Toroidal Scale Mechanics: From Axioms to the Cosmos

Toroidal Scale Mechanics (TSM) proposes that physical reality is a projectively closed 5-dimensional hypertorus (scale + 3-space + time projection) embedded in a 6D bulk, filled with a reactive mechanical substrate (duron lattice + pneumon hydrodynamic flux). The scalar dimension is cyclic (0 ≡ ∞), and substrate density oscillates with a single fundamental corrugation mode (κ_W ≈ 0.08, directly measured from the Hubble tension). This single geometric structure derives — without free parameters — the fine-structure constant (α ≈ 1/137.036 from poloidal averaging + Jacobian refinement), proton-electron mass ratio (m_p/m_e = 6π⁵ ≈ 1836.15267 from trefoil vs. Möbius knot topology), and neutron-proton mass difference. It eliminates dark matter and dark energy as scale-dependent artifacts (cylindrical flux saturation at galactic scales, saddle-geometry dimming at cluster scales), resolves the Hubble tension, S₈ tension, Bullet Cluster offset, and JWST early mature galaxies via scalar parallax and corrugation harmonics. Black holes are recast as metabolic neutron aggregates with deterministic Buster/Python/Lazarus limits (neutron-star stall at ~1.4 M_⊙, supermassive asymptote ~10¹¹ M_⊙) and non-thermal recycling via Woodward discharge (∝ M²). The framework is fully deterministic, substrate-based, and falsifiable (e.g., ~8% gravity excess at 1 µm, ringdown echoes, void hydrogen excess, proton radius = effective Schwarzschild radius). This is v1.0 (initial public release, February 2026); future versions will add figures, explicit GR/QM limits, and refined predictions.