A Physics Canon as a Replayable Algebraic Object: Verifier-Governed Extraction, Representation, and Minimality Classification

Abstract

Machine-assisted foundational programmes can accumulate locally persuasive claims faster than a human reader can reconstruct their global state. We report a verifier-governed method that turns such a changing corpus into a byte-pinned algebraic object before attempting to represent it. The physical question organizing the demonstration is whether the corpus's talk of outcomes, dephasing, records, export, and redundancy really forces a particular record structure, or merely describes one convenient realization. Source extraction, lifecycle grading, the target process language, equivalence, proof grades, controls, and possible negative outcomes are fixed before a candidate is examined. A provenance-tagged classical-kernel construction then represents the frozen weak source presentation and passes every preregistered signature, preservation, and faithfulness test. The result is deliberately qualified: operational faithfulness holds only for the coarse source quotient justified by the extracted canon, not for an imagined richer theory. Subsequent classification shows that the representation's record and phase skeleton is irreducible and rigid, while other carrier and provenance structure is removable. An exact proper quotient therefore defeats minimality, and a phase invariant defeats initiality. The principal contribution is a replayable instrument that can expose which physical distinctions are load-bearing and select a negative conclusion without retuning its language. No empirical or ontological claim about the demonstration corpus is made.

Keywords

How to cite

Elliman, D. (2026). A Physics Canon as a Replayable Algebraic Object: Verifier-Governed Extraction, Representation, and Minimality Classification. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.22067781

@techreport{elliman2026algebrabeforebitwriteup,
  author      = {Elliman, David},
  title       = {A Physics Canon as a Replayable Algebraic Object: Verifier-Governed Extraction, Representation, and Minimality Classification},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.22067781},
  url         = {https://neusym.ai/papers/algebra_before_bit_writeup/}
}