Mathematics · Physics · Foundations
Mathematics as
an Evolving Archive
“Mathematics begins when pattern becomes necessity: when what seemed to be our description reveals a structure that no longer permits us to choose the answer.”— J. Scott Little
Organized by ideas. Proven by mathematics. Governed by honesty.
certify → select → realize → reconstruct → close
The board is a research-room surface, not a claim-free decoration.
Open-ended by design. The archive does not close the future around the current taxonomy.
Board fragments are source-governed; claim status and access boundaries remain explicit.
New to the Website · 27 October 2026 · Release 1.1.1
The full five-paper Yang–Mills series is now available.
Read the manuscripts and supplements, explore the new research notes, and revisit the AI and philosophy papers.
Download the five-paper series · Research notes · AI & Philosophy · What changed in this release
Complete five-paper series
Read the manuscripts and supporting materials
The full Yang–Mills author preprints are available below, together with each paper’s technical supplement and computational archive. The papers have not undergone external peer review.
- Paper I — Manuscript PDF · Supplement PDF · Code and certificates
- Paper II — Manuscript PDF · Supplement PDF · Code and certificates
- Paper III — Manuscript PDF · Supplement PDF · Code and certificates
- Paper IV — Manuscript PDF · Supplement PDF · Code and certificates
- Paper V — Manuscript PDF · Supplement PDF · Code and certificates
Start here
Find your way into the research.
Read the complete Yang–Mills series, explore the mathematical framework, or browse definitions and open problems. Each paper states its own scope and assumptions.
I want to read the five papers
Open all five manuscripts, their technical supplements, and the code and certificate archives. The architecture note provides a guide to the sequence.
Read the complete series →I want the mathematical framework
Enter Geometry of Admissible Transport through its structural spine, then choose proof architecture, definitions, physics, or open problems.
Enter GAT →I want exact terminology
Use the canonical Definitions and Objects indexes when a phrase, projection, carrier, sector, or transport statement needs a precise mathematical home.
Open definitions →I want the frontier
Go directly to formal conjectures, bridge problems, and open research questions with claim boundaries and closure criteria kept visible.
Open research problems →Research rooms
One archive. Different mathematical territories.
Each room uses the same blackboard language but carries its own mathematical composition. New problems can enter, branch, mature, or become archival without redesigning the site.
The Long Proof
The five-paper Yang–Mills reconstruction program, with complete author preprints, technical supplements, computational materials, and a guide to their dependencies.
Enter room →Geometry of Admissible Transport
The core Geometry of Admissible Transport series together with downstream phenomenological papers. The room is designed to grow without assuming that the current sequence exhausts the subject.
Enter room →Interface Problems in Mathematical Physics
A modular research room for problems of passage between mathematical structures: local-to-global descent, continuation, admissible comparison, reconstruction, and the conditions under which an interface is actually realizable.
Enter room →Research Notes
Technical research notes with explanations, examples, reading routes, and explicit research status.
Enter room →Operator Algebras, Rigidity & Reconstruction
Four papers on Connes fusion, analytic descent, finite-to-total reconstruction, joint reconstruction, and direct relational reconstruction.
Enter room →A View from the Mountain
A historical research-development series. The introduction and all fifteen numbered notes have public website editions.
Enter room →AI & Philosophy
Papers and formal notes on recognition under opacity, reciprocal admissibility, operational interiority, finite-memory reasoning, emergence, and the epistemic limits of inference about artificial systems.
Enter room →Current research map
The archive is larger than any one proof.
Research territories are shown at program scale. Bridges appear only when a record is intentionally shared across rooms or the typed graph contains a source-verified cross-program relation. Mathematical dependence, shared ownership, and historical/provenance context are kept distinct; no thematic connection is invented for visual completeness.
Text alternative to the current research map
- Geometry of Admissible Transport ↔ Interface Problems in Mathematical Physics · GAT III — Admissible Yang–Mills Fibrations and Thin Haag–Kastler Reconstruction
- Geometry of Admissible Transport ↔ The Long Proof · imports the frozen five-paper construction
Mathematical Index
Definitions, objects, theorems, conjectures, claim boundaries, and open problems.
These are transverse archive entities: they can belong to any research room and retain stable identities as papers and topics evolve.
For students and early-career researchers
Try the open problems yourself first.
The open problems are research-caliber questions. Before consulting an LLM, reconstruct the definitions, test examples and counterexamples, identify the hypotheses, and develop an independent understanding of what is being asked. Use an LLM later to test, organize, or extend reasoning—not to replace the first encounter with the mathematics.
New to the Website