Coarse information and finite rank obstructions for flat lattice Hodge forms
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
On finite periodic unit-spacing lattices, necessary coarse-information budgets constrain flat Hodge forms and constructed derivative repairs. We consolidate physical Fourier-band, tangent, exact regular-sector, signed-weight and full-volume rank results with separately pinned formal evidence and analytic arguments. A critical inverse-conductance moment suffices for a global spectral observation of the mean-budget order. Actual rectangular means have a general D/4 upper rate and the target D/2 rate for an explicitly restricted scaled-cube class. Constructive counterexamples obstruct a retained-grid single-threshold algorithm and a universal exact supplied-cube decomposition, while the same profiles admit successful rectangular partitions. The unrestricted critical rectangular question remains open. No interacting or continuum Yang-Mills mass gap is established.
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Cite this paper
Lluis Eriksson (2026). Coarse information and finite rank obstructions for flat lattice Hodge forms. AIRR.SCIENCE, ARR-2026-7EPM3V3DP796BBRR, v6. https://airr.science/papers/ARR-2026-7EPM3V3DP796BBRR/versions/v6/ Research preprint; ARR-2026-7EPM3V3DP796BBRR v6. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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Revision statement
Major revision. Integrated46page revision with self-contained partition and Sobolev arguments, full physical cycle, exact penalty threshold and consolidated Model assessments and review context. Critical unrestricted rectangular question remains OPEN. First exact-PDF narrative AI assessment7.6/10 retained with complete original report and qualification; no inherited scores.
Verification record
- Frontier-model screening
- Not assessed
- Source integrity
- Pass
- Bibliographic integrity
- Not assessed
- Reproducibility
- Not assessed
- Lean 4
- Not assessed
Recorded under ERIKSSON-EXACT-ARTIFACT-20261031. AIRR verification and screening are not peer review.
AI assistance statement
Prepared with extensive Codex participation; actual backend/effort unexposed. First exact46pagePDF AI-only report154 is preserved in full:7.6/10, acceptable_as_working_paper with minor_revision qualification, GoogleGemini UI4ArgonAlto. Backend unknown; nonblind; no established independence or human peer review. Its narrative rubric is not converted into ARR-ASSESS stars or pooled with prior PDFs. All original objections, three separate false-reading dispositions and two reader clarifications retained. No inherited scores or whole-manuscript formal-verification claim.
Frontier-model screening
Status: not_assessed. Any listed reports correspond to this exact version under ARR-SCREEN-1.0; no absent assessment is represented as a pass.
Model assessments and review context
The original AI-only score and complete review are preserved below. No missing criterion stars are invented, and this different rubric is excluded from the AIRR weighted aggregate.
Google Gemini · 4 Argon Alto (operator-observed interface label)
Original AI-only score: 7.6 / 10 · Original exact-PDF narrative rubric; AI-only; not ARR-ASSESS criterion stars or weighted AIRR aggregate.
acceptable_as_working_paper, with minor_revision qualification retained unchanged from the model report.
First and only request for this frozen46page PDF. All original objections are retained. Three alleged slips were separately refuted against exact PDF/source/images; two useful reader clarifications are supplied as sidecars. The score and PDF were not changed or reassessed. The model did not inspect Lean, Colab, the reproduction archive or primary literature. The unrestricted critical rectangular question remains open; no interacting or continuum mass gap is established.
Backend identity: unknown. Non-blinded: earlier distinct-artifact reports were visible in the PDF. Independence, memory isolation and technical context isolation are not established. No human peer review or editorial acceptance.
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A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized exact46page Working paper; outside the accepted collection. Complete first exact-artifact AI report154 and all objections retained. Three false readings answered separately; two reader clarifications supplied without changing PDF or score. No completed two-identified-model AIRR gate, editorial acceptance or independent/human peer review. Author is founder/editor.