{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FLF7EN3ZV56PZKVUGN63MCUIBQ","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":"c33d23cab47b057e42eaa942e3ccbfabc32eab7b68c4472974f5c5a95ee831dc","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-08-30T13:19:21Z","title_canon_sha256":"08a62308e9213a7d29ca3f06abab40a22cbdbd7fe3578291fd951d4d506f5ef3"},"schema_version":"1.0","source":{"id":"2008.13165","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.13165","created_at":"2026-07-05T07:35:33Z"},{"alias_kind":"arxiv_version","alias_value":"2008.13165v3","created_at":"2026-07-05T07:35:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.13165","created_at":"2026-07-05T07:35:33Z"},{"alias_kind":"pith_short_12","alias_value":"FLF7EN3ZV56P","created_at":"2026-07-05T07:35:33Z"},{"alias_kind":"pith_short_16","alias_value":"FLF7EN3ZV56PZKVU","created_at":"2026-07-05T07:35:33Z"},{"alias_kind":"pith_short_8","alias_value":"FLF7EN3Z","created_at":"2026-07-05T07:35:33Z"}],"graph_snapshots":[{"event_id":"sha256:cae8aa1f349322ed0e639657a1be15e27148a181ff6c59fcf8c86a1845d23bcb","target":"graph","created_at":"2026-07-05T07:35:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.13165/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We initiate the study of multiplicative structures on cones and show that cones of Floer continuation maps fit naturally in this framework. We apply this to give a new description of the multiplicative structure on Rabinowitz Floer homology and cohomology, and to give a new proof of the Poincar\\'e duality theorem which relates the two. The underlying algebraic structure admits two incarnations, both new, which we study and compare: on the one hand the structure of $A_2^+$-algebra on the space $\\mathcal{A}$ of Floer chains, and on the other hand the structure of $A_2$-algebra involving $\\mathca","authors_text":"Alexandru Oancea, Kai Cieliebak","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-08-30T13:19:21Z","title":"Multiplicative structures on cones and duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.13165","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:ddb1137401909adf34306b55000efa56c2a7f1677a874c7bece55bf474d63b22","target":"record","created_at":"2026-07-05T07:35:33Z","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":"c33d23cab47b057e42eaa942e3ccbfabc32eab7b68c4472974f5c5a95ee831dc","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-08-30T13:19:21Z","title_canon_sha256":"08a62308e9213a7d29ca3f06abab40a22cbdbd7fe3578291fd951d4d506f5ef3"},"schema_version":"1.0","source":{"id":"2008.13165","kind":"arxiv","version":3}},"canonical_sha256":"2acbf23779af7cfcaab4337db60a880c0d2dfe649919fe73976c5fb5309153ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2acbf23779af7cfcaab4337db60a880c0d2dfe649919fe73976c5fb5309153ee","first_computed_at":"2026-07-05T07:35:33.423017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:35:33.423017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z6pDYcLkj+pDE1A0NCW0mF+N/G74M4nEUHQQ68/2hca+wttRpelr17/sSeVi9JodXXAmObfFgkTcqWHQVoVyAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:35:33.423531Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.13165","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddb1137401909adf34306b55000efa56c2a7f1677a874c7bece55bf474d63b22","sha256:cae8aa1f349322ed0e639657a1be15e27148a181ff6c59fcf8c86a1845d23bcb"],"state_sha256":"97251e4324b642d8e260346e23c59c374d12b07884131566da44c29b911455c4"}