the unchanged bit lower is 255384852701747 / 250000000000000000.

python -B research/e8-grouped210-target-prefixes/verify.py /absolute/path/to/new/output

The complete development replay and clean committed Git archive replay passed before publication. All staged package blobs were compared with the 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. No unchanged legacy gx/gxcore acceptance, Lean certificate or unconditional multiplication theorem is claimed.

Provenance: frozen #411 (f58d95f2c5da03445e704ea9c72cc55df9e68190), #410 and #408; Dugongue #404 (12f488264cdd74a3b60d0fb534f4955792384f5c); Chafik Boukhalfa/Anthropic Claude #402 (7883c63ec724999b921c2304b66648cbb9e7a112); applecrusher #376; and the retained E8, bit, compiler and analytic lineage. Rohan Arun's concurrent #409 (212e03d7665d08fc6a037d3e33612cb7fc60874d) inspired this grouped ordered-promotion search. Earlier enlarged206 work and the bank marginal derivation were independently obtained; no exclusive priority for ordered entrance gauges is claimed. New grouped selection, reconstruction and composition audits were prepared for eumemic with substantial OpenAI Codex assistance. All 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: Grouped entrance promotion with target prefixes.

Review and limits: Native chronological construction with arbitrary dirt, phase pairs and owners. The legacy checker restriction and paid-dyadic contract remain distinct.

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: 7132ca3ebee286fbb01ff5a2f61a6fc32d36ecd4. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.