We present the Danieletto axiom — dT/dF = 0 (the Menabrea-Castigliano condition generalized to fields) — and derive from it four results in fundamental physics. From the stationarity condition of the work functional T with respect to the force functional F of a 4-dimensional elastic medium: (1) the Yang-Mills equations of motion for SU (N) gauge fields, including the self-interaction (cubic and quartic) terms, emerge from applying the axiom to the medium work functional Tₘedium with N constituent types; (2) the canonical commutation relations â, â†=1 and ĉ, ĉ†=1 emerge from the integer and half-integer winding number constraint on closed orbits in the medium; (3) the canonical algebra q̂, p̂=iħ holds on the Hilbert space L² (0, L) selected by the winding number boundary condition, as established by geometric quantization; (4) a structural connection to the Dirac equation emerges from the Clifford algebra e_μ, e_ν=2g_μν satisfied by the tangent vectors of the 4D helicoid (rigorous derivation in companion paper 16, submitted). As a direct application, the Z₃ circulant operator of the charged lepton sector yields the Koide formula Q (Σmₖ) / (Σ√mₖ) ²=2/3 (0. 0009% error) and the algebraic identity ∏√mₖ=A³· (cos (3θ) /√2−1/2) (derived in Section 6). All results emerge from the axiom without free parameters. The derivation of the full electroweak symmetry breaking sector (Higgs mechanism, W and Z masses, fermion chirality) is identified as the key open problem for a companion program.
Danieletto et al. (Tue,) studied this question.