Mathematical Articulation of the Indexical-Fiber Framework: The Postulate and the Relational Structural Register
Abstract
The formal reference record for the representation developed in the indexical-fiber preprint. Definiteness as Index gives the minimal reading of quantum outcomes; this document states the representation in which that reading is computed: a flat ℤ/2 local system over spacetime with a binary index, the structure-fact fence, the section-level content and the relational register. The rules of the typing are kept in the Typing Schema, Rev 4.6.
Revision 5.8 places the index relative to observer gaps: restricted to any region, the index class is a pull-back, so it is zero on every loop around a gap lying inside spacetime; a point-like observer's path adds no loop class, while the edge of the observer's causal diamond adds exactly one, on which the index is zero, and the two are Alexander duals; and every class the index can carry is detected on a single Cauchy surface. The base is stated from one typed primitive, the causal order, and one orientation datum, with strong causality forced. This revision supersedes both issues numbered Revision 5.7.
Submitted for technical scrutiny, not belief.
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BibTeX
@misc{reid2026mathematical,
title = {{Mathematical Articulation of the Indexical-Fiber Framework: The Postulate and the Relational Structural Register}},
author = {Aron Reid},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23552626},
url = {https://zenodo.org/records/23552626},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mathematical Articulation of the Indexical-Fiber Framework: The Postulate and the Relational Structural Register
AU - Aron Reid
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23552626
UR - https://zenodo.org/records/23552626
AB - The formal reference record for the representation developed in the indexical-fiber preprint. Definiteness as Index gives the minimal reading of quantum outcomes; this document states the representation in which that reading is computed: a flat ℤ/2 local system over spacetime with a binary index, the structure-fact fence, the section-level content and the relational register. The rules of the typing are kept in the Typing Schema, Rev 4.6. Revision 5.8 places the index relative to observer gaps: restricted to any region, the index class is a pull-back, so it is zero on every loop around a gap lying inside spacetime; a point-like observer's path adds no loop class, while the edge of the observer's causal diamond adds exactly one, on which the index is zero, and the two are Alexander duals; and every class the index can carry is detected on a single Cauchy surface. The base is stated from one typed primitive, the causal order, and one orientation datum, with strong causality forced. This revision supersedes both issues numbered Revision 5.7. Submitted for technical scrutiny, not belief.
ER -