perf(hex-int-factor): complete decomposed Phase-4 evidence

[kim-em]

Closes #9634.

This implements the issue's rewritten, preregistered Phase-4 contract:

• measures public factor?, raw rho splitting, and post-split completion as three distinct surfaces, explicitly identifying the 32-bit public rung as table-complete and the 40--80-bit rungs as rho-driven;
• keeps only the output-agreeing table gate and treats unequal-API ratios as explanatory;
• normalizes PARI to one Hex factorization and pins GMP-ECM explicitly to -sigma 0:7, B1=1000, stage 2 disabled, with one fixed 256-input protocol;
• uses identical seeds and canonical complete outputs for exponents 12 through 80, retaining the power split at 0.946x;
• keeps scientific budgets in the pinned-host collector, leaving verify timing-free;
• records actual rotated fresh-module checkFactorization replays for k=1..10, ending with a 61-bit factor, including both null controls and all raw paired samples;
• commits clean compiled profile summaries for all five declared families; the smooth-family runner now profiles ECM stage 1, and private Hex symbols are correctly attributed as repository code;
• marks HexIntFactor complete through Phase 4 and declares its proof-probe tree.

Key evidence:

• table public/direct: 1.181x (gate <= 1.25)
• power split/generic: 0.946x (retention gate <= 0.98)
• all seven parametric verdicts: consistent_with_declared_complexity
• all 31 fixed scientific budgets and hashes pass
• all 49 default-fuel cases succeed
• explicit GMP-ECM curve: parameterization 0, sigma 7; one of six rows is overhead-eligible under the unchanged preregistered rule
• kernel artifact: release-quality, all ten cases below 5 s, null/raw measurements reported
• all five profiles pass calibration, retained-sample, off-thread-noise, and sensitivity diagnostics

Fresh independent Claude Opus review completed while CI was running. Substantive findings were addressed: route and RNG-trajectory descriptions, null/raw replay reporting, actual ECM attribution, private-symbol categorization, committed profile summaries, Phase-4 metadata, residual-exponent semantics, power-margin disclosure, and the Concerns narrative. Two suggestions were rejected with concrete verification: GMP-ECM verbose output confirms the original command already selected sigma=0:7 (the collector now states it explicitly), and the exact issue contract requires the combined comparator name PARI factor and GMP-ECM plus the preregistered <=50% overhead eligibility calculation.

Local verification:

• lake build (10,500 jobs)
• lake build HexIntFactor HexIntFactor.Conformance hexintfactor_bench
• .lake/build/bin/hexintfactor_bench verify (40/40)
• .lake/build/bin/hexintfactor_bench control-audit
• .lake/build/bin/hexintfactor_bench default-fuel (49/49)
• clean native artifact validation/render and five clean sampling captures
• python3 scripts/check_phase4.py
• full CI structural/lint suite, including trust surface, DAG, copyright, file-line, conformance matrix, 41 Mathlib-free bench executables, 178 proof probes, and 72 fresh-module tests

[kim-em]

Closing without merge after premise validation. The clean measurements contradict the pre-registered comparator expectation, the GMP-ECM curve is overhead-ineligible on five of six rungs, and the required kernel replay family is absent. Full evidence and corrected-scope requirements are recorded on #9634.

[kim-em]

Closing after fresh Opus review and CI established the revised comparator premise is still unsound; concrete evidence is recorded on #9634. No merge performed.

[kim-em]

Fresh Claude Opus second-opinion disposition:

Addressed:

• documented that the 32-bit public balanced rung is table-complete, not a rho decomposition;
• documented that public and direct-rho executions have different RNG trajectories;
• added both kernel null-control summaries and every raw rotated paired delta;
• changed the smooth-family profile runner from a second rho capture to actual ECM stage 1;
• classified compiler-generated _private.Hex... symbols as Hex own code and added unit coverage;
• committed all five full profile summaries;
• set HexIntFactor to done_through: 4 with its proof-probe declaration;
• kept residualExponent = 1 whenever residualBase = 1, including through scaling;
• disclosed the power retention margin and replaced the empty Concerns section with the informational external gaps.

Verified but not adopted:

• Opus inferred that -sigma 7 selected different parameterizations. ecm -v -sigma 7 1000 1 reports sigma=0:7 for every admitted operand; the collector now uses explicit -sigma 0:7 to eliminate ambiguity.
• Opus suggested splitting the comparator declaration and withdrawing the sole eligible GMP-ECM row. The rewritten issue explicitly fixes the name PARI factor and GMP-ECM and preregisters eligibility as protocol overhead <=50% of raw time. The clean recapture gives 45.63% at 48 bits, so the row remains eligible without changing the rule after measurement. Equal discovered factors do not require equal stage-1 wall time across different cofactors.