{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YYZ2W7VOY3GNKJLVJQ4ZQBCKSY","short_pith_number":"pith:YYZ2W7VO","canonical_record":{"source":{"id":"1003.0598","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2010-03-02T20:40:14Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"26f57e02e2db0a075f1effb9a3f20ead14f832311d84147f72599f93bad199ca","abstract_canon_sha256":"b2fa09cf5c439bb9f9d66943bfd834ff9f4461227f3fa92b544781a0d69c1d41"},"schema_version":"1.0"},"canonical_sha256":"c633ab7eaec6ccd525754c3998044a961793119961f48046398d20a51d61a3a2","source":{"kind":"arxiv","id":"1003.0598","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0598","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0598v4","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0598","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"YYZ2W7VOY3GN","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YYZ2W7VOY3GNKJLV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YYZ2W7VO","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YYZ2W7VOY3GNKJLVJQ4ZQBCKSY","target":"record","payload":{"canonical_record":{"source":{"id":"1003.0598","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2010-03-02T20:40:14Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"26f57e02e2db0a075f1effb9a3f20ead14f832311d84147f72599f93bad199ca","abstract_canon_sha256":"b2fa09cf5c439bb9f9d66943bfd834ff9f4461227f3fa92b544781a0d69c1d41"},"schema_version":"1.0"},"canonical_sha256":"c633ab7eaec6ccd525754c3998044a961793119961f48046398d20a51d61a3a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:29.383086Z","signature_b64":"2q5ds2RGq9e9K9XCESQWTC6p8uFULvDVA9kwEo5/92M1Ab4HhjcKwhy7hrq5ks0yPTpsrr5mDxudxVC6ogDgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c633ab7eaec6ccd525754c3998044a961793119961f48046398d20a51d61a3a2","last_reissued_at":"2026-05-18T01:22:29.382388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:29.382388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.0598","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ynw2A95Yx43Rn5vUT5CAYijkXS+SPq9ip8RUNFS1+IMn2cRi6x0+14ApB+uOTu5WALtnTgDthOOYZBuaxzBzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:48:58.869230Z"},"content_sha256":"5fa0fd1ad40bd887a9329238d38bfd1563f48ab0690d493e81b6898d2c942d1c","schema_version":"1.0","event_id":"sha256:5fa0fd1ad40bd887a9329238d38bfd1563f48ab0690d493e81b6898d2c942d1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YYZ2W7VOY3GNKJLVJQ4ZQBCKSY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bimodules in bordered Heegaard Floer homology","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Dylan P. Thurston, Peter S. Ozsvath, Robert Lipshitz","submitted_at":"2010-03-02T20:40:14Z","abstract_excerpt":"Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A(F). In this paper, we establish naturality properties of this invariant. Changing the diffeomorphism between F and the boundary of Y tensors the bordered invariant with a suitable bimodule over A(F). These bimodules give an action of a suitably based mapping class group on the category of modules over A(F). The Hochschild homology of such a bimodule is identified with the knot Floer homology of the associated op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0598","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n/+1kEDhkQ2611GLSIa40G+5IwqHwSAVd0YP2HQAHItWVKq3LICvMYk4z2N9P11/xMXh1Ko5rTdbKSwVirouDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:48:58.869911Z"},"content_sha256":"822b3c17c5753052ae25cf817238b4ebb4f5054a7452ed06e98b2ebc973ecbd5","schema_version":"1.0","event_id":"sha256:822b3c17c5753052ae25cf817238b4ebb4f5054a7452ed06e98b2ebc973ecbd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYZ2W7VOY3GNKJLVJQ4ZQBCKSY/bundle.json","state_url":"https://pith.science/pith/YYZ2W7VOY3GNKJLVJQ4ZQBCKSY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYZ2W7VOY3GNKJLVJQ4ZQBCKSY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T14:48:58Z","links":{"resolver":"https://pith.science/pith/YYZ2W7VOY3GNKJLVJQ4ZQBCKSY","bundle":"https://pith.science/pith/YYZ2W7VOY3GNKJLVJQ4ZQBCKSY/bundle.json","state":"https://pith.science/pith/YYZ2W7VOY3GNKJLVJQ4ZQBCKSY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYZ2W7VOY3GNKJLVJQ4ZQBCKSY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YYZ2W7VOY3GNKJLVJQ4ZQBCKSY","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":"b2fa09cf5c439bb9f9d66943bfd834ff9f4461227f3fa92b544781a0d69c1d41","cross_cats_sorted":["math.SG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2010-03-02T20:40:14Z","title_canon_sha256":"26f57e02e2db0a075f1effb9a3f20ead14f832311d84147f72599f93bad199ca"},"schema_version":"1.0","source":{"id":"1003.0598","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0598","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0598v4","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0598","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"YYZ2W7VOY3GN","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YYZ2W7VOY3GNKJLV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YYZ2W7VO","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:822b3c17c5753052ae25cf817238b4ebb4f5054a7452ed06e98b2ebc973ecbd5","target":"graph","created_at":"2026-05-18T01:22:29Z","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":"Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A(F). In this paper, we establish naturality properties of this invariant. Changing the diffeomorphism between F and the boundary of Y tensors the bordered invariant with a suitable bimodule over A(F). These bimodules give an action of a suitably based mapping class group on the category of modules over A(F). The Hochschild homology of such a bimodule is identified with the knot Floer homology of the associated op","authors_text":"Dylan P. Thurston, Peter S. Ozsvath, Robert Lipshitz","cross_cats":["math.SG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2010-03-02T20:40:14Z","title":"Bimodules in bordered Heegaard Floer homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0598","kind":"arxiv","version":4},"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":"sha256:5fa0fd1ad40bd887a9329238d38bfd1563f48ab0690d493e81b6898d2c942d1c","target":"record","created_at":"2026-05-18T01:22:29Z","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":"b2fa09cf5c439bb9f9d66943bfd834ff9f4461227f3fa92b544781a0d69c1d41","cross_cats_sorted":["math.SG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.GT","submitted_at":"2010-03-02T20:40:14Z","title_canon_sha256":"26f57e02e2db0a075f1effb9a3f20ead14f832311d84147f72599f93bad199ca"},"schema_version":"1.0","source":{"id":"1003.0598","kind":"arxiv","version":4}},"canonical_sha256":"c633ab7eaec6ccd525754c3998044a961793119961f48046398d20a51d61a3a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c633ab7eaec6ccd525754c3998044a961793119961f48046398d20a51d61a3a2","first_computed_at":"2026-05-18T01:22:29.382388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:29.382388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2q5ds2RGq9e9K9XCESQWTC6p8uFULvDVA9kwEo5/92M1Ab4HhjcKwhy7hrq5ks0yPTpsrr5mDxudxVC6ogDgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:29.383086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.0598","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fa0fd1ad40bd887a9329238d38bfd1563f48ab0690d493e81b6898d2c942d1c","sha256:822b3c17c5753052ae25cf817238b4ebb4f5054a7452ed06e98b2ebc973ecbd5"],"state_sha256":"897ca8eef821704393fa0423001f3d72b444c6fde66f17a4d7c1ccd30b9e9200"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hXktfGYAMcXDet7v/MMgJ1siLF8/R0bXyuD1qPAYIXGA2iv6pZkZQMuLsPih0CIAqirot0GDzxuxkEaTjlzyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:48:58.873542Z","bundle_sha256":"f96630bba85eb9d77ba04ffd4ed91f8590ba70e1f1194a2c5c27d2e2e8737c43"}}