{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DSEIFPBDNXRB7TU4AEDNY7BKBD","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":"1878eeb78b94a27b657472463a82096dd3ddc32a7d614010c63c285165930fce","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-13T23:16:03Z","title_canon_sha256":"5bda379ebabcf206bb0cb8d0a07ede38a4bc8436ef1c940d8abc437e8b64389e"},"schema_version":"1.0","source":{"id":"1205.2914","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2914","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2914v2","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2914","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"DSEIFPBDNXRB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DSEIFPBDNXRB7TU4","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DSEIFPBD","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:4bc98a47ebeffe2f0a75a647dddf16f3bbe703fd3b4f1c4b7457bdf737c81c0c","target":"graph","created_at":"2026-05-18T03:22:17Z","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 paper we prove a version of Lie-B\\\"acklund theorem for overdetermined systems of scalar PDEs, whose general solution depends on 1 function of 1 variable. This generalizes the case of involutive system of the second order on the plane treated by E.Cartan in 1910. Many examples are provided.","authors_text":"Boris Kruglikov","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-13T23:16:03Z","title":"Generalized Lie-B\\\"acklund theorem for Lie class \\omega=1 overdetermined systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2914","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:ed2210d38f004659cef3bcee0a40da888b2867f7cdd51bba3acf1e041b0b7db0","target":"record","created_at":"2026-05-18T03:22:17Z","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":"1878eeb78b94a27b657472463a82096dd3ddc32a7d614010c63c285165930fce","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-13T23:16:03Z","title_canon_sha256":"5bda379ebabcf206bb0cb8d0a07ede38a4bc8436ef1c940d8abc437e8b64389e"},"schema_version":"1.0","source":{"id":"1205.2914","kind":"arxiv","version":2}},"canonical_sha256":"1c8882bc236de21fce9c0106dc7c2a08fedd3fc9380d064e3ae69e7718079612","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c8882bc236de21fce9c0106dc7c2a08fedd3fc9380d064e3ae69e7718079612","first_computed_at":"2026-05-18T03:22:17.485348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:17.485348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hYkSFWpHFtDZvh9Lne7gjp9kL1Z7GGsV+JUows0Rb5BeKLBS7bmvWf6OEGFDwagUQ1AvuB0M7GaEDjgbpWm/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:17.486039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2914","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed2210d38f004659cef3bcee0a40da888b2867f7cdd51bba3acf1e041b0b7db0","sha256:4bc98a47ebeffe2f0a75a647dddf16f3bbe703fd3b4f1c4b7457bdf737c81c0c"],"state_sha256":"40a30f33dbb25f83e9998deaed940aab20c0fadfbbead45de899ad1d493c2870"}