{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TM7ZVAZYJSPQOUJ6ORBVITDEX6","short_pith_number":"pith:TM7ZVAZY","schema_version":"1.0","canonical_sha256":"9b3f9a83384c9f07513e7443544c64bf9e27010ba25a7158ec7f62be8fb21f95","source":{"kind":"arxiv","id":"2604.12974","version":2},"attestation_state":"computed","paper":{"title":"Fine projection complex and subsurface homeomorphisms with positive stable commutator length","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface.","cross_cats":["math.DS","math.GR"],"primary_cat":"math.GT","authors_text":"Yongsheng Jia, Yusen Long","submitted_at":"2026-04-14T17:08:10Z","abstract_excerpt":"Drawing inspiration from [BBF15], we construct a family of unbounded quasi-trees for a connected closed oriented surface $S_g$ of genus $g\\geq 2$, upon which the group $\\mathrm{Homeo}_0(S_g)$ acts coboundedly by isometries. As an application, we show that some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in $\\mathrm{Homeo}_0(S_g)$. Moreover, we provide a version of projection complex that does not require the finiteness condition."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2604.12974","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-04-14T17:08:10Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"d147b15c64deb46ed8be28b7afaeda1c6679a989ea0fa9c4a660e33e14f09c46","abstract_canon_sha256":"7fc5b675b54567ed0445281818fb68807b9f5450e0bb8e5e794696260aad9b25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:15.251654Z","signature_b64":"IS8eRjiiO9pkpNUz1hFDAJbtA3VTr7u2o23Ye6bw5hGc4DVYgwCTq7YialF5dAlvZumn2o6GUJUjQTZTD9E7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b3f9a83384c9f07513e7443544c64bf9e27010ba25a7158ec7f62be8fb21f95","last_reissued_at":"2026-05-25T02:02:15.250862Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:15.250862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fine projection complex and subsurface homeomorphisms with positive stable commutator length","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface.","cross_cats":["math.DS","math.GR"],"primary_cat":"math.GT","authors_text":"Yongsheng Jia, Yusen Long","submitted_at":"2026-04-14T17:08:10Z","abstract_excerpt":"Drawing inspiration from [BBF15], we construct a family of unbounded quasi-trees for a connected closed oriented surface $S_g$ of genus $g\\geq 2$, upon which the group $\\mathrm{Homeo}_0(S_g)$ acts coboundedly by isometries. As an application, we show that some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in $\\mathrm{Homeo}_0(S_g)$. Moreover, we provide a version of projection complex that does not require the finiteness condition."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in Homeo_0(S_g)","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The family of unbounded quasi-trees exists with the stated cobounded isometric action for every closed oriented surface of genus g >= 2, and the projection complex construction succeeds without the usual finiteness conditions on the subsurface data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A finiteness-free projection complex yields unbounded quasi-trees for Homeo_0(S_g) with cobounded isometric actions, proving positive scl for subsurface-preserving homeomorphisms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8e5d41e8c794c17009929756acdd0c39835718ca131e462487fc88fd81b10f15"},"source":{"id":"2604.12974","kind":"arxiv","version":2},"verdict":{"id":"0f4f21f8-2293-433d-bb27-00512d600fcb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T13:51:21.566805Z","strongest_claim":"some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in Homeo_0(S_g)","one_line_summary":"A finiteness-free projection complex yields unbounded quasi-trees for Homeo_0(S_g) with cobounded isometric actions, proving positive scl for subsurface-preserving homeomorphisms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The family of unbounded quasi-trees exists with the stated cobounded isometric action for every closed oriented surface of genus g >= 2, and the projection complex construction succeeds without the usual finiteness conditions on the subsurface data.","pith_extraction_headline":"Some surface homeomorphisms that preserve a non-sporadic essential subsurface or a once-bordered torus have positive stable commutator length inside the identity component of the homeomorphism group of a closed surface."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.12974/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2604.12974","created_at":"2026-05-25T02:02:15.250961+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.12974v2","created_at":"2026-05-25T02:02:15.250961+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.12974","created_at":"2026-05-25T02:02:15.250961+00:00"},{"alias_kind":"pith_short_12","alias_value":"TM7ZVAZYJSPQ","created_at":"2026-05-25T02:02:15.250961+00:00"},{"alias_kind":"pith_short_16","alias_value":"TM7ZVAZYJSPQOUJ6","created_at":"2026-05-25T02:02:15.250961+00:00"},{"alias_kind":"pith_short_8","alias_value":"TM7ZVAZY","created_at":"2026-05-25T02:02:15.250961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6","json":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6.json","graph_json":"https://pith.science/api/pith-number/TM7ZVAZYJSPQOUJ6ORBVITDEX6/graph.json","events_json":"https://pith.science/api/pith-number/TM7ZVAZYJSPQOUJ6ORBVITDEX6/events.json","paper":"https://pith.science/paper/TM7ZVAZY"},"agent_actions":{"view_html":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6","download_json":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6.json","view_paper":"https://pith.science/paper/TM7ZVAZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.12974&json=true","fetch_graph":"https://pith.science/api/pith-number/TM7ZVAZYJSPQOUJ6ORBVITDEX6/graph.json","fetch_events":"https://pith.science/api/pith-number/TM7ZVAZYJSPQOUJ6ORBVITDEX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6/action/storage_attestation","attest_author":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6/action/author_attestation","sign_citation":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6/action/citation_signature","submit_replication":"https://pith.science/pith/TM7ZVAZYJSPQOUJ6ORBVITDEX6/action/replication_record"}},"created_at":"2026-05-25T02:02:15.250961+00:00","updated_at":"2026-05-25T02:02:15.250961+00:00"}