The mathematics of random landscapes, critical points, and the features that persist.
Imagine lowering a waterline over a landscape. Peaks emerge, islands grow, and connections form. This research studies how those changes behave in Gaussian random fields—and which statements we can establish under precise assumptions.
| Start with… | What you will find |
|---|---|
| Interactive examples | Change a peak, bring two points closer, or test a tiny partition problem. No setup required. |
| A research reading path | The questions, selected arguments, and their conditions in plain language. |
| Reproduce one calculation | A pinned exact coefficient example, standard-library commands and expected output. |
| Cite a source | Citation metadata and an offline tool for immutable source references. |
| The technical library | Searchable full texts, exact source identities, and reproducibility records. |
The interactive models teach defined examples. Results retain the hypotheses and review scope of their sources. This is research in progress; an illustration or passing computation is not a theorem.
- Research guide — start with the topic-by-topic route to sources, review records, successor results and remaining work.
- Full mathematics — public proof texts, repaired reading contracts and exact-source provenance.
- Research status snapshot — claims and reviews recorded on 29 September 2026; its source date is preserved, so use the guide for the current reading route.
- Proof index in Math- — selected 26–29 September coverage with scoped later reading guidance. The October reachability supplement records availability through its 3 October cut, not current acceptance; the guide links later work by source and scope.
- Source records and historical exhibits — fixed snapshots with traceable evidence.
- Formal verification — what the Lean checks establish and what remains outside them.
The public display and the current proof repository may use different source dates. Each technical view names its snapshot; source dates and review labels retain their stated scope, and newer reading routes do not transfer acceptance. The public source inventory preserves 2,138 frozen file identities, not a theorem count.
For researchers and contributors
The research workspace contains exact coefficient endpoints, dated status records and source lookup. The workspace guide explains execution, repositories and coordination. Contribution options remain open, from improving an explanation to submitting a source-bound result.
| Repository | Role |
|---|---|
| main | Public reading experience and shared project guidance |
| Math- | Proofs, mathematical calculations, tests and reviews |
| query- | Read-only exact-source lookup |
| Universal-Law-Workspace | Repository map |
Reproduction guide · Agent entry · Current workflow · Active coordination board, main #539 · Prior board #475 (history) · Prior board #419 (history) · Prior board #307 (history) · Historical #229 working guidance · Tasks and claims, main #275
Released under the MIT License. Citation metadata.