Conditional κ = 7.11948953756315e-4: target-prefix compression (209 square groups) composed with the multi-cut kernel condensation

[rohanarun]

Conditional κ = 142389790751263/(2·10^17) = 7.11948953756315e-4: +4.9 × 10⁻⁷ over #270 (7.114579e-4), +5.2 × 10⁻⁷ over #269/#266, +9.2 × 10⁻⁶ (+0.129 %) over #259. Stacked on #269's branch (PR259's package + supplementary families + retiming).

Full replay: PASS. verify.py --output /tmp/multicut-target-prefix-replay on the committed package (45f13d0): baseline regenerated from source, transform with the supplementary families, target-prefix stage, retiming stage, all seven native checkers, every pinned receipt matched — PASS: kappa = 0.000711948953756315, PASS_ALL_SEVEN_NATIVE_CHECKERS_AND_PINNED_RECEIPTS. (#272 appeared while this was running and is higher; see its comparison in the body.)

What is new: eumemic's target-prefix compression, composed with the kernel condensation

#268 (eumemic) introduced exact F₂ target-prefix compression on the #251 + 132-pair word. Nobody had composed it with the multi-cut condensation lineage; this PR does, natively, as a stage code/target_prefix.py between cohort-transform and the native checkers.

On this word every target reads five rank-20 entrance helpers at a 20-dimensional frame right after the forward phase. In each of 209 squares of four targets, each such helper is read by exactly two of the four, so the dependent target's prefix response is the F₂ sum of its three square-mates' responses. The dependent's 1,057 frame-20 reads are omitted; it receives t −= p_j at the zero frame at the cut (record 670,678) and t += p_j at the square's common nondegenerate 21-dimensional frame at the close (right after the frame-20 block), where all four members are moved; the dependent's later reads at that frame and above are unchanged. Its chain ZERO →(20)→(1)→ 21 becomes ZERO →(21)→ 21. Histogram delta: {1: −209, 2: −7, 3: −1, 8: −1, 12: −1, 17: −1, 18: −7, 20: −200, 21: +209} at unchanged rank mass; the price moves from 7.11426e-4 to 7.11946e-4 before the retiming.

The stage recomputes every member's literal prefix response from the actual transcript (no group is trusted), requires the dependency and 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 then folds its delta into the replay receipt so the native price checker still regresses the #249 baseline exactly. Setup/restore gates carry two new category ids.

Also in this package (from #269): 365 net-positive supplementary equal-response pivot families (366 entrance-rank units, 363 kept by the transform's mod-3 normalization) supplied through cohort-transform's own extra-candidate interface, and the 25-gate concave-descent retiming re-searched on the final transcript. Normalized retained profile: stock 173,313, 3,962,600 calls, rank mass 20,762,360, deficit 35,200.

Reproduce

python3 -m pip install -r research/multicut-kernel-condensation/requirements.txt
python3 research/multicut-kernel-condensation/verify.py --output /tmp/multicut-target-prefix-replay

Python 3.11+, SymPy 1.14.0, C++17 GNU-compatible compiler and Boost headers; new output directory outside the package; no network. verify.py pins and checks the transcript hash after each stage (cohort_record_sha256, target_record_sha256, new_record_sha256 in RESULT.json); cohort-transform.cpp uses stable_sort so the transcript is byte-identical across standard libraries.

Scope and credits

Exactly #259's hypotheses and conditional interfaces; #259's caveat applies (the public eight-stage Python command is not replayed on this word; the native checkers are). No unconditional multiplication bound, benchmark or Lean certificate is claimed. The fixed-prime refinement (#265-style) is not included here and composes on top.

eumemic (#268: the target-prefix compression mechanism; #249, #244, #210), Dugongue (#259, #254: the multi-cut condensation, native checkers and packaging), and the retained lineage. The native target-prefix stage, the square search on this word, the supplementary families, the retiming 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: Target-prefix compression and supplementary pivot families.

Review and limits: Fresh full native replay passed for the final target-compressed transcript, stable ordering, paid frames and independent prefix/column checks. Historical conditional witness only.

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: 45f13d0568033c3c27a96abc99f65a50a3a9133f. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.