[1337isnot1337]

This adds an independently replayed, source-bound conditional certificate for the retimed p17 native/direct controller:

κ = 0.003001053, with exact tested saving 0.003001054.

This is 11.7099% above #4416's 0.00268647 and 1.3869% above #4440's 0.00296. Updated #4441 independently contains the same complete combined profile at κ = 0.00300105. The additional endpoint increment is only 0.000000003; the substantial result is shared concurrent work, not claimed as a new independent discovery.

Parent and prior work

This branch directly extends the updated #4441 head 5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39, leaving its tree untouched and adding only research/kappa-hybrid-controller/ (38 files). Earlier contributions by #4440 (query thinning) and #4441 (helper retiming and subsequent combination) are retained and credited, as are zxv's native construction, the #4412/#4414/#4416 line, Jacob Alan Sussman's Theorem 1G, and the source BIT/transfer proofs. Source inputs and SHA256/Git blob hashes are pinned.

Construction

• Balanced p17/cut-8 controller: 19 full native invocations, 16 direct forward rank-one shears. The direct shears for stages 2, 4, …, 32 are individually paid and earn no native helper output credit.
• Reuse the retimed native helper supplier from Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441, including its unchanged main/scalar/warp/owned-center logic. Both local literal interpreters replay 632 arbitrary input columns in both orientations. All 320 changed absolute-phase recipes are checked.
• Physical factorization audit: 1,156 Laurent entries, 8,512 native contacts, 3,808 main endpoints, every idle and 112 direct rank-one kernels. Exact complete invoice: 11,560 productive independent fields, 69,273 paid requests, and rank-one mass 260,798 versus 259,998 (surplus 800).
• Chronological composition with 17,160 native factors; paid completion of small productive targets and splitting of all original and completion tails at 18^17160. Productive floor is 19^17160. The exact normalized paid-moment bound is 262144250000429/262144449839104 < 1.
• Separate p6 native BIT certificate admits ordinary BIT saving 0.00312. The complete conditional transfer checks 54 strict outer predicates plus four functional guards. This proof retains ambient 281 and does not import Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441's smaller higher-moment sufficient constants.

The raw p17 profile threshold is bounded near 0.00300105418317. A bounded dynamic search over the specified minimal-cut path family through p = 120 supports p17 as its best candidate; this is not a global optimality claim. The search uses floating-point discovery, but the selected construction has exact Laurent, native, phase and outward rational interval certificates.

Reproduction

Run from repository root under Python 3.12:

python3 -I -O -B research/kappa-hybrid-controller/verify.py
python3 -I -O -B research/kappa-hybrid-controller/frontier/audit.py

The complete default replay passed under CPython 3.12.14 with -I -O -B in 126.674 seconds, exactly matching the saved receipt. The independent outward-integer-interval frontier audit also passed against the full saved receipt of updated #4441. VERIFY.json registers the two checks and 51 live source inputs. SOURCES.json, VALIDATION.md, REPLAY.json, PROOF.md, and certificates/ describe source closure, exact checks, replay results and limitations.

Scope: This is an author-checked conditional construction awaiting external review. It retains inherited all-column native, matching, spectator, compiler, analytic, precision, owned-stock, fixed-tape and exact-recovery premises. Passing finite certificate checks does not prove the full multiplication theorem or modify the selected frontier. The large tensor and uniform programs are described by finite reproducible recipes, not materialized.

Prepared for Cinna Davis (1337isnot1337) with substantial OpenAI assistance; concurrent sources are attributed in the package. Apache-2.0.