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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.","authors_text":"Yongsheng Jia, Yusen Long","cross_cats":["math.DS","math.GR"],"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.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-04-14T17:08:10Z","title":"Fine projection complex and subsurface homeomorphisms with positive stable commutator length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.12974","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T13:51:21.566805Z","id":"0f4f21f8-2293-433d-bb27-00512d600fcb","model_set":{"reader":"grok-4.3"},"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","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.","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)","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."}},"verdict_id":"0f4f21f8-2293-433d-bb27-00512d600fcb"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e3c0881ddf3c09534c4357bc3d7132eb487005f018686ffff0ce313c6e9fe244","target":"record","created_at":"2026-05-25T02:02:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7fc5b675b54567ed0445281818fb68807b9f5450e0bb8e5e794696260aad9b25","cross_cats_sorted":["math.DS","math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-04-14T17:08:10Z","title_canon_sha256":"d147b15c64deb46ed8be28b7afaeda1c6679a989ea0fa9c4a660e33e14f09c46"},"schema_version":"1.0","source":{"id":"2604.12974","kind":"arxiv","version":2}},"canonical_sha256":"9b3f9a83384c9f07513e7443544c64bf9e27010ba25a7158ec7f62be8fb21f95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b3f9a83384c9f07513e7443544c64bf9e27010ba25a7158ec7f62be8fb21f95","first_computed_at":"2026-05-25T02:02:15.250862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:15.250862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IS8eRjiiO9pkpNUz1hFDAJbtA3VTr7u2o23Ye6bw5hGc4DVYgwCTq7YialF5dAlvZumn2o6GUJUjQTZTD9E7DA==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:15.251654Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.12974","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3c0881ddf3c09534c4357bc3d7132eb487005f018686ffff0ce313c6e9fe244","sha256:b23ac2d623f36b1856d26171a6e55610e71de36e03eddd212561026bc7268054"],"state_sha256":"50eb36cf59b092748e0422d7db7cade0e9eec19e09213f72a3b6847b61159fa8"}