{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:HWW5BO2TWCZO3POGMWNC2MTWFC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3dde86bef570263d596f1df5614105320afd433d73fb3dc7cfb500156d51a133","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2004-05-16T21:44:42Z","title_canon_sha256":"5bd80a1efab8af097b933a17ef23655883fc1e3e89959308252256063d24872e"},"schema_version":"1.0","source":{"id":"math/0405314","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0405314","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0405314v2","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0405314","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"HWW5BO2TWCZO","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"HWW5BO2TWCZO3POG","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"HWW5BO2T","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a1490a049760c39ea51822aff3a3feda31e77bd1cb5bca502a884ab47a8c55a3","target":"graph","created_at":"2026-05-18T02:41:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We calculate the Heegaard Floer homologies$HF^+(M,s) for mapping tori M associated to certain surface diffeomorphisms, where s is any Spin^c structure on M whose first Chern class is non-torsion. Let gamma and delta be a pair of geometrically dual nonseparating curves on a genus g Riemann surface Sigma_g, and let sigma be a curve separating Sigma_g into components of genus 1 and g-1. Write t-gamma, t_delta, and t_sigma for the right-handed Dehn twists about each of these curves. The examples we consider are the mapping tori of the diffeomorphisms t_gamma^m circ t_delta^n for m,n in Z and that ","authors_text":"Stanislav Jabuka, Thomas Mark","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-05-16T21:44:42Z","title":"Heegaard Floer homology of certain mapping tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405314","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a5bff2617e093101493d8eedc7313dfa9b3bef8801096478aaa4c169e4ed2450","target":"record","created_at":"2026-05-18T02:41:32Z","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":"3dde86bef570263d596f1df5614105320afd433d73fb3dc7cfb500156d51a133","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2004-05-16T21:44:42Z","title_canon_sha256":"5bd80a1efab8af097b933a17ef23655883fc1e3e89959308252256063d24872e"},"schema_version":"1.0","source":{"id":"math/0405314","kind":"arxiv","version":2}},"canonical_sha256":"3dadd0bb53b0b2edbdc6659a2d32762882030d5eef634b1e8b01796049334d86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dadd0bb53b0b2edbdc6659a2d32762882030d5eef634b1e8b01796049334d86","first_computed_at":"2026-05-18T02:41:32.452015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:32.452015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"roL3m54XnzsD02fE8YPa6oLhghzY2xkBB8bw80O93QL5Sz1jUcgwgLfQ23ByV0MRrsaJVtYopwQCzrdeor6BCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:32.452460Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0405314","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5bff2617e093101493d8eedc7313dfa9b3bef8801096478aaa4c169e4ed2450","sha256:a1490a049760c39ea51822aff3a3feda31e77bd1cb5bca502a884ab47a8c55a3"],"state_sha256":"bd5a75bff30f1682bfb0de78e2bdc608f6815d98323357f8200a640a0f08bf6e"}