INTEGRAL SECONDARY MAPS IN AN OBSERVATION FOUR-CYCLE
Brian Theory | Technical addendum, version1.0 | 9 November 2026

Read manuscript.pdf. Editable source: manuscript.tex. The addendum answers the
fixed v0.5 observation-refinement four-cycle question and proves its row-zero
boundary. The 35-state RP2 realization is separate from the uniform24k+11 family.

Contents
  manuscript.pdf / manuscript.tex: complete theorem-and-proof note
  source-proof-ledger.txt: assumptions, proof dependencies, primary references
  AI-review-summary.txt / responses-to-reviewers.txt: review status and revisions
  data/q1/: five exact constructed models and full signed certificates
  data/q0/: four exact lowest-degree examples, including nontrivial d1
  verification/: newly written independent portable JavaScript verifiers
  retained-checks/: earlier independent raw Smith results, clearly identified
  results/: fresh portable verification output
  publication-manifest.json: file hashes, destination/status/open limits

Reproduce finite checks with Node.js18 or later; no npm packages are required:
  node verification/run.mjs
This reads only package-relative data and writes results/ within this package.
The q1 orders are rebuilt from facets and anchor generators. The q0 checks use
recorded complete strict orders, then independently rebuild actual product links,
boundaries, fundamental graph cycles and integral quotient lattices. The seed
checker covers k2..9; the theorem for arbitrary k is the manuscript's proof.
These verifiers do not certify arbitrary input complexes: they assert the stated
finite models and exact residual forms. Inspect the code and assumptions.

Historical Python/SymPy raw Smith results corroborate the new integer-reduction
route, but their old environment is not required to run these portable checks.
The normal-form reductions use exact BigInt arithmetic, not field ranks.

Compile the source twice using an existing LaTeX installation with the listed
standard packages. For MiKTeX, keep automatic installation disabled:
  pdflatex --disable-installer -interaction=nonstopmode -halt-on-error manuscript.tex
  pdflatex --disable-installer -interaction=nonstopmode -halt-on-error manuscript.tex
With other TeX distributions omit the MiKTeX-specific --disable-installer option.
No package installation is requested by this bundle. Recompilation may produce
different PDF bytes from timestamps; verify the distributed PDF against its
manifest hash and compare mathematical text for regenerated builds.

Release status: internally AI-reviewed mathematical research addendum.
The compiled seven-page PDF was rendered and visually inspected. It has resolved
references and no overfull boxes; a harmless underfull bibliography paragraph
remains. This does not certify tagged-PDF accessibility.
Human specialist review remains recommended and priority unconfirmed.
No refined homotopy classification, minimum-state theorem, physical/cognitive
claim or architectural benefit is asserted. The public parent is not modified.
