Scoped negative result: CK target-forest floor holds for all dyadic weights (no new kappa)

[adamgall]

Status

Scoped negative complex-supplier result / research note; no new κ. Extends the historical PR626 CK target-forest floor from signed powers of two to every nonzero dyadic rational under the same independent binary-Horner lowering and leaf-before-parent one-parent forest contract. Only research/ck-all-dyadic-forest-seed23/ is added.

New evidence

• Exact 13,501,152-case CK census: 12,432 ordered target pairs × 1,086 dyadics n/8, 1 <= |n| <= 543; written valuation/magnitude tails close the infinite remainder.
• Every nonunit finite-core edge loses to a root or same-parent signed unit, with minimum excess 63 component primitives. The existing 16,364-component-primitive floor remains attained; no new circuit saving is claimed.
• A necessary correction to the natural proof strategy: 941 nonunit CK cases beat their root, minimum −116 at child114/parent184/λ=−3. Thus PR964's stronger root-only power-weight comparison cannot simply be generalized; the same-parent forest exchange is essential.
• Primary exact gcd/histogram/16-bit-lane checker and separately implemented dense/integer/20-bit-lane oracle agree on the complete census, histogram and cost-stream digest.
• Rechecks the predecessor's unit floor using dense Prim and all 12,544 cycle inequalities; all 716 arbitrary logical input columns in both orientations pass for the existing witness and a mixed nonunit forest with106 overlapping parent edges. Ten mathematical controls plus source-corruption/missing-input packaging controls pass.

Novelty and credit

Initial powers-of-two exploration was abandoned after discovering Gareth Davidson's incorporated #964, which already closes that CK domain. This is the explicitly open non-power dyadic numerator class, not a larger repeat of that search. The universal tails and forest-exchange method are credited to woklerx's #961, which applies to the different X4 matrix. Credit @dd-hemant #816 for the CK forest, attaining witness and original scalar savings, plus ToikY #909, Oscar Fennell #759, Sricharan Vagvala #749, Ross Richardson #917/#932, David Awad #807, and the retained Chafik Boukhalfa/Jeremy Kothe/icekylinx/DreamingOfClouds/eumemic lineage. Related #1080/#1081 change helper-side assumptions; their savings are not composed here.

OS assignment seed 23, complex-supplier track. Exact base 1b59b62, also the final refreshed upstream. Three candidates, one overlap-driven pivot, complete domain/stopping rule, source pins, proof, certificate, controls and validation receipts are included. Selected PR1094 conditional κ remains 0.001672660197076918.

Reproduce

python3 -I -O -B research/ck-all-dyadic-forest-seed23/verify.py && python3 -I -O -B research/ck-all-dyadic-forest-seed23/independent.py
python3 -I -O -B research/ck-all-dyadic-forest-seed23/test_package.py

Observed on Linux x64 / CPython3.14.4:

PASS_CK_ALL_DYADIC_FOREST cases=13501152 floor=16364 margin=63 columns=716x2 controls=10 no_new_kappa
PASS_CK_PACKED_ORACLE cases=13501152 exact_lane_bits=20 full_receipt_match
PASS_CK_DYADIC_PACKAGE source_corruption=2 missing_source=1 optimized=1 outputs_preserved=1

Final primary+oracle command: 609.15 seconds in the shared environment; packaging controls18.87 seconds. These are observed execution records, not controlled performance claims. Interrupted development invocations and exact successful replacements are disclosed in VALIDATION.md.

Limits

This fixes the source matrix, one-parent forest schedule and historical independent binary-Horner tariff. It does not settle multiple parents, arbitrary sequential shears, helper-basis changes, shared coefficient work, stronger scalar lowerings or folded boundaries. No changed supplier, fresh native/emitter/Clifford replay, prefix/precision claim, global hosting/invoice/assembly, selected cold replay, repository-wide suite, hosted CI or full multiplication theorem is claimed. Inherited all-size/compiler, realization, hosting, precision/tape and analytic assumptions remain. upstream/ and selected frontier are unchanged.

Prepared by Adam Gall (@adamgall) with substantial OpenAI Codex assistance in research, implementation, proof, tests and writing. Both implementations are AI-written; no independent human review is claimed. Apache-2.0; existing source notices and licenses remain intact.

[Mister-Meeseeks]

100-PR batch review at 9cd42fb94d2b74e7308ad783b20081aa85b868a1.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: CK all-dyadic one-parent forest floor16364: valuation/magnitude tails plus13501152 finite coefficient cases and signed-unit/root exchange. Directed nonunit costs are reduced before MST; no broader circuit optimum.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.