This is a Physics Breakthrough. We now know the why and how of the constants. Why the Constants Have the Values They Have: The Equivalence Cost of the Universe The fine structure constant is derived from a single self-referential axiom (σ = 1 + 1/σ) with zero free parameters: α⁻¹ = 360/φ² − 2/φ³ + 3⁻⁵/φ⁵ + 7⁻⁷/φ⁷ = 137.035999207 Experimental value (Morel et al. 2020): 137.035999206 ± 0.000000011. Discrepancy: 0.05σ. The paper shows that in atomic units, E = mc² = m × α⁻² ≈ m × 18,779, so the entire content of mass-energy equivalence for one electron is a single number: the square of the self-referential winding count on a 360-point discrete lattice. The Hartree energy identity m_e c² = α⁻² × E_h, a textbook result of atomic physics, is shown to be the structural bridge connecting the mathematical axiom to physical rest mass: the Hartree self-consistent field method is itself self-referential iteration to a fixed point, instantiating the axiom in the space of wavefunctions. The formula has two equivalent series representations (prime spectrum and zeta-rung form), connected by Euler products, converging within 5 × 10⁻⁹. An 81,225-formula ablation test finds no competitor within 340× of the derived value. Seven representative constants (α, c², λ_H, sin²θ_W, m_p/m_e, G, Λ) are tabulated with experimental comparisons. Explicit falsification criterion: any future consensus value of α differing from 137.035999207 by more than 1 ppb rules out the framework. Part of the Pentagon Physics Programme. Companion papers: Solving Alpha (doi:10.5281/zenodo.18648550), MFH: Master Framework Handbook (doi:10.5281/zenodo.18742684). Keywords: fine structure constant, golden ratio, self-reference, fundamental constants, mass-energy equivalence, Hartree energy, Pentagon Physics

Version 2 Notes Structural and rhetorical revision responding to five independent reviews. We tried to improve the paper through clarification and a few major and minor improvements.Principal changes: Axiom form corrected. Abstract and body now consistently state σ = 1 + 1/σ (positive root φ). The v2 abstract used the conjugate form σ = 1/(1+σ), creating a contradiction with Eq(3). Experimental comparison reframed. All comparisons now lead with the CODATA 2022 recommended value (1.4σ), presenting the Morel/Parker tension as context rather than foregrounding the most favourable measurement. Constant count corrected. "Seven further constants" replaced by "five further constants," all five named explicitly. Hartree section recast. Renamed from "The Hartree Evidence" to "The Hartree Parallel." Claims of evidential force softened to structural resonance throughout. Sections reordered. Kill conditions (now §6) precede "Eight Questions Answered" (now §7), establishing falsifiability before explanatory reach. Weinberg angle sharpened. Now specifies that Standard Model two-loop running gives sin²θ_W = φ⁻³ at μ ≈ 243 GeV (within 0.03% of the Higgs VEV), replacing the vague "+0.004 to +0.007" range. Independent literature added. Four non-self-citations added: Weyl (1916), Hardy and Wright (2008), Khinchin (1964), Harary and Palmer (1973), with corresponding in-text citations in Section 2. Minor improvements. Maxwell solenoid citation softened; false-positive analysis given its own paragraph; numerology defence reframed; lexical variation applied; precision-units sentence added to constants table.