Mathematical Atlas & Taxonomic Index
Topological Navigation, Formal Object Trees & Proof Infrastructure
Spine Position
Mathematics Root · Formal Mathematical Atlas & Taxonomic Spine
Public Status Boundary. This atlas provides an architectural index mapping formal definitions, axiomatic state spaces, invariant transport theorems, and Lean 4 proof campaigns across the Science of Fabric Reality.
1. Mathematical Taxonomy & Subsystem Tree
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MATHEMATICS SPINE
├── Foundational Ontologies & Primitives
│ ├── Axiomatic State Spaces (/04-mathematics/axioms)
│ └── Mathematical Invariants & Admissibility (/04-mathematics/invariants)
├── Operator Algebras & Dynamics
│ ├── Bilinear Trace Reciprocity (/04-mathematics/inventions/trace-reciprocity)
│ ├── Pasev Gauge Connections (/04-mathematics/inventions/gauge-principle)
│ └── Transfinite Infinite Symmetry (/04-mathematics/inventions/infinite-symmetry)
├── Proof Governance & Verification
│ ├── 9-Tier Status Taxonomy (/04-mathematics/proof-governance)
│ ├── Theorem Candidates Registry (/04-mathematics/theorem-candidates)
│ ├── Lean 4 Formalization Roadmap (/04-mathematics/formalization-roadmap)
│ └── Formalization Batch 1 Specs (/04-mathematics/formalization-batch-1)
└── Numerical Testbeds & Falsification
├── Diagnostic Simulation Bridge (/04-mathematics/formalization-simulation-bridge)
└── Discrete Simulation Atlas (/04-mathematics/simulations/)2. Interactive Runtime Graph
MATHEMATICS
> STATUS BOUNDARY: This graph represents the internal mapping topology only. It is not a complete graph, not a unified theory, and not fully mapped. Coverage is partial and expanding.
3. Formalization & Diagnostic Diagnostics
The mathematical compendium connects abstract theorem proving in Lean 4 (35 verified proofs across 11 formal modules) to discrete numerical testbeds through the Formalization ↔ Simulation Bridge, verifying mathematical stability while maintaining a strict firewall against overclaiming (ACTIVE_P4_SEALS = 0).
4. Canonical Continuations
| Direction | Node | Route | Focus / Purpose |
|---|---|---|---|
| Results Ledger | Scientific Results Ledger | /science/results | 35 machine-verified Lean 4 theorems and negative null benchmark ( |
| Reproducibility | Computational Reproducibility | /science/reproducibility | RFC 8785 JCS verification receipts and reproducible Lean 4 proof environment |
| Proof Tracker | Lean 4 Formalization Roadmap | /04-mathematics/formalization-roadmap | 35 machine-verified theorem records and lemma dependency DAGs |
| Formalization Batch 1 | Lean 4 Module Specifications | /04-mathematics/formalization-batch-1 | Direct Lean 4 code specifications across all 11 verified modules |
| Mathematical Inventions | Inventions Gateway | /04-mathematics/inventions/ | Trace reciprocity, relational gauge principle, and infinite symmetries |
| Axioms Register | Constitutional Axioms & Object Register | /04-mathematics/axioms | Source-backed primitives and quarantined formal proposals |
| Proof Governance | Proof Governance & Verification Scale | /04-mathematics/proof-governance | Orthogonal status coordinates |
| Simulation Lab | Simulation Atlas & Numerical Testbeds | /04-mathematics/simulations/ | Discretized numerical solvers, null tests ( |