perf(number-field): complete core Phase-4 evidence

[kim-em]

Closes #9664.

Summary

• re-audit the post-audit-found: HexNumberField's advertised API surface is not fully registered for Phase 4 #9722 compiled API surface and confirm all 89 registrations still cover every advertised operation
• rerun the normalized QAdjoin.inv scientific ladder, all six PARI inversion pairs, the process-driver overhead probe, and the affected timed-region profile
• replace the stale pre-normalization comparator trend with current hash-joined evidence and add complete reproduction traceability
• confirm every direct dependency is through Phase 4, empty the report's Concerns section, and advance HexNumberField to done_through: 4

Performance rationale

runQAdjoinInvLadder uses mode 1 with the independently traced finite-word family proxy n²(n+7), which models the measured bounded-height fixture's cubic limb work plus its quadratic limb-rounding transition. This is deliberately narrower than the SPEC's unchanged conservative O(n³ log n) worst-case bit-cost contract; the completion rerun is consistent (β = -0.106, cMin = 101.713, cMax = 137.605, worst five-trial spread 1.85%), and the current profile attributes the dominant normalized extended-gcd work to the registered target.

Verification

• lake build HexNumberField hexnumberfield_bench
• lake exe hexnumberfield_bench list (13 parametric + 76 fixed = 89)
• lake exe hexnumberfield_bench verify with python-flint/PARI available (all 89 pass)
• final five-trial runQAdjoinInvLadder scientific run
• five-trial runPariPolmodOverhead plus all six current Lean/PARI inversion pairs (all hashes agree)
• current runQAdjoinInvLadder n=64 profile: calibration, confidence, and ±5 ms sensitivity pass
• lake build HexNumberField.Conformance hexnumberfield_emit_fixtures
• fresh NumberField fixture matches committed fixture
• NumberField FLINT/PARI oracle: 11 cases, 0 failures
• python3 scripts/check_phase4.py
• python3 scripts/check_dag.py