Optimal stability and all equality cases at balanced inertia (5,5)
We determine the optimal forward stability coefficient 113/152 for inverse Hilbert-Schmidt self-commutator cost at balanced inertia (5,5), uniformly for every fixed number of ambient zero eigenvalues. The inherited finite vertex reduction gives 267 ordered spectral pairs. Rational Horn primal-dual certificates establish the bound; an ambient-independent obstruction and boundary family prove sharpness. We classify all four equality pairs on the compact spectral closure and show strictness for exact inertia. The verifier checks 51,282,604 integer Horn conditions, with a separate LR-tableau reconstruction. Balanced multiplicities at least six and general interior costs remain open; polynomial vertex counts do not assert polynomial total running time.
Verification record
- Frontier-model screening
- Pass · 1 models
- Source integrity
- Pass
- Bibliographic integrity
- Partial
- Reproducibility
- Pass
- Lean 4
- Not applicable
Recorded under ARR-VERIFY-1.0. ARR verification and screening are not peer review.
Version history
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- v1 · source snapshot available · viewing
AI assistance statement
Codex assisted with derivation, computation, literature comparison and drafting. A separate GPT-6 Astra task configured with extra-high effort audited the proofs and certificates and accepted the subsequent delta. The producing model family is involved in manuscript preparation; this is not independent human peer review. The author expressly directed final verification and publication.
Frontier-model screening
Status: pass. Any listed reports correspond to this exact version under ARR-SCREEN-1.0; no absent assessment is represented as a pass.
- gpt-6-astraOpenAI · pass
Independent model assessments
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No model reports are published for this version.
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Editorial disclosure
Author-directed founder-pilot publication under the explicit instruction to finalize, verify with AI and send to ARR. The author is also the operator; no independent human editor or peer review is claimed. The scoped exception and exact artifacts are recorded in DEPOSIT_DECISION.json; ordinary independent-editor requirements are not fulfilled.