{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:FV7M3LP5HEGGQE5LDXNAQC6RCL","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":"6aa5ae6e5f6ff48ed2b02bf890bed8a5e088047b69ec13ec3f96d33833e2715d","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-04-07T12:18:28Z","title_canon_sha256":"4689302a2cf417f5a6cd8d03bd777568abcbd880a5ac052b5b76211811489d57"},"schema_version":"1.0","source":{"id":"math/0404162","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404162","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404162v3","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404162","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"FV7M3LP5HEGG","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"FV7M3LP5HEGGQE5L","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"FV7M3LP5","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:352d290448f8c57bbcc34a90620082f9b4fded2fd42a86a6ceace3e30453dfa3","target":"graph","created_at":"2026-05-18T02:38:00Z","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":"This is the third in our series of papers relating gauge theoretic invariants of certain 4-manifolds with invariants of 3-manifolds derived from Rohlin's theorem. Such relations are well-known in dimension three, starting with Casson's integral lift of the Rohlin invariant of a homology sphere. We consider two invariants of a spin 4-manifold that has the integral homology of a 4-torus. The first is a degree zero Donaldson invariant, counting flat connections on a certain SO(3)-bundle. The second, which depends on the choice of a 1-dimensional cohomology class, is a combination of Rohlin invari","authors_text":"Daniel Ruberman, Nikolai Saveliev","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-04-07T12:18:28Z","title":"Rohlin's invariant and gauge theory III. Homology 4--tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404162","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":"sha256:96da033ffdb279e116e353bcc00b8fbbfc94a1c167c61289e346e0e0464e6200","target":"record","created_at":"2026-05-18T02:38:00Z","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":"6aa5ae6e5f6ff48ed2b02bf890bed8a5e088047b69ec13ec3f96d33833e2715d","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2004-04-07T12:18:28Z","title_canon_sha256":"4689302a2cf417f5a6cd8d03bd777568abcbd880a5ac052b5b76211811489d57"},"schema_version":"1.0","source":{"id":"math/0404162","kind":"arxiv","version":3}},"canonical_sha256":"2d7ecdadfd390c6813ab1dda080bd112c963379815a972dffcf5f6653511eb58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d7ecdadfd390c6813ab1dda080bd112c963379815a972dffcf5f6653511eb58","first_computed_at":"2026-05-18T02:38:00.127053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.127053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2QyDNpJMjY5gs/Ge3aVZRXdJ3yUN5EPcy8+5LxLqg4HJTVEmDuMydIVqBQjtGdZqtf1f3Ykae20VPMVf2GY4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.127501Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404162","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96da033ffdb279e116e353bcc00b8fbbfc94a1c167c61289e346e0e0464e6200","sha256:352d290448f8c57bbcc34a90620082f9b4fded2fd42a86a6ceace3e30453dfa3"],"state_sha256":"43f6798b41007a32ae035e267c415c85d830c39debeed7ff2597a18a3cc66100"}