Frontier Mathematics & Proofs Hub ​

Exploratory Research Programs, Invariant Mappings & Epistemic Boundaries

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Mathematics Root · Frontier Mathematics & Exploratory Proof Frameworks

Public Status Boundary. The Frontier Mathematics sector documents authorial theoretical research programs investigating foundational problems in mathematical physics, operator theory, and discrete geometry. All entries in this hub are categorized as exploratory research frameworks (RESEARCH_PROGRAM / UNVERIFIED_HEURISTIC); they do not assert completed or externally verified Millennium Prize solutions (ACTIVE_P4_SEALS = 0).

1. Epistemic Architecture & Governance ​

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┌─────────────────────────────────────────────────────────────────────────────┐
│                    FRONTIER MATHEMATICS EPISTEMIC LADDER                    │
├─────────────────────────────────────────────────────────────────────────────┤
│ • M3-LEAN4 Core: 28 machine-verified theorems across 9 Lean modules (0 sorry)│
│ • OBJ-PRG-NEG: Proven negative identifiability theorems & Fisher bounds     │
│ • Exploratory Programs: Architectural proof frameworks (Riemann, NS, YM)    │
│ • Hard Rule: Exploratory models NEVER claim external prize resolution       │
└─────────────────────────────────────────────────────────────────────────────┘

2. Exploratory Proof Programs Register ​

Dynamic Harmonic Stabilization and prime distribution analogies on discrete relational lattices.
Status: Research Program — Unverified
Global regularity frameworks applying CKN partial regularity alongside strict epsilon-bounded scaling factors.
Status: Research Program — Unverified
Conditional separation bounds tracking witness space collapse across observer projections.
Status: Research Program — Unverified
Constructive non-perturbative framework translating Wilson plaquette actions to OS axiom preservation.
Status: Research Program — Unverified
Elliptic curve algebraic rank, $L$-series vanishing orders, and bilinear trace pairing duals.
Status: Research Program — Unverified
Algebraic cycle projections, Dolbeault cohomology classes, and boundary-free simplicial 1-cycle conservation.
Status: Research Program — Unverified

3. Adjacent Research Context ​

This page is part of the authorial SFR research program. It connects to external literature on automated verification, physical simulations, and machine-assisted mathematics:

  • Towards Verifiable and Self-Correcting AI Physicists for Quantum Many-Body Simulations (arXiv preprint, 2026) — Documents multi-agent setups verifying complex quantum numerical simulations via decoupled software systems enforcing invariant physical boundaries. See Deng, Luo, et al., 2026.
  • Scientific discovery in the age of artificial intelligence (Nature, 2023) — Examines how automated workflows and geometric deep learning verify physical field equations and boundary constraint properties. See Wang et al., 2023.

4. Canonical Continuations ​

DirectionTarget ResourcePurpose
Proof GatewayLean 4 Formalization Roadmap →28 machine-verified theorem records and lemma dependency DAGs
Axioms RegisterConstitutional Axioms & Object Register →Source-backed primitives and quarantined formal proposals
Proof GovernanceProof Governance & Verification Scale →Six-stage M0–M5 verification and publication lifecycle
Mathematics RootFormal Mathematics Spine →Complete 9-tier status taxonomy, axioms, and dedicated manuscript surfaces