The canonical UFFT electron mass formula (Paper #10, Paper #31) is mₑ = r₁ MP exp (−Swalk), with Swalk = (E − F) (2Δ + √Δ) /16, evaluating to Swalk = 52. 41927 and mₑ = 510. 97 keV (0. 006%). This paper establishes three structural theorems on the cell-integer content of Swalk and identifies the form consistent with a closed-disturbance walk action over the foam. Theorem 74. 1: the step count (E − F) = 22 admits three equivalent topological readings, (E − F) = (V − χ) = (Eface − F) = 22, coinciding because the truncated octahedron has Eface = E and V − χ = E − F by Euler's formula. Theorem 74. 2: the factor (2Δ + √Δ) admits the spectral factorisation (r₂ − r₁) ·2 (r₂ − r₁) + 1, where r₁, r₂ are the two T₁u eigenvalues of the face Laplacian (roots of λ² − 9λ + 16 = 0). Theorem 74. 3: the colour-group identity |G|/CA = 2·Fₕx = 16, so the denominator is simultaneously the colour-averaged group-order normalisation and twice the hexagonal-face count. Together: Swalk = (E − F) · (r₂ − r₁) ·2 (r₂ − r₁) + 1·CA/|G|. This form is consistent with, and naturally suggests, a closed-disturbance walk action on the T₁u sector of the face graph: (E − F) topological steps, per-step amplitude controlled by the T₁u spectral spread, colour-averaged over Oₕ. The explicit path-integral construction is stated as conjecture C74. 4, the natural follow-up. This paper does not yet derive Swalk from a foam Hamiltonian; it establishes the structural identities any such derivation must satisfy and identifies the missing step explicitly. All identities verified numerically by direct substitution of cell integers; verification snippets included inline.
Luke Martin (Sun,) studied this question.