Exact family reconstruction
Fifteen package gates cover theorem reconstruction, explicit witnesses, database-scoped checks, archive integrity, and public-safe packaging.
Methods and verification
Research that carries its audit trail
The workflow is designed to preserve mathematical scope while making computation, provenance, corrections, and release decisions inspectable. Verification supports a claim; it does not silently enlarge one.
Verification workflow
From target selection to human-final release
A reusable control loop supports both mathematical projects and research operations.
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Choose a bounded target
Define the exact question, admissible evidence, stopping conditions, and what would remain open after success.
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Make the argument explicit
Separate theorem logic from discovery notes, rebuild key derivations, and record dependencies and assumptions.
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Use exact checks where they fit
Prefer integer, rational, symbolic, or exhaustive methods when the claim admits them; label numerical evidence precisely.
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Run independent paths
Pair primary scripts with independent checkers, clean-environment reproduction, manifests, and content hashes.
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Audit hostile cases
Search for boundary failures, schema conflicts, archive defects, counterexamples, and prior work before promotion.
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Correct, supersede, or stop
Preserve failed routes and valid artifacts, issue explicit corrections, stage privately, and require human-final publication approval.
Evidence architecture
What the packages actually verify
The three featured packages expose their own verification summaries rather than relying on a portfolio-level assertion.
Proof plus finite corroboration
Fifteen gates pair proof reconstruction with exact finite checks across 318,667 cases, while keeping unrestricted parametric closure open.
Theorem-only structural audit
Twenty-one of twenty-one gates pass for the canonical package. Excluded finite-SAT and multipole routes do not enter the theorem claim.
Autonomous Scientific Director workflow
METHODS CASE — VERIFIED WORKFLOW SUMMARY
A governed orchestration method coordinates problem selection, proof reconstruction, exact computation, independent replay, correction and supersession, privacy-aware staging, and human-final publication controls across several research programs.
Operational contribution
- Maintains a claim registry that distinguishes open, conditional, finite, internally verified, public-release, external-review, and submission states.
- Freezes contracts and dependencies before costly runs, then records precise obstructions instead of improvising past them.
- Preserves negative results, stopped routes, immutable certificate packets, and correction history.
- Routes public-safe outputs separately from raw logs, internal bundles, credentials, and private staging identifiers.
Current demonstrated status
The workflow produced three canonical packages that are now public GitHub preprint releases with passing package-specific gates, plus the public pointwise Erdős #409 certificate F(400000287233629)=104. That is process and artifact evidence, not external peer review, independent audit, or evidence that the method is causally superior to alternatives.
Public artifact: this public-safe methods summary and the employer-readable brief. Raw orchestration events, internal handoffs, email drafts, bundles, and private storage identifiers are intentionally excluded.
AI use
Assistance disclosed; responsibility retained
AI systems assisted source discovery, proof and code development, checker construction, workflow coordination, and manuscript production. AI-generated output is not itself mathematical evidence.
Human-final controls
- AI systems are not listed as authors or external reviewers.
- Zackary Loevseth is the proposed human author and accountable decision-maker.
- Final inspection, authorship confirmation, licensing, and public release require human approval.