{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SX5FKPXWJJDL734NKJGECPATZI","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":"e44037588a936ce3f00b45f8252448c4d7af84e691dadd520e26495179dda068","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-09-27T13:16:11Z","title_canon_sha256":"438c97cf8a24e1b14b83993a9cd7868a150dda811b92e41ee19e0e7d93cc5b66"},"schema_version":"1.0","source":{"id":"1609.08400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08400","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08400v2","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08400","created_at":"2026-05-18T01:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"SX5FKPXWJJDL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SX5FKPXWJJDL734N","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SX5FKPXW","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:358ab05e8106165c60274f232f92316a0c3a30ab845fad1ee72b5b4e922366b9","target":"graph","created_at":"2026-05-18T01:03:42Z","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 prove that a pairing between the Fukaya category and the oo-category of Lagrangian cobordisms respects mapping cones. This is another step toward constructing a lift of Fukaya categories to the level of spectra (in the sense of stable homotopy theory). As corollaries, we show that the map in our previous work from cobordism groups to Floer cohomology lifts to the level of spectra, and one also recovers some results of Biran and Cornea for what we call \"vertically collared\" cobordisms.","authors_text":"Hiro Lee Tanaka","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-09-27T13:16:11Z","title":"The Fukaya category pairs with Lagrangian cobordisms exactly"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08400","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:e6f5ee65d90d2bf84b68433445445bc7b36ae03b74697ef60b5b46f0c8c985d0","target":"record","created_at":"2026-05-18T01:03:42Z","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":"e44037588a936ce3f00b45f8252448c4d7af84e691dadd520e26495179dda068","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-09-27T13:16:11Z","title_canon_sha256":"438c97cf8a24e1b14b83993a9cd7868a150dda811b92e41ee19e0e7d93cc5b66"},"schema_version":"1.0","source":{"id":"1609.08400","kind":"arxiv","version":2}},"canonical_sha256":"95fa553ef64a46bfef8d524c413c13ca1aa84cebdfd27210c24f81049a2c6a22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95fa553ef64a46bfef8d524c413c13ca1aa84cebdfd27210c24f81049a2c6a22","first_computed_at":"2026-05-18T01:03:42.405190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:42.405190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xeR5bGEgoq8357MK/Lr/Y3kUHyP3Xp/ScgDFY2PyN3zw2/8a7h6Q41PnskVNZeE1qBavdMPjqlSL3nCdIppCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:42.405850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08400","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6f5ee65d90d2bf84b68433445445bc7b36ae03b74697ef60b5b46f0c8c985d0","sha256:358ab05e8106165c60274f232f92316a0c3a30ab845fad1ee72b5b4e922366b9"],"state_sha256":"d634f4fe090dd61210ad068abbd9e3dcdc0d954e68d66fd08ac51abfbbfcdd1e"}