κ = 0.001133508328719775: early resets + kernel re-derived on the R747 bit word (+0.41% over #435)

[rohanarun]

Conditional κ = 1133508328719775/10¹⁸ = 0.001133508328719775. That is +4.08e-7 over #434's current head (0.001133100552284434), +0.414 % over #435 and +1.13 % over #433. The bit supplier binds; #433's split-centre complex supplier (b = 0.001183986549206329) is unchanged.

Stacked on #433. One package, research/split-centres-kernel-r747/. The bit word is built in four steps:

1. Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433's R758 source-centre word;
2. Conditional kappa 0.001249035299298004: hosting-selected rank147 kernel #434's eleven chronological clean resets (R747), using Conditional kappa 0.001249035299298004: hosting-selected rank147 kernel #434's own reconstruction, vendored;
3. E8 bit supplier c ≈ 1.044064·10⁻³ in the nine-stage word (+2.2 % bit cap; no new κ, complex-bound) #417's shared-donor response kernel, re-derived on the R747 word with E8 bit supplier c ≈ 1.044064·10⁻³ in the nine-stage word (+2.2 % bit cap; no new κ, complex-bound) #417's discovery tools (40 ILS chains at m = 64): 118 entries, total entrance rank 160, 119 donor slots, no new frames;
4. Compressed nine-stage E8 windows and whole-block banking for a conditional κ = 9.98243154231047e-4 > 2^-10 bound #386's compressed nine-stage geometry with exact mixed-width bank tiling, as introduced in κ = 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%) #435: 727 banks per stage, live stock 14,223, rank deficit 2,496.

bit word	bit lower
R758 (#433)	0.001122122700265139
R747 resets (#434 v1)	0.001129525236098816
R758 + kernel (#435)	0.001130108533947480
R747 + kernel re-derived on R747 (this PR)	0.001134794627881866

Verification (passed): python3 -B research/split-centres-kernel-r747/verify.py /tmp/out (~30 s, standard library only) → PASS conditional kappa 0.001133508328719775. It runs every check from #433, plus the reset reconstruction with its three controls; the kernel stage with exact replay (legality, F₂ on all 987 columns, source spans); the mixed-width bank tiling in bit_global and in the independent bit_audit, with mutation controls; a fresh finite invoice (226-bit prefix charged at 256); and six bootstrap levels with all 47 strict outer inequalities.

Credits: icekylinx (#433), rohanarun / OpenAI Codex (#434 resets), chafreaky (#417 kernel, 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: Early resets composed with a freshly derived R747 kernel.

Review and limits: The kernel and tiling depend on the reset word; transferring indices or reusing an inherited CI label is insufficient. The complete composition is checked separately.

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: e3b56de7869f6af88d48ac0ab1d7959c4c9e6176. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.