Diversify and deepen automatic math research

[guyz]

What changed

• Add an automatic probe-to-deep tournament: probe 12 diverse, vetted problems in six parallel slots, score measured progress, and resume the two strongest saved threads for persistent deep work.
• Keep partial leads inside the solver loop; only complete proofs or counterexamples enter independent verification.
• Run GPT-5.6 Sol solver turns at Ultra with built-in multi-agent delegation while keeping discovery and support roles at their configured effort.
• Rank problems using decisive-artifact readiness and concrete blockers in addition to interest, source quality, tractability, verifier leverage, diversity, and bounded counterexample opportunity.
• Continue with a new tournament round if finalists terminate without a solution and campaign time remains.
• Prefer the ChatGPT app-bundled Codex CLI on macOS to avoid model-cache incompatibility with separately installed CLI versions.
• Simplify the dashboard around two explicit phases: broad probing and deep solving. No new operator knobs were added.

Reliability

• Fresh campaigns, safe stops, resumes, deadline extensions, crashes, continuous subscription call-budget renewal, probe promotion, and exact run-directory reuse are covered by regression tests.
• Every strict structured-output schema is recursively checked so newly added fields cannot silently break live model calls.
• Failed Codex calls now preserve the useful JSONL diagnostic instead of reporting a blank error.

Validation

• npm run check
• npm test — 118 tests passed
• npm run dashboard:build
• Live subscription discovery call launched successfully with the ChatGPT-bundled Codex CLI
• Staged payload scanned for credentials, tokens, private keys, personal filesystem paths, and local campaign data
• runs/ remains ignored; local campaign databases and archives are not included