Conditional κ = 0.001600770286423653: joint prefixes in all 72 complex calls

[jon314159]

#571 applies its joint prefix to 63 width-seven calls but retains nine ordinary four-cold providers. This change extends the compatible eight-cold joint-prefix construction to those nine calls, giving conditional κ = 0.001600770286423653: 0.00549033407% above #571, 0.01465183% above #572, and 0.002240338% above the newer #574. The conservative model independently gives κ = 0.001600770283642087.

The 63 existing providers reproduce #571's canonical word and both program hashes exactly. Four helper swaps per remaining call preserve every physical slot, owner window, offset and complete family; exactly 72 of 36,288 helper labels change. Complete accounting improves the global profile by −108e2 + 72e3 with rank mass 520704, live stock 7168 and physical stock 7682 unchanged.

Validation

The self-contained standard-library verifier reconstructs the retained baseline, both complete providers and the literal owner assignment from pinned source inputs. Completed, source-frozen Windows 3.14 and Linux 3.12 replay receipts are retained in research/complex-joint-prefix-validation.

• All 728 scalar columns, both reflected programs, dirty restoration, native frames and normalized wrappers.
• 135 fresh kernel omission cases per provider, eight final rank-five omissions, and 15 independent literal-prefix/coverage mutations per provider.
• All 2928/3004 directed phase edges and 224 endpoint adapters per provider, including global phase.
• Complete physical owner admission, a fresh finite cost invoice, seven packing mutations, 16 controller mutations and 93 assembly mutations.
• Both exact rational moment engines, seven bootstrap steps, all 47 strict outer inequalities in each model, and rejection of the adjacent exponent grid points.
• Recompression, semantic-identity and reference mutation controls. Exact claims and all seven generated provider identities agree across both runtimes.

The previously completed 18-group mandatory repository baseline is retained with a source comparison establishing applicability to the unchanged baseline. It is identified as reused evidence, not a new full-suite execution. The #543 bit profile is repriced with its surcharge retained; its bit circuit is not freshly rebuilt.

Sources and scope

#571 supplies the literal 57-gate prefix, complete width-seven composition and source owner geometry; #568 supplies the eight cold kernels; #569 supplies paid width-seven entrances; #567 supplies portable replay and artifact-identity work. Immutable sources, licenses, original contributor credits and AI disclosures are preserved. The new nine-call extension, independent audits and packaging were prepared with OpenAI Codex assistance under Apache-2.0.

All inherited all-size compiler, common-label/mutable-source, whole-call hosting, normalized interfaces, precision/tape, analytic-transfer and bit H1-H5 obligations remain conditional. This is a stronger finite witness, not an unconditional multiplication theorem or a measured practical speedup. The historical selected certificate is unchanged.

Reproduce from the repository root:

python3 -B research/complex-joint-prefix/verify.py --work /tmp/joint-prefix-replay

[Mister-Meeseeks]

Thank you @jon314159. This contribution at eac6f7e378ab622dac50a2fd4b7ef6eab014de44 is incorporated in the reviewed family through #588, published in 9594b61.

Shared prefix is rebuilt and all final kernels rechecked on that word, including rank-five omission coverage; a prior proof for a different prefix does not suffice. Both plain and promoted variants require complete phase and owner checks.

Preserved implementation and research:

• research/complex-joint-prefix
• research/complex-joint-prefix-validation

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.