Conditional κ = 7.25113717934416e-4: target-prefix compression (280 groups) composed with #280's gen4 retiming, early restorations and dirty entrances

[rohanarun]

Conditional κ = 725113717934416422443945/10^27 = 7.25113717934416e-4: +9.25 × 10⁻⁷ (+0.128 %) over #280 (7.24189082265949e-4), +2.24 × 10⁻⁶ over #276. Stacked on #280's branch at its head (codex/gen4-compatible-improvement), as a copy of its package with one added stage; #280's own package is untouched.

Full replay: PASS on the committed package: #276 baseline (nine stages), #280's export/retime/cleanup/entrances, the target-prefix stage, columns, charts, price and admission — PASS kappa = 0.000725113717934416422443945, PASS_IMMUTABLE_COMPOSED_GEN4_CONSTRUCTION. #283 (Dugongue), published meanwhile, composes #279's squares and #280's levers with 741 fresh gen4 kernel pivots and sixteen sinks at 7.26111e-4 and is above this PR; this package remains the verified #280 + target-prefix composition.

What is composed

#280 = gen4 (#276) + the 880 common-frame retimings (the same ones as #279) + 440 early helper restorations + 60 transported dirty entrances + fixed prime. #279 = gen4 + the 880 retimings + 220 target-prefix squares. The two were complementary; this PR adds the target-prefix compression onto #280's final word as a native stage (code/target_prefix.py, the stage of #273/#279; the mechanism is eumemic's #268).

On #280's word, 280 disjoint target groups qualify: the 220 squares of four targets (three retained, one dependent) plus 60 pairs created by #280's transported entrances. Each dependent's frame-20 prefix response is the F₂ sum of its retained group-mates'; its 1,190 frame-20 reads are omitted, it receives t −= p_j at the zero frame at the cut and t += p_j at the group's common nondegenerate 21-dimensional frame at the close, where all members are moved (1,440 setup/restore additions). Local paid histogram delta {1: −220, 2: −54, 3: −36, 18: −66, 19: −24, 20: −190, 21: +280} at unchanged rank mass: normalized calls 5,808,240 → 5,789,640, stock 255,841 and deficit 52,800 unchanged.

The stage recomputes every member's literal prefix response from the actual transcript and requires the dependency before emitting anything; it also requires that no member is used as a source or receives a target before its close, rebuilds every MOVE from the actual needs, checks nested chains, fixed endpoints and COPY lifetimes, nondegenerate endpoint bases, and runs both all-column replays with an omitted-setup negative control. It rewrites candidate/COHORT249-RECORDS.bin (keeping the pre-compression word alongside) and every downstream #280 checker re-reads the word. Changes to #280's files are confined to code/price.py (the pinned call count 5,789,640 and κ) and verify.py (the new stage and the composed word's SHA-256 00704c44a562a115454152cff41f1b39ec5491be192b1e792855a8541c3f34ee).

Reproduce

python3 -m pip install -r research/gen4-retiming-entrances-target/requirements.txt
python3 -B research/gen4-retiming-entrances-target/verify.py --output /tmp/gen4-target-replay

Python 3.11+, SymPy 1.14.0, C++17 compiler and Boost headers; new output directory outside the package; no network.

Scope and credits

Exactly #280/#276's hypotheses and conditional interfaces; no unconditional multiplication bound, benchmark or new Lean proof is claimed.

utcorvusvolat (#280: retiming, early restorations, dirty entrances, emitters, checkers, pricer and admission), DreamingOfClouds (#276: the gen4 word and its five-stage bank package), eumemic (#268: the target-prefix mechanism; #244 lineage), and the retained contributors. The target-prefix search on this word, the native stage and this package's rebinding were prepared by Rohan Arun with Anthropic Claude assistance.

🤖 Generated with Claude Code

[Mister-Meeseeks]

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

Contribution: 280 target-prefix groups on PR280's restored word.

Review and limits: Fresh full nine-stage target-package replay passed in 583s, including the parent, 280 target-prefix groups, column checks, exact charts, pricing and admission. Inherited CI alone had covered only the parent folder.

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: 7542b215a7ff49d264e2b4691ca7fa9bc3be82d9. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.