Nuclear Precursors on the Charlton Stage: The Regulator Silence Test. Among the Regular Polychora only the 24-Cell Keeps Quiet
Abstract
We introduce the Ontological Filter in Charlton Geometry (CG): a non-invertibility discriminator that selects which E4-native regulator templates can persist as stable macro-identities in a lossy-quotient macrostate. The filter is a silence criterion: admissible regulators must be dual fixed-points of the inside/outside incidence swap at the level of macro-observable boundary signatures, i.e. they must remain re-identifiable under the vacuum symmetries that cannot be avoided once the Householder-type reflected metric η = δ − 2 ω ⊗ ω is admitted. Restricting a first-pass search to regular convex 4-polytopes, (a declared search domain at this stage), the silence criterion reduces candidates to the self-dual polychora. This leaves the 5-cell and the 24-cell. We then show that the 5-cell fails a non-degeneracy constraint that is already required at the ontological stage: a symmetry-respecting three-sector facet labeling compatible with η-transport. Because the 5-cell has five tetrahedral facets, any partition into three equal sectors is obstructed by 5 mod 3 ̸= 0; the remainder forces an unavoidable anisotropic residue in the η-reflected bookkeeping, preventing the 5-cell from being a silent dual fixed-point. The result is uniqueness (in the regular class): the 24-cell (the D4 regulator) is the only regular silent template. All uniqueness claims in this manuscript are within this regular convex search domain; extension to non-regular cell complexes is deferred as an explicit obligation. We then show that the silent 24-cell is kinematically locked: admissible transport lifts to a double cover, so observable macroclasses close after 2π while microdata closes only after 4π, yielding a 720◦ spin lock as a geometric constraint of the lossy quotient. Finally, we derive a hard-core exclusion rule on facet-coordinate bookkeeping Aij : two admissible regulator instances cannot share the same facet-coordinate, because multi-occupancy collapses distinct identities under the projection. Together these results complete the ontological gate: the 24-cell is the unique regular chassis compatible with silence, double-cover transport, and collision-free indexing.
Fields of Study & Subjects
Relativity and Gravitational Theory
Mathematics and Applications
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 14 January 2026
- Document type
- Preprint