{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RPCDNR2VH2RKBT6FLEXRJHIMPA","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":"d2207d08a63d7c31bd53d831bfb1726ab934c1b332e2bd9c3ed6ba890fb2f7fe","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-26T12:51:54Z","title_canon_sha256":"d6e0410c251ad976c218269c656284a35f9fe7ba3f1ace76d39dc2411c50ca17"},"schema_version":"1.0","source":{"id":"1202.5754","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5754","created_at":"2026-05-18T02:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5754v5","created_at":"2026-05-18T02:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5754","created_at":"2026-05-18T02:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"RPCDNR2VH2RK","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RPCDNR2VH2RKBT6F","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RPCDNR2V","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:99babea84a63f4f4925fab2ce1cee4700ede0e48c08f29b801d2ec9353ded78e","target":"graph","created_at":"2026-05-18T02:16:48Z","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 give a generalization of Fukaya's Morse homotopy theoretic approach for 2-loop Chern--Simons perturbation theory to 3-valent graphs with arbitrary number of loops at least 2. We construct a sequence of invariants of integral homology 3-spheres with values in a space of 3-valent graphs (Jacobi diagrams or Feynman diagrams) by counting graphs in an integral homology 3-sphere satisfying certain condition described by a set of ordinary differential equations.","authors_text":"Tadayuki Watanabe","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-26T12:51:54Z","title":"Higher order generalization of Fukaya's Morse homotopy invariant of 3-manifolds I. Invariants of homology 3-spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5754","kind":"arxiv","version":5},"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":"sha256:774a442e144dcd850a448d1ac3569303dd4f9392bb49f5e39ff4651d3486adfc","target":"record","created_at":"2026-05-18T02:16:48Z","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":"d2207d08a63d7c31bd53d831bfb1726ab934c1b332e2bd9c3ed6ba890fb2f7fe","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-02-26T12:51:54Z","title_canon_sha256":"d6e0410c251ad976c218269c656284a35f9fe7ba3f1ace76d39dc2411c50ca17"},"schema_version":"1.0","source":{"id":"1202.5754","kind":"arxiv","version":5}},"canonical_sha256":"8bc436c7553ea2a0cfc5592f149d0c783d3c48d23638b22931744fcf415eba14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bc436c7553ea2a0cfc5592f149d0c783d3c48d23638b22931744fcf415eba14","first_computed_at":"2026-05-18T02:16:48.288415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:48.288415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F6NmBw5mGdeI6BOHracmBa64woaOQQFAH/fjXSW0N/r2cbumER87w8sloiBubATB1UtCLzdzdxWNXNHbEUHbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:48.289095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5754","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:774a442e144dcd850a448d1ac3569303dd4f9392bb49f5e39ff4651d3486adfc","sha256:99babea84a63f4f4925fab2ce1cee4700ede0e48c08f29b801d2ec9353ded78e"],"state_sha256":"575a564704d091dada0b6bd50284a51170a73b1da246d5c473a47daad9fed808"}