{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SJLHNOXPFNMKYP5QN5VT3OSJVW","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":"309faea4422bc349dc2eea58cbef07cdfc5d5e48e7ac3e9621fc32d5a0ce2c0f","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-04T15:59:19Z","title_canon_sha256":"c9567d16445c52af058241dc8ad0b39bb96afb11b4d087c9cfa6f9c6b546062b"},"schema_version":"1.0","source":{"id":"1509.01511","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01511","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01511v3","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01511","created_at":"2026-05-18T00:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"SJLHNOXPFNMK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SJLHNOXPFNMKYP5Q","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SJLHNOXP","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:f8b3f968779d832a3ae806cf64fc67e0590eab2cf6ce33edc56476aa23a84e06","target":"graph","created_at":"2026-05-18T00:13:38Z","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":"For a nullhomologous Legendrian knot in a closed contact 3-manifold Y we consider a contact structure obtained by positive rational contact surgery. We prove that in this situation the Heegaard Floer contact invariant of Y is mapped by a surgery cobordism to the contact invariant of the result of contact surgery. In addition we characterize the spin-c structure on the cobordism that induces the relevant map. As a consequence we determine necessary and sufficient conditions for the nonvanishing of the contact invariant after rational surgery when Y is the standard 3-sphere, generalizing previou","authors_text":"B\\\"ulent Tosun, Thomas E. Mark","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-04T15:59:19Z","title":"Naturality of Heegaard Floer invariants under positive rational contact surgery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01511","kind":"arxiv","version":3},"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:a925c9c1f93f915e6c4587f19459c4a3f714fd971e7d28f5478009352042cb42","target":"record","created_at":"2026-05-18T00:13:38Z","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":"309faea4422bc349dc2eea58cbef07cdfc5d5e48e7ac3e9621fc32d5a0ce2c0f","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-04T15:59:19Z","title_canon_sha256":"c9567d16445c52af058241dc8ad0b39bb96afb11b4d087c9cfa6f9c6b546062b"},"schema_version":"1.0","source":{"id":"1509.01511","kind":"arxiv","version":3}},"canonical_sha256":"925676baef2b58ac3fb06f6b3dba49adbbf99ce1729f538fe53f8f9ddd6057be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"925676baef2b58ac3fb06f6b3dba49adbbf99ce1729f538fe53f8f9ddd6057be","first_computed_at":"2026-05-18T00:13:38.285881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:38.285881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0SwgOJ4uzR+VDZsWJhoTxpX6Sbb2OGwx27ItYNKrkBp3TgKNrz04ls+2KbQ1wNO4Vid52UKr1TZr12QzULHgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:38.286489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01511","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a925c9c1f93f915e6c4587f19459c4a3f714fd971e7d28f5478009352042cb42","sha256:f8b3f968779d832a3ae806cf64fc67e0590eab2cf6ce33edc56476aa23a84e06"],"state_sha256":"f673f936efd4cd4766dadec108e32b197e4264013b2ff18ca11aadda4b070c42"}