+ "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. Each field is associated with a constant as a notational label, but only π is a genuine structural scale (the phase-wrap bound of the phase sector); γ, e and φ are notational, not derived structural scales.</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>",
0 commit comments