chore(number-field-tower-mathlib): audit and complete Phases 3–4

[kim-em]

library: HexNumberFieldTowerMathlib
depends-on: #9665
depends-on: #9666

Current state

HexNumberFieldTowerMathlib is currently recorded through Phase 7, but its Phase-3/4 correspondence-only claim must be re-audited after the Tower core evidence and the lower NumberField bridge classification are corrected. Treat the existing counter as a conclusion to verify, not evidence.

The bridge appears to contain only correspondence/proof glue over HexNumberFieldTower and HexNumberFieldMathlib, with no independent conformance or benchmark target.

Deliverables

• Audit the complete bridge source, SPEC, imports, and public API.
• If it owns executable, tactic, proof-producing, or kernel-cost behavior, report the concrete surface and give it ordinary Phase-3/4 evidence.
• Otherwise:
  • map transported operations to their computational conformance owners;
  • add the canonical correspondence-only-layer declaration and explicit registry classification;
  • name the Tower and lower NumberField performance owners;
  • confirm that no dedicated conformance, bench, report, or proof-probe artifact is required.
• Correct or re-attest the existing Phase-3/4 record after perf(number-field-tower): complete core Phase-4 scientific evidence #9665 and chore(number-field-mathlib): audit and complete Phases 3–4 #9666, retaining later phases only if their artifacts remain valid.

Verification

• lake build HexNumberFieldTowerMathlib
• relevant Tower and NumberField conformance targets
• phase/status consistency checks
• python3 scripts/check_dag.py
• python3 scripts/check_phase4.py
• full CI