κ = 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%)

[rohanarun]

Conditional κ = 1128832830332521/10¹⁸ = 0.001128832830332521: +0.712 % over #433 (0.001120864952258278). The bit supplier binds; #433's split-centre complex supplier (b = 0.001183986549206329) is unchanged.

Stacked on #433 (icekylinx). One new package, research/split-centres-kernel/.

Change (bit side only). chafreaky's #417 shared-donor response kernel, re-derived with #417's own discovery tools (ILS, χ scored at m = 64, 40 chains) on #433's R758 source-centre word:

• 128 entries, with pivots entering at existing root-closed frames of rank 1 and 4;
• total entrance rank 200;
• 124 donor slots;
• no new frames.

code/bit_kernel.py applies the frozen selection. It then re-runs #417's exact replay: legality, F₂ on all 998 columns with dirt, and the source-span rule. Two assertions are widened for #433's source-row destinations and retained totals. The script also binds the output hash.

Compressed geometry with entrances. A helper entering at rank e has residual width 8 − e. The 8 × 758 helper slots per stage tile exactly into width-64 banks, 733 per stage instead of 758:

• eight width-7 slots plus one width-8 slot;
• sixteen width-4 slots;
• eight width-8 slots.

Live stock is 14,277 (was 14,502), and the rank deficit stays 2,496. bit_global.py and the independent bit_audit.py check every owner route (bank, offset, width = 8 − entrance rank) and exact, padding-free coverage of every bank.

	bit lower	κ
#433	0.001122122700265139	0.001120864952258278
this PR	0.00113010853394748	0.001128832830332521

Verification (passed): python3 -B research/split-centres-kernel/verify.py /tmp/out (~30 s, standard library only) → PASS conditional kappa 0.001128832830332521. It covers all of #433's checks: both changed words, reflected programs, bank ownership, two rational moment engines and the 47 strict outer inequalities. The new kernel stage, mixed-width bank tiling and audit are included. The bit audit's mutation controls (including a re-used bank slot and understated live stock) are rejected.

Credits: icekylinx (#433), chafreaky (#417 kernel mechanism and code, vendored), ai-nanachi (#426), Zhihao Chen / jacklightChen (#425, #386), Dylan Crow (#370), J. Sussman (E8).

🤖 Generated with Claude Code

https://claude.ai/code/session_01TGoMCHAqctZe4wtb4qr7vv

[Mister-Meeseeks]

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

Contribution: Shared-donor kernel on the R758 bit word.

Review and limits: Kernel relations are re-derived for this word, with mixed-width bank ownership and assembly. An inherited split-centres CI job alone does not cover the added kernel package.

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: 2c9c833ac8709402c37fc88a6a23393fb0d397fb. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.