Methods
The project separates mathematical exploration from evidential assessment.
Discovery and audit
##
Discovery is deliberately exploratory. Alternative representations, computational experiments, provisional conjectures and speculative mechanisms are used to search for structure, test ideas and expose failure.
##
Failed approaches are preserved when they eliminate possibilities, reveal hidden assumptions or sharpen the remaining problem.
##
The public Research section contains bounded examples of this process. One records a stronger sufficient route that was retired after hostile numerical testing. Another records an exact countermodel showing that the intuition behind that route was too strong. Their public versions state what changed and why without reproducing the underlying construction.
##
Audit is deliberately stricter. Results are tested, as appropriate, by exact derivation, recomputation using different representations or methods, boundary and limiting cases, counterexample searches, sign and normalisation checks, dependency analysis, comparison with the mathematical literature, and genuinely independent external review where such review exists.
##
Numerical agreement is evidence, not proof. An attractive mechanism is not a theorem.
##
Scientific status
The project distinguishes established mathematics, exact project-derived identities, numerical evidence, conjectures, failed hypotheses and counterexamples, observations of uncertain novelty, and statements whose proof would constitute new mathematical progress.
These categories are not interchangeable. Numerical evidence does not become proof through scale or precision, and novelty is not claimed without appropriate literature checking.
The Riemann Hypothesis is not treated as proved without a complete rigorous argument and a separate hostile audit directed at gaps, circularity, unjustified limiting operations and hidden assumptions equivalent to the result being sought.
Computation and reproducibility
Computation is used to explore conjectures, search for counterexamples, test limiting cases, reproduce calculations and construct or verify mathematical objects.
Research-relevant code, data, generators, dependencies and intermediate artifacts are preserved where required for reproducibility. A reproducible computational result requires a traceable provenance path from source and inputs to the resulting object.
AI systems are used in exploration, derivation, computation, criticism and synthesis. AI-generated reasoning carries no special evidential status and is subject to the same mathematical, computational and literature checks as any other contribution.
For a closer look at what AI-native representation search means in practice — and how exploratory structures are separated from evidence — read Research Dispatch 001: Beyond Human-First Mathematics.
Substantive human, computational and AI-assisted contributions are recorded for provenance. AI systems are not treated as human authors.
The research record is cumulative. Failed conjectures, counterexamples and corrections remain part of the record when later work changes the project’s understanding.