{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HBUMZWA73PJJHHG6XTYOT3N2A2","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":"aede5448b73b14096b82d7486202ef26849c41944485e5d1025a8af52f78c19c","cross_cats_sorted":["math-ph","math.AG","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SG","submitted_at":"2012-10-19T05:41:29Z","title_canon_sha256":"22897b86eed873ffb667c1c19dc74af11a6040f67cae4341b9f2cf0b5fffd7f4"},"schema_version":"1.0","source":{"id":"1210.5320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5320","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5320v1","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5320","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"HBUMZWA73PJJ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HBUMZWA73PJJHHG6","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HBUMZWA7","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ca1d801c6cfe4e9c64d46b453fa1608d1a46ead959361321a8da8f87b4c0f7e0","target":"graph","created_at":"2026-05-18T03:42:45Z","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":"In this note I exhibit a \"discrete homotopy\" which joins the category of F-manifolds to the category of Poisson-Nijenhuis manifolds, passing through the category of Frobenius manifolds.","authors_text":"Franco Magri","cross_cats":["math-ph","math.AG","math.MP","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SG","submitted_at":"2012-10-19T05:41:29Z","title":"Recursion Operators and Frobenius Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5320","kind":"arxiv","version":1},"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":"sha256:569b73d65067968265211d6fd5db403883395c8305f1e05abb6cb6fabde57f0d","target":"record","created_at":"2026-05-18T03:42:45Z","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":"aede5448b73b14096b82d7486202ef26849c41944485e5d1025a8af52f78c19c","cross_cats_sorted":["math-ph","math.AG","math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SG","submitted_at":"2012-10-19T05:41:29Z","title_canon_sha256":"22897b86eed873ffb667c1c19dc74af11a6040f67cae4341b9f2cf0b5fffd7f4"},"schema_version":"1.0","source":{"id":"1210.5320","kind":"arxiv","version":1}},"canonical_sha256":"3868ccd81fdbd2939cdebcf0e9edba06b7585f9dea1999d0eac970b22b295af2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3868ccd81fdbd2939cdebcf0e9edba06b7585f9dea1999d0eac970b22b295af2","first_computed_at":"2026-05-18T03:42:45.552056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:45.552056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4TUORTfBBOEb6LGyWslKmH90A28PF4BG9NvTiU+HtjI0+RgBzQQoZz/AhS4YJ0STYhynJ2hUaIug2N3k81nIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:45.552744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:569b73d65067968265211d6fd5db403883395c8305f1e05abb6cb6fabde57f0d","sha256:ca1d801c6cfe4e9c64d46b453fa1608d1a46ead959361321a8da8f87b4c0f7e0"],"state_sha256":"e68335e29181222fbd39847251e88f0e5d8acc1090c681711f79e737078b758f"}