{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NP7DWRRMOCSYIP7NMKHV6C2V76","short_pith_number":"pith:NP7DWRRM","schema_version":"1.0","canonical_sha256":"6bfe3b462c70a5843fed628f5f0b55ffa96cfc755663d91888a7284af8f98d1a","source":{"kind":"arxiv","id":"1711.07062","version":4},"attestation_state":"computed","paper":{"title":"A Morse theoretic description of the Goresky-Hingston product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Arun Maiti","submitted_at":"2017-11-19T19:19:01Z","abstract_excerpt":"The Goresky-Hingston coproduct was first introduced by D. Sullivan and later extended by M. Goresky and N. Hingston. In this article we give a Morse theoretic description of the coproduct. Using the description we prove homotopy invariance property of the coproduct. We describe a connection between our Morse theoretic coproduct and a coproduct on Floer homology of cotangent bundle."},"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":"1711.07062","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-19T19:19:01Z","cross_cats_sorted":[],"title_canon_sha256":"f0d111827d0af847848e3bdd7ccff4b7253550cee4703e255bc1f3968ba38eee","abstract_canon_sha256":"f4c83ede9d009be45e6321db07b23d274fe739d43bc63ce0b6fa46a00026e939"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:45:21.763920Z","signature_b64":"lbEUpz7QXMfY9mtqasF2QlSpFOJ08mhgvR8HNCt2+SDNdPM4KI1OINcKT91KP6IUcCLQVKkeXRc1GEmCVOirCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bfe3b462c70a5843fed628f5f0b55ffa96cfc755663d91888a7284af8f98d1a","last_reissued_at":"2026-07-05T05:45:21.763510Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:45:21.763510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Morse theoretic description of the Goresky-Hingston product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Arun Maiti","submitted_at":"2017-11-19T19:19:01Z","abstract_excerpt":"The Goresky-Hingston coproduct was first introduced by D. Sullivan and later extended by M. Goresky and N. Hingston. In this article we give a Morse theoretic description of the coproduct. Using the description we prove homotopy invariance property of the coproduct. We describe a connection between our Morse theoretic coproduct and a coproduct on Floer homology of cotangent bundle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07062","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1711.07062/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":"1711.07062","created_at":"2026-07-05T05:45:21.763568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.07062v4","created_at":"2026-07-05T05:45:21.763568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07062","created_at":"2026-07-05T05:45:21.763568+00:00"},{"alias_kind":"pith_short_12","alias_value":"NP7DWRRMOCSY","created_at":"2026-07-05T05:45:21.763568+00:00"},{"alias_kind":"pith_short_16","alias_value":"NP7DWRRMOCSYIP7N","created_at":"2026-07-05T05:45:21.763568+00:00"},{"alias_kind":"pith_short_8","alias_value":"NP7DWRRM","created_at":"2026-07-05T05:45:21.763568+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/NP7DWRRMOCSYIP7NMKHV6C2V76","json":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76.json","graph_json":"https://pith.science/api/pith-number/NP7DWRRMOCSYIP7NMKHV6C2V76/graph.json","events_json":"https://pith.science/api/pith-number/NP7DWRRMOCSYIP7NMKHV6C2V76/events.json","paper":"https://pith.science/paper/NP7DWRRM"},"agent_actions":{"view_html":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76","download_json":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76.json","view_paper":"https://pith.science/paper/NP7DWRRM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.07062&json=true","fetch_graph":"https://pith.science/api/pith-number/NP7DWRRMOCSYIP7NMKHV6C2V76/graph.json","fetch_events":"https://pith.science/api/pith-number/NP7DWRRMOCSYIP7NMKHV6C2V76/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76/action/storage_attestation","attest_author":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76/action/author_attestation","sign_citation":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76/action/citation_signature","submit_replication":"https://pith.science/pith/NP7DWRRMOCSYIP7NMKHV6C2V76/action/replication_record"}},"created_at":"2026-07-05T05:45:21.763568+00:00","updated_at":"2026-07-05T05:45:21.763568+00:00"}