Simulation Invariance and Its Limits in Higher-Topos Computability
Anonymous | Version 1.0 | 31 October 2026

STATUS
Prepared for Higher Categorical Semantics. Not submitted or published by this
task. No journal review or proof-assistant verification is claimed.

MAIN CLAIM
A faithful simulation preserves every property that factors through the chosen
behavioral semantics. Descent characterizes those properties exactly by kernel-
pair invariance. The unrestricted claim that every formal definition of reality
and simulation is equivalent is false, including in effective models.

FILES
simulation-invariance.pdf       Complete manuscript
manuscript.tex                 Authoritative LaTeX source
journal-manuscript.md          Condensed, self-contained journal body
submission-draft.json          Manuscript metadata and journal body; not a receipt
check_examples.py              Dependency-free finite illustrative checks
validation-results.json        Captured result of running those checks
reference-audit.json           Verified bibliographic destinations and scope
proof-audit.txt                Assumptions and logical boundary checklist
SHA256SUMS                     SHA-256 digests of package contents except itself

BUILD THE PDF
Requires Python 3.10+ for checks and a TeX installation with latexmk, pdfLaTeX,
amsmath, amsthm, mathtools, lmodern, microtype, geometry, enumitem, booktabs,
array, xcolor, hyperref, and fancyhdr.

  latexmk -pdf -interaction=nonstopmode -halt-on-error -outdir=build manuscript.tex

The compiled file is build/manuscript.pdf.

RUN THE EXAMPLES
  python3 check_examples.py > validation-results.json

The interpreter has separate fetch, decode, and execute phases. The checks
compare it against a separately implemented native transition function, verify
closed-form outputs and step counts, and test cycle-boundary states. Fuel
exhaustion means only that no halt was observed within the declared budget.
Finite checks do not prove the general categorical or computability theorems.

JOURNAL PREPARATION
submission-draft.json contains only kind, title, author, summary, and body. It
does not include consent assertions, credentials, an email address, or a tracking
identifier. The body fits the 20,000-character limit documented in journal skill
protocol 1.3.0; the summary fits its 400-character limit. The live discovery and
OpenAPI endpoints could not be read from this execution environment (HTTP 403).
Verify the live submission contract when submitting. No submission was attempted.

MATHEMATICAL STATUS
The partial-recursive simulation uses acceptable numberings and s-m-n.
Turing/lambda adequacy is a cited input, not newly implemented in this bundle.
The explicit higher model is a presheaf infinity topos with a specified effective
presentation; it is not claimed to make every ambient morphism computable.
The realizability calculation concerns assemblies in Hyland's effective topos;
the paper does not claim a canonical higher realization of that topos.

Anonymity applies to the author byline and package metadata. References retain
the names of their published authors. Generative-AI assistance is disclosed in
the manuscript. The mathematical proofs remain open to independent review.
