{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:EZUCJL432G4DHS423QS2ZTW3FF","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":"8059f841efe0f0a77631ea262ef301beab1c3110da92a45d6aaa0a4abc3770ac","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-04-09T11:24:32Z","title_canon_sha256":"afe3fefe730f7a3abe66a41a2a1b98fd3fb60968fdb92e2628756d879f86dd32"},"schema_version":"1.0","source":{"id":"math/0404196","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404196","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404196v2","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404196","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"pith_short_12","alias_value":"EZUCJL432G4D","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"EZUCJL432G4DHS42","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"EZUCJL43","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:25ec57a2e367bff0f75b7b904119a7b2e1db30e321dcd1ddd7cb16dfd62ed232","target":"graph","created_at":"2026-05-18T01:38:28Z","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 construct nontrivial cohomology classes of the space $Imb(S^1,\\R^n)$ of imbeddings of the circle into $\\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\\geq 4$, a de Rham cohomology class on $Imb(S^1,\\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.","authors_text":"Riccardo Longoni","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-04-09T11:24:32Z","title":"Nontrivial classes in $H^*(Imb(S^1,\\R^n))$ from nontrivalent graph cocycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404196","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":"sha256:86eda8905ce367ac98b8bcc0658c462b9a6e4675868edc6e2e8d441cb7a65997","target":"record","created_at":"2026-05-18T01:38:28Z","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":"8059f841efe0f0a77631ea262ef301beab1c3110da92a45d6aaa0a4abc3770ac","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-04-09T11:24:32Z","title_canon_sha256":"afe3fefe730f7a3abe66a41a2a1b98fd3fb60968fdb92e2628756d879f86dd32"},"schema_version":"1.0","source":{"id":"math/0404196","kind":"arxiv","version":2}},"canonical_sha256":"266824af9bd1b833cb9adc25accedb2949fe44c52c425f16523b17b6e534ce0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"266824af9bd1b833cb9adc25accedb2949fe44c52c425f16523b17b6e534ce0f","first_computed_at":"2026-05-18T01:38:28.421550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:28.421550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jkh4oyXXPdY89hMGfRCNlBkgRbPb/ssq3lH5BV864ObmDV0pQlU92ifHjq5mYDEB974I3WO5Ytvlh4CU0s4OBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:28.422285Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404196","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86eda8905ce367ac98b8bcc0658c462b9a6e4675868edc6e2e8d441cb7a65997","sha256:25ec57a2e367bff0f75b7b904119a7b2e1db30e321dcd1ddd7cb16dfd62ed232"],"state_sha256":"7c6ac15d152227dfb51b3a5a7e719ce729bb6a67f5e23209db0f78e73ec15807"}