HCSM-60 The Kernel Diagonal Theorem: Three Framework Coefficients from One Projector
Year: 2026
Type: preprint
Abstract: We prove that the orthogonal projector Pker onto the kernel of the winding generator Hwind = i sin(πM/8) on the 14-mode multiplet at λ = 4 has a diagonal that takes exactly two values: 2/d on the D4 orbit O0, and (d−1)/d on O1 ∪O2. Three coefficients of the Hodge Complex Standard Model are then traces of this single diagonal. The EFT coefficient c = (d+1)/Tr(Pker|O1∪O2) = 5/9; the mass-map coefficient diag(Pker)|O1∪O2 / diag(Pker)|O0 = (d − 1)/2 = 3/2; and the dimension of the kernel Tr(Pker) = (d − 1)2 + 1 = 10. All three are read off one object. The theorem is HCSM-native; every numerical claim is verified at machine precision.
Author: Preschutti, Stanley
Institution: Information Physics Institute
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214715853