{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:7QH3PTP5XKTA4BF75LNQDJ3OTS","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":"85fe1bd29819d6d3d243b8d2ad9bd4b0449cd0e5a00e1c987dbcc8b817a661d4","cross_cats_sorted":["hep-th","math-ph","math.MP","nlin.SI","solv-int"],"license":"","primary_cat":"math.DG","submitted_at":"1999-12-10T15:12:05Z","title_canon_sha256":"e892705490705c6a9303d497bf218a7068f2ff191aa6e3d5fb61d31cdfa5950e"},"schema_version":"1.0","source":{"id":"math/9912081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9912081","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9912081v1","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9912081","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"7QH3PTP5XKTA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"7QH3PTP5XKTA4BF7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"7QH3PTP5","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:de255d12a694235e788fc2c9f2dc237e6b242c5afcce1806298e25e416ffdde7","target":"graph","created_at":"2026-05-18T01:38:22Z","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":"The notion of a Frobenius submanifold - a submanifold of a Frobenius manifold which is itself a Frobenius manifold with respect to structures induced from the original manifold - is studied. Two dimensional submanifolds are particularly simple. More generally, sufficient conditions are given for a submanifold to be a so-called natural submanifold. These ideas are illustrated using examples of Frobenius manifolds constructed from Coxeter groups, and for the Frobenius manifolds governing the quantum cohomology of CP^2 and CP^1 \\times CP^1.","authors_text":"I.A.B. Strachan","cross_cats":["hep-th","math-ph","math.MP","nlin.SI","solv-int"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"1999-12-10T15:12:05Z","title":"Frobenius submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9912081","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":"sha256:26459e8aa0948a3b9ae1646bea06826074b985d5693454556f04013eba233961","target":"record","created_at":"2026-05-18T01:38:22Z","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":"85fe1bd29819d6d3d243b8d2ad9bd4b0449cd0e5a00e1c987dbcc8b817a661d4","cross_cats_sorted":["hep-th","math-ph","math.MP","nlin.SI","solv-int"],"license":"","primary_cat":"math.DG","submitted_at":"1999-12-10T15:12:05Z","title_canon_sha256":"e892705490705c6a9303d497bf218a7068f2ff191aa6e3d5fb61d31cdfa5950e"},"schema_version":"1.0","source":{"id":"math/9912081","kind":"arxiv","version":1}},"canonical_sha256":"fc0fb7cdfdbaa60e04bfeadb01a76e9cac37d57693dbcc31f0eb70063cc18504","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc0fb7cdfdbaa60e04bfeadb01a76e9cac37d57693dbcc31f0eb70063cc18504","first_computed_at":"2026-05-18T01:38:22.281019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:22.281019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YutUY6aFWysPFNXFpxkTmw2hwz5Y8rGYUpP6rQqkAOkzknJ4wo1T8tMZikn4dMR02Cqa12wS9U1OYH1a5ws+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:22.281693Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9912081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26459e8aa0948a3b9ae1646bea06826074b985d5693454556f04013eba233961","sha256:de255d12a694235e788fc2c9f2dc237e6b242c5afcce1806298e25e416ffdde7"],"state_sha256":"f10cfc1ff1b62e55784d1f8b53b4357b952ae0561a03073e78a199f7e4849ea7"}