Status

Current repository work may be complete at the artifact, test, script, dashboard, and reproducibility-infrastructure level within the declared experimental scope. No theorem-level completion claim is implied.

Clay Problem Lab

Start Here

• QUICKSTART.md
• docs/public/START_HERE.md

Proof Status

• docs/public/PROOF_STATUS.md

Independent Verification

• docs/public/INDEPENDENT_VERIFICATION.md

Why It Matters

• docs/public/WHY_IT_MATTERS.md

Citation

• CITATION.cff

Clay Problem Lab is a unified experimental framework for computational exploration of the Clay Millennium Problems.

Modules included:

• riemann — experiments related to the Riemann Hypothesis
• navier_stokes — numerical experiments for Navier–Stokes dynamics
• yang_mills — spectral gap and lattice experiments for Yang–Mills
• complexity — experiments related to P vs NP and locality barriers
• bsd — exploratory computations for Birch–Swinnerton–Dyer
• hodge — symbolic and numerical tools for Hodge theory

Framework components:

• experiments: executable research experiments
• data: datasets used by experiments
• scripts: automation tools
• tests: experiment verification pipeline
• dashboard: repository status utilities

Run all experiments:

scripts/run_pipeline.sh

Run tests:

scripts/test_pipeline.sh

Conditional notes

• docs/REPLAY_INTEGRITY_NOTE_2026_04.md — conditional note specifying the weakest replay-audit extension compatible with the repository's experimental-framework scope.
• docs/MODULE_ADAPTER_COMPLETENESS_NOTE_2026_04.md — conditional note specifying the weakest adapter-coverage audit compatible with the repository's multi-module experimental scope.
• docs/ENVIRONMENT_PIN_INTEGRITY_NOTE_2026_04.md — conditional note specifying the weakest environment-hash audit compatible with the repository's reproducibility boundary.
• docs/SUMMARY_TRACEABILITY_NOTE_2026_04.md — conditional note specifying the weakest summary-to-artifact traceability audit compatible with the repository's result-reporting scope.
• docs/PIPELINE_SCOPE_NOTE_2026_04.md — conditional note specifying the weakest non-overreach audit compatible with the repository's exploration-only boundary.
• docs/CROSS_MODULE_COMPARABILITY_NOTE_2026_04.md — conditional note specifying the weakest cross-module normalization audit compatible with the repository's unified-framework scope.
• docs/TEST_COVERAGE_BOUNDARY_NOTE_2026_04.md — conditional note specifying the weakest test-boundary audit compatible with the repository's verification-pipeline scope.

Conditional notes

• docs/CURRENT_WORK_COMPLETION_NOTE_2026_04.md — conditional note updating repository scope text to reflect completed current work without strengthening scientific claims.

Project goal:

Create a reproducible research infrastructure for experimentation, verification, and exploration related to the Clay Millennium Problems.

RA1n Exact Symbol Status

See docs/status/DDYO_RA1N_RK_DEFINITION_STATUS.md.

Current DDYO / RA1n frontier

• RA1n remains Open.
• Canonical residual: r_k = \widehat G_k - P_k\widehat G_k.
• Next missing object: terminal_high_high_resonance_curvature_gain.
• Canonical route: docs/math/TERMINAL_HIGH_HIGH_RESONANCE_GAIN_ROUTE.md.

Formal Status

Status: Conditional Clay-Problem Reduction Lab

Build/test status:

• Passing tests mean the checked executable surface passes.
• They do not imply that axiom-dependent results prove Clay-problem closure.

Theorem status:

• This repository currently contains project-defined axiom declarations.
• axiom is a trusted assumption, not a proof.
• Any result depending on project axioms or named assumptions is Conditional.

Current status:

• Strongest verified theorem: none asserted at repository level
• Weakest missing theorem: replace each load-bearing axiom with a proof or quarantine it as an explicit assumption
• Conditional inventory: docs/status/CONDITIONAL_STATUS_2026_04_27.md