{"paper":{"title":"Uniform spectral gap of scl in $2$-orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Compact hyperbolic 2-orbifolds have a uniform spectral gap for stable commutator length relative to peripheral subgroups.","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Lvzhou Chen, Nicolaus Heuer","submitted_at":"2026-04-22T20:02:16Z","abstract_excerpt":"We show a uniform spectral gap of stable commutator length for all compact hyperbolic $2$-orbifolds relative to the peripheral subgroups. Except for the case of a sphere with three cone points, we have an explicit uniform gap $1/36$. These estimates are needed in understanding stable commutator length in $3$-manifolds. Our methods use explicit quasimorphisms for the generic case, and use hyperbolic geometry (pleated surfaces) for the exceptional case of a sphere with three cone points."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show a uniform spectral gap of stable commutator length for all compact hyperbolic 2-orbifolds relative to the peripheral subgroups. Except for the case of a sphere with three cone points, we have an explicit uniform gap 1/36.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the orbifolds are compact and hyperbolic, together with the existence of sufficiently many explicit quasimorphisms or pleated surfaces that achieve the gap without depending on the particular orbifold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Stable commutator length admits a uniform spectral gap of 1/36 relative to peripheral subgroups in all compact hyperbolic 2-orbifolds except the sphere with three cone points.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Compact hyperbolic 2-orbifolds have a uniform spectral gap for stable commutator length relative to peripheral subgroups.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6362842ec64612fa51defd1c91f65128f1592a0f58b795621908e94dd7533e36"},"source":{"id":"2604.21059","kind":"arxiv","version":2},"verdict":{"id":"edd6310e-f794-4691-b09c-be5d31858144","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T22:25:32.446767Z","strongest_claim":"We show a uniform spectral gap of stable commutator length for all compact hyperbolic 2-orbifolds relative to the peripheral subgroups. Except for the case of a sphere with three cone points, we have an explicit uniform gap 1/36.","one_line_summary":"Stable commutator length admits a uniform spectral gap of 1/36 relative to peripheral subgroups in all compact hyperbolic 2-orbifolds except the sphere with three cone points.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the orbifolds are compact and hyperbolic, together with the existence of sufficiently many explicit quasimorphisms or pleated surfaces that achieve the gap without depending on the particular orbifold.","pith_extraction_headline":"Compact hyperbolic 2-orbifolds have a uniform spectral gap for stable commutator length relative to peripheral subgroups."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.21059/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T13:38:12.057387Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T01:21:54.284920Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"40ed31c5dff71f918d362ecd79a6ba73f5968e1bd5e9cff5dd83151f2a8d2109"},"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"}