{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FRD4G4WDNTG5I2XIGFYE4TYASN","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":"388ff2921196e071571048682dd30b7a5475ae2123730e02db4f52a1491c9303","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-01T19:23:43Z","title_canon_sha256":"2002315c4236cd88aed2a08bca51d73bb7cdbe4c81f4b7dec6a8b19350178021"},"schema_version":"1.0","source":{"id":"1908.00585","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00585","created_at":"2026-07-05T00:28:23Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00585v2","created_at":"2026-07-05T00:28:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00585","created_at":"2026-07-05T00:28:23Z"},{"alias_kind":"pith_short_12","alias_value":"FRD4G4WDNTG5","created_at":"2026-07-05T00:28:23Z"},{"alias_kind":"pith_short_16","alias_value":"FRD4G4WDNTG5I2XI","created_at":"2026-07-05T00:28:23Z"},{"alias_kind":"pith_short_8","alias_value":"FRD4G4WD","created_at":"2026-07-05T00:28:23Z"}],"graph_snapshots":[{"event_id":"sha256:9ac0bf5d3d5294336bbad42538bb7e6b2849821cb7482bf00aee05b59db254bc","target":"graph","created_at":"2026-07-05T00:28:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.00585/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such systems dual if the corresponding ruled surfaces are dual. We show that a Hamiltonian system is autodual, its ruled surface sits in some quadric, and the generators of this ruled surface form a Legendre submanifold for the contact structure on Fano variety of this quadric. We also give a complete geometric description of 3-component nondiagonalizable systems of Temple class: such systems admit two additional conservation ","authors_text":"Sergey I. Agafonov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-01T19:23:43Z","title":"Duality for systems of conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00585","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":"sha256:9e9c455da54a26f7cb0413c02f8f3ac90adf21cef0ef808d41e495cad0f1cf6b","target":"record","created_at":"2026-07-05T00:28:23Z","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":"388ff2921196e071571048682dd30b7a5475ae2123730e02db4f52a1491c9303","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-01T19:23:43Z","title_canon_sha256":"2002315c4236cd88aed2a08bca51d73bb7cdbe4c81f4b7dec6a8b19350178021"},"schema_version":"1.0","source":{"id":"1908.00585","kind":"arxiv","version":2}},"canonical_sha256":"2c47c372c36ccdd46ae831704e4f00937d667f955ff6a8f6826a66e7f88002db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c47c372c36ccdd46ae831704e4f00937d667f955ff6a8f6826a66e7f88002db","first_computed_at":"2026-07-05T00:28:23.574156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:28:23.574156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"poKJWZ6WcukKAyg1iV37bZFXxwcQt90pGTPR5Bkf9fB9cJ5EyOizmNjCwygr9Ai3jO5vT1bdBHpOMiGZTfe0AA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:28:23.574661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00585","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e9c455da54a26f7cb0413c02f8f3ac90adf21cef0ef808d41e495cad0f1cf6b","sha256:9ac0bf5d3d5294336bbad42538bb7e6b2849821cb7482bf00aee05b59db254bc"],"state_sha256":"000875e37f9495f6f3306bbd6a544639ee346ce94ba75bb8ac9033a5d11eef85"}