Spin(2,3) programme concept map

This directory contains the canonical, machine-readable concept graph for the research programme. It is a semantic map, not a claim that every visible connection is a derivation.

Reading rule

Every edge has a type and status. In particular:

• derives records a construction established at the stated scope;
• identifies records an exact isomorphism or identification;
• realizes records a concrete model or effective realization;
• requires records an unresolved dependency;
• obstructs records a proved failure of a direct route;
• separates records a no-identification result;
• extends records a live but conditional continuation;
• analogous records structural resemblance only.

The graph deliberately keeps the mathematical spine, physical realization programme, projective/orientation branch, and exceptional/arithmetic horizon visually distinct. A path through the graph inherits the weakest status on that path.

Compact fallback

flowchart LR
  R[Positive response data] --> H[H2(R)+]
  H --> P[Peirce-Schur recursion]
  P --> J[Jordan triple]
  J --> T[TKK prolongation]
  T --> S[sp(4,R)]
  S <--> Q[Spin0(2,3)]

  F[Furey matter module] --> X[Furey channel rotation]
  X --> S
  F --> C[Candidate SM source plane]
  C -. frame unresolved .-> H
  C --> A[External-source action]
  A --> W[Ward / causal response]
  W --> H

  X --> M[S1 mediator completion]
  M -- forces --> E[Third Wilson edge]
  E --> PS[Pati-Salam source split]
  PS --> B[Baryon triality]

  O[Odd three-cycle] --> D[Connected double cover]
  D --> Z[Central -I holonomy]
  Z -. is not .-> OR[Physical orientation]
  OR --> N[Target-blind observable]

  H -. Peirce slice .-> AO[J3(O)]
  AO -. conditional .-> EX[E6 / E8]
  L[Golay / Leech] -. pair-Gram bridge .-> H
  EX -. analogy only .-> MO[Monster / moonshine]
  MO --> GJ[Sym24 Griess fixed Jordan sector]
  GJ --> H
  MO --> IE[Ising-pair affine-E8 atlas]
  IE -- diagram, not current symmetry --> EX

The last three solid arrows are algebraic existence statements, not a claim that the Monster dynamically chooses a unique physical two-port face. The \(\operatorname{Sym}_{24}(\mathbb R)\) fixed sector contains 276 coordinate \(H_2(\mathbb R)\) corners, so physical projection and corner selection remain separate gates. The Ising-pair arrow is independently exact: the nine Norton--Sakuma pair types carry the affine-\(E_8\) marks. It separates that finite operator-composition atlas from a continuous \(E_8\) symmetry; the Monster VOA has no weight-one current algebra.

Files

• 0 is the source of truth.
• 0 is the generated interactive Three.js reading surface.
• 0 is the stricter gate DAG on which the physical-status portion of this map is based.

The interactive page is generated by tooling/publication/generate_concept_map.mjs; do not edit generated files in docs/concept-map/ directly.