.zenodo.json

{
  "title": "TNFR-Python-Engine: Resonant Fractal Nature Theory Implementation",
  "description": "<p>TNFR-Python-Engine is the canonical computational implementation of Resonant Fractal Nature Theory (TNFR): a mathematical framework for modeling coherent patterns in complex systems through resonance-based dynamics on networks. A single nodal equation drives every node; from it a complete transport and geometric structure emerges, measured by the engine, verified to machine precision, and anchored to classical, experimentally-established physics. The graph is only the substrate — the dynamics generates its own geometry.</p><p>All systems evolve via the nodal equation ∂EPI/∂t = νf · ΔNFR(t). Structural change occurs exclusively through 13 canonical operators (AL, EN, IL, OZ, UM, RA, SHA, VAL, NUL, THOL, ZHIR, NAV, REMESH) governed by the unified grammar rules U1–U6; each operator acts on exactly one channel of the nodal equation — the form EPI, the capacity νf, the phase θ, or the pressure ΔNFR — at node or network scale. System state is characterized by four structural fields, the structural-field tetrad (Φ_s structural potential, |∇φ| phase gradient, K_φ phase curvature, ξ_C coherence length), the four orders of the discrete structural-derivative tower. Only π is a genuine structural scale (the phase-wrap bound of the phase sector); the coherence length is set by the spectral gap (ξ_C ∝ 1/√λ₂) and the structural-potential confinement bound is π-derived. φ, γ and e are not structural scales — everything other than π emerges from the nodal dynamics.</p><p>From this single equation a transport layer (graph-Laplacian diffusion, synchronization/Kuramoto, random walks, effective resistance, and standing-wave modes) and an emergent symplectic substrate (a phase space with conserved Noether charges, a Hamiltonian equal to the energy functional, complete integrability, and a Stokes/Poincaré polarization structure) emerge as the two orthogonal Helmholtz–Hodge components of one flow. This reorganizes known mathematics and physics inside a single framework, verified in code; it is a characterization of structure the nodal equation already contains, not a claim of new physics.</p><p>The engine, the tetrad, grammar U1–U6, conservation laws, and the emergent transport and symplectic geometry are implemented, anchored to experimentally-established phenomena, and covered by 2,041 tests. TNFR is also used to probe famous open problems through honest, in-progress research programs that do not claim proofs: TNFR–Riemann, TNFR–Navier–Stokes, TNFR–Yang–Mills, TNFR–P vs NP, TNFR–Birch–Swinnerton-Dyer, and TNFR–Hodge. The corresponding classical problems (the Riemann Hypothesis, 3D Navier–Stokes global regularity, the Yang–Mills mass gap, P vs NP, BSD, and Hodge) remain open.</p><p>Install: pip install tnfr · Documentation and source: https://github.com/fermga/TNFR-Python-Engine</p>",
  "version": "0.0.3.5",
  "publication_date": "2026-06-24",
  "doi": "10.5281/zenodo.17602860",
  "creators": [
    {
      "name": "FMG",
      "affiliation": "TNFR Research",
      "orcid": "0009-0007-6116-0613"
    }
  ],
  "keywords": [
    "TNFR",
    "complex systems", 
    "fractals",
    "resonance",
    "networks",
    "structural dynamics",
    "structural analysis",
    "nodal equation",
    "coherence",
    "phase synchronization"
  ],
  "license": "MIT",
  "upload_type": "software",
  "access_right": "open",
  "language": "eng",
  "related_identifiers": [
    {
      "identifier": "https://github.com/fermga/TNFR-Python-Engine",
      "relation": "isSupplementTo",
      "resource_type": "software"
    },
    {
      "identifier": "https://pypi.org/project/tnfr/",
      "relation": "isIdenticalTo",
      "resource_type": "software"
    }
  ],
  "subjects": [
    {
      "term": "Complex Systems",
      "scheme": "keyword"
    },
    {
      "term": "Network Theory",
      "scheme": "keyword"
    },
    {
      "term": "Fractal Dynamics",
      "scheme": "keyword"
    },
    {
      "term": "Structural Analysis",
      "scheme": "keyword"
    }
  ]
}