Mathematical note retained; algorithmic NO-GO

Equations in these preserved Markdown records retain their TeX notation where present; this is not a newly typeset proof edition.

Next research gate

D. MATHEMATICAL NOTE SURVIVES; ALGORITHMIC NO-GO.

Stop this algorithmic extension in its tested form. The frozen exact results survive, but M5 does not clear the registered total-runtime or practical residual-work gate. Preserve this negative result; do not retune on the held-out set or market a factor-count improvement as a solver speedup.

Nothing remains required to reproduce or archive this Phase 5B result. The mathematical note remains a working note, not a novelty-cleared paper. Defer further computation unless there is a concrete mechanism to reduce search/recompilation overhead or a separately justified scientific need. No new thread/model run is recommended merely to seek a positive outcome.

If a later request reopens the algorithm branch, require a new preregistration: native local SDD transformations for all objectives, fair search-budget accounting, a stronger decomposition-to-vtree baseline, carrier-compatible residual refinement, structurally distinct held-out families, and licensed public instances at meaningful scale. Freeze ablations, hardware/resource budget and censoring policy before executing. Retain exact SAT and oracle isolation. The present negative pilot cannot settle that different implementation, but it gives no license to assume improvement.

A concrete publication attempt first needs a theorem-level comparison against relational factorization, Boolean bi-decomposition, MSMP and the 2026 semantic-vtree work, plus an external specialist review. Do not add a paper draft until that identifies a substantive contribution.

Conditional handoff for a separately requested campaign

Use a new task for a genuinely new native-search implementation/campaign; the compact verified package is a better starting point than carrying this completed execution history. Recommended model/effort if that substantial research is authorized: gpt-6-astra, high, because correctness, experimental design and theorem/priority boundaries interact. This is a qualitative reliability recommendation, not a measured cost claim or permission to launch work.

Starter prompt:

Continue Structured Factorization from the delivered phase5b_output/PHASE5B_MASTER_REPORT.md, NEXT_RESEARCH_GATE.md, HOSTILE_REVIEW_LEDGER.md, and REPRODUCIBILITY.md; keep sibling continuity_archive unchanged. Phase 5B reproduced all frozen claims and validated real PySDD/Glucose exactness, but the small recompilation-based pilot does not establish industrial improvement. Inspect code/hybrid_core.py and code/benchmark.py and the frozen raw results before designing a different native-vtree campaign. Preserve nonsingleton prime certification, U/W defect semantics, final carrier exactness, ground-truth isolation and negative findings. Create a new output directory, freeze independently structured inputs, fair baselines, budgets and success criteria before any new held-out run. Workspace implementation/read-only diagnostics are authorized only within the new user's requested scope; do not publish, commit, push or incur spending without applicable authorization.