Located, Not Forced: A Scoped Two-Primary Audit of a Clifford Rarita-Schwinger Generation Carrier

We study chirality and generation structure in an explicit Clifford Rarita-Schwinger carrier motivated by the matter proposal of Geometric Unity, while marking every GU-specific step. For `Cl(9,5)=M(64,H)`, the irreducible real module has real dimension 256; the computations use its 128-dimensional complex realization. For the exact encoded finite type `C_fin`, finite torsion constraints are 2-primary; integer equality/divisibility, representation dimensions, and diagnostics remain separately typed; none supplies a mod-3 congruence or selects a particular odd integer. A bounded finite deduction is machine-checked in Lean. The lift toward broader semantic `C_inv` remains conditional. The finite complex Krein theorem proves an intersection-difference nullity, not a physical handedness count or Fredholm index. Its compact `(96,96)` instance does not transfer unchanged: one Lorentzian Hodge half is Krein-null and the computed stable closure has signature `(192,192)`. The standard decomposition `pi_3^s = Z/24 = Z/8 + Z/3` applies only to data explicitly mapped into that torsion group. The exhibited framed class has order 12 and a nonzero order-3 projection, but it cannot itself be an integer count because `Hom(Z/3,Z)=0`. The result is a scoped exhibition and non-derivation statement, not a claim of three generations or a universal no-go. Lorentzian bundle transfer, non-equivariant constructions, and the true-`Y14` source-action pushforward remain open. All reported checks are internal-tier reproduction from the same AI-directed process that produced the paper. External replication and peer review are welcome as optional later validation; they are not prerequisites for Zenodo publication.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-23
DOI
https://doi.org/10.5281/zenodo.21515142
Primary Topic
Algebraic and Geometric Analysis
Type
preprint
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preprint

Located, Not Forced: A Scoped Two-Primary Audit of a Clifford Rarita-Schwinger Generation Carrier

Joseph Hernandez
Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
preprint

Located, Not Forced: A Scoped Two-Primary Audit of a Clifford Rarita-Schwinger Generation Carrier

Joseph Hernandez
preprint en

Abstract

We study chirality and generation structure in an explicit Clifford Rarita-Schwinger carrier motivated by the matter proposal of Geometric Unity, while marking every GU-specific step. For `Cl(9,5)=M(64,H)`, the irreducible real module has real dimension 256; the computations use its 128-dimensional complex realization. For the exact encoded finite type `C_fin`, finite torsion constraints are 2-primary; integer equality/divisibility, representation dimensions, and diagnostics remain separately typed; none supplies a mod-3 congruence or selects a particular odd integer. A bounded finite deduction is machine-checked in Lean. The lift toward broader semantic `C_inv` remains conditional. The finite complex Krein theorem proves an intersection-difference nullity, not a physical handedness count or Fredholm index. Its compact `(96,96)` instance does not transfer unchanged: one Lorentzian Hodge half is Krein-null and the computed stable closure has signature `(192,192)`. The standard decomposition `pi_3^s = Z/24 = Z/8 + Z/3` applies only to data explicitly mapped into that torsion group. The exhibited framed class has order 12 and a nonzero order-3 projection, but it cannot itself be an integer count because `Hom(Z/3,Z)=0`. The result is a scoped exhibition and non-derivation statement, not a claim of three generations or a universal no-go. Lorentzian bundle transfer, non-equivariant constructions, and the true-`Y14` source-action pushforward remain open. All reported checks are internal-tier reproduction from the same AI-directed process that produced the paper. External replication and peer review are welcome as optional later validation; they are not prerequisites for Zenodo publication.

Zenodo (CERN European Organization for Nuclear Research)
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Algebraic and Geometric Analysis
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Located, Not Forced: A Scoped Two-Primary Audit of a Clifford Rarita-Schwinger Generation Carrier — Joseph Hernandez · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS