{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:HL5BJWWZUILMX5JGDMSQZFKCBR","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":"67c330e37f0b0a68b6e16ba7b18a29d71ae80ece89493a5248492c452d503423","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2003-07-16T10:10:08Z","title_canon_sha256":"376a8653d48994f99b342a334d52aeb1ad624846a602b9ce0d043d89f3829a1a"},"schema_version":"1.0","source":{"id":"math/0307218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307218","created_at":"2026-07-04T14:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307218v2","created_at":"2026-07-04T14:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307218","created_at":"2026-07-04T14:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"HL5BJWWZUILM","created_at":"2026-07-04T14:37:36Z"},{"alias_kind":"pith_short_16","alias_value":"HL5BJWWZUILMX5JG","created_at":"2026-07-04T14:37:36Z"},{"alias_kind":"pith_short_8","alias_value":"HL5BJWWZ","created_at":"2026-07-04T14:37:36Z"}],"graph_snapshots":[{"event_id":"sha256:ea7d6e450518986ec15d0fe788c9043e554ac3e167181860ac54e88d6f1782f7","target":"graph","created_at":"2026-07-04T14:37:36Z","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/math/0307218/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in R^3.","authors_text":"Alberto S. Cattaneo, Paolo Cotta-Ramusino, Riccardo Longoni","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2003-07-16T10:10:08Z","title":"Algebraic structures on graph cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307218","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":"sha256:86fad6788b1dfbd2eea3d2ff8c8c915f6aaef08f8dedf95c14aa53a2e9ffce39","target":"record","created_at":"2026-07-04T14:37:36Z","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":"67c330e37f0b0a68b6e16ba7b18a29d71ae80ece89493a5248492c452d503423","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2003-07-16T10:10:08Z","title_canon_sha256":"376a8653d48994f99b342a334d52aeb1ad624846a602b9ce0d043d89f3829a1a"},"schema_version":"1.0","source":{"id":"math/0307218","kind":"arxiv","version":2}},"canonical_sha256":"3afa14dad9a216cbf5261b250c95420c53f4c24c3bd6b25af06446abb9a4572e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3afa14dad9a216cbf5261b250c95420c53f4c24c3bd6b25af06446abb9a4572e","first_computed_at":"2026-07-04T14:37:36.079727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:37:36.079727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5B4kqhFv/2HupjeM5Ud5rUTHHtuxksFR5lPXdEyrwbBGd55Y8X7tqv143XHCNbzrGwvfGAhVWNSlFAGHtfdEBg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:37:36.080111Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0307218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86fad6788b1dfbd2eea3d2ff8c8c915f6aaef08f8dedf95c14aa53a2e9ffce39","sha256:ea7d6e450518986ec15d0fe788c9043e554ac3e167181860ac54e88d6f1782f7"],"state_sha256":"ddbbc34a2632f91edea597a94a3599a902599f958596d61619a74defd0bad25d"}