{"paper":{"title":"Stable systolic inequalities via mod n covering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A refinement of the cowaist inequality for Hermitian line bundles yields sharp stable two-systolic inequalities for odd-dimensional complex projective spaces.","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Aditya Kumar","submitted_at":"2026-04-29T17:00:59Z","abstract_excerpt":"We introduce a mod $n$ covering based approach to stable systolic inequalities. The idea is to prescribe a cohomology class mod $n$ which forces the desired cup product or index to be nonzero, and then find a short integral lift of that class. The method is especially effective in rank two as we can compute the covering constant. As a curvature free application, we improve the stable two systolic bound for $S^2\\times S^2$ to $2$. The same bound holds for every oriented four manifold with $b_2=2$. Under a positive scalar curvature lower bound, the mod $n$ covering method combined with a sharp c"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove a refinement of Gromov's cowaist inequality in the case of Hermitian line bundles. Combined with the cowaist-systole estimates in recent work of Stryker, this gives sharp stable two-systolic inequalities for odd-dimensional complex projective spaces.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The refinement of the cowaist inequality is valid specifically for Hermitian line bundles, and the combination with Stryker's cowaist-systole estimates applies directly without further restrictions on the manifolds or bundles.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A refinement of Gromov's cowaist inequality for Hermitian line bundles produces sharp stable two-systolic inequalities for odd-dimensional CP^n and improves the stable two-systole upper bound for n-fold S^2 products from O(n^4 log n) to O(n^3 log n).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A refinement of the cowaist inequality for Hermitian line bundles yields sharp stable two-systolic inequalities for odd-dimensional complex projective spaces.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"371263f6f32fc4290b9741baa69991bfec1e447da744547f335e9294426c6890"},"source":{"id":"2604.26891","kind":"arxiv","version":2},"verdict":{"id":"96988af7-9029-49aa-98dd-5b5a72b3c562","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T11:42:09.187606Z","strongest_claim":"We prove a refinement of Gromov's cowaist inequality in the case of Hermitian line bundles. Combined with the cowaist-systole estimates in recent work of Stryker, this gives sharp stable two-systolic inequalities for odd-dimensional complex projective spaces.","one_line_summary":"A refinement of Gromov's cowaist inequality for Hermitian line bundles produces sharp stable two-systolic inequalities for odd-dimensional CP^n and improves the stable two-systole upper bound for n-fold S^2 products from O(n^4 log n) to O(n^3 log n).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The refinement of the cowaist inequality is valid specifically for Hermitian line bundles, and the combination with Stryker's cowaist-systole estimates applies directly without further restrictions on the manifolds or bundles.","pith_extraction_headline":"A refinement of the cowaist inequality for Hermitian line bundles yields sharp stable two-systolic inequalities for odd-dimensional complex projective spaces."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26891/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T19:43:43.616171Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e987991d08fa922f531aa261dc8ceca878d237e799d4821cbf56f36e66b5eecc"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}