{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XPROSMFQXIFZKZ7PR7JDQFKKDR","short_pith_number":"pith:XPROSMFQ","canonical_record":{"source":{"id":"1108.5854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-30T07:27:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b9a7ec0d16e0de6f27919774f62aa5c9f42bbd303e37a5e27f400beabc2512f3","abstract_canon_sha256":"709469def37f9828d217cddceb5566a9db684b7d83b4b516a871d974de185aa3"},"schema_version":"1.0"},"canonical_sha256":"bbe2e930b0ba0b9567ef8fd238154a1c786cfdea44a0be09919e5787d0f2e5d9","source":{"kind":"arxiv","id":"1108.5854","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5854","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5854v1","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5854","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"XPROSMFQXIFZ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XPROSMFQXIFZKZ7P","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XPROSMFQ","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XPROSMFQXIFZKZ7PR7JDQFKKDR","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-30T07:27:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b9a7ec0d16e0de6f27919774f62aa5c9f42bbd303e37a5e27f400beabc2512f3","abstract_canon_sha256":"709469def37f9828d217cddceb5566a9db684b7d83b4b516a871d974de185aa3"},"schema_version":"1.0"},"canonical_sha256":"bbe2e930b0ba0b9567ef8fd238154a1c786cfdea44a0be09919e5787d0f2e5d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:28.406434Z","signature_b64":"9vmTAZlUGdxsb0+qmf57RHFm2Tow04q4b4uR1wNnj77WPfXGqdQqaZnDeZoSOvI1si9xUIWkBmMugTIMKYoZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbe2e930b0ba0b9567ef8fd238154a1c786cfdea44a0be09919e5787d0f2e5d9","last_reissued_at":"2026-05-18T04:14:28.405954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:28.405954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5854","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gvCA1+zj7aXgw+u2N9j7APUe5IhHC+wC44zqQlX043oqB02b5BkEoCu0B5RGDH7CInQ5psNBLnTOB7qRGNOcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:18:02.999822Z"},"content_sha256":"527d27d0cb211c7500546bdb065874d7ce2de1ee85f1203d9ca4c1bc072016f8","schema_version":"1.0","event_id":"sha256:527d27d0cb211c7500546bdb065874d7ce2de1ee85f1203d9ca4c1bc072016f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XPROSMFQXIFZKZ7PR7JDQFKKDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie theorem via rank 2 distributions (integration of PDE of class \\omega=1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Boris Kruglikov","submitted_at":"2011-08-30T07:27:49Z","abstract_excerpt":"In this paper we investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we relate this to the geometry of rank 2 distributions. We find a criterion for integration in quadratures and in closed form, as in the method of Darboux, and discuss nonlinear Laplace transformations and symmetric PDE models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5854","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qyOvHpgJnA+Fg1f3Q1PgyC8gOK5h7eVGcYl7E3wOVJhqCSsnAzBwXTHmYlyPxraN0DsAcITnlHHTJwq+Qs2sBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:18:03.000168Z"},"content_sha256":"1a8c09f01123d24a45eea7dd8f0f46c71ca216d5f1d1bd8edf9b1601920a702d","schema_version":"1.0","event_id":"sha256:1a8c09f01123d24a45eea7dd8f0f46c71ca216d5f1d1bd8edf9b1601920a702d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPROSMFQXIFZKZ7PR7JDQFKKDR/bundle.json","state_url":"https://pith.science/pith/XPROSMFQXIFZKZ7PR7JDQFKKDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPROSMFQXIFZKZ7PR7JDQFKKDR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T21:18:03Z","links":{"resolver":"https://pith.science/pith/XPROSMFQXIFZKZ7PR7JDQFKKDR","bundle":"https://pith.science/pith/XPROSMFQXIFZKZ7PR7JDQFKKDR/bundle.json","state":"https://pith.science/pith/XPROSMFQXIFZKZ7PR7JDQFKKDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPROSMFQXIFZKZ7PR7JDQFKKDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XPROSMFQXIFZKZ7PR7JDQFKKDR","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":"709469def37f9828d217cddceb5566a9db684b7d83b4b516a871d974de185aa3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-30T07:27:49Z","title_canon_sha256":"b9a7ec0d16e0de6f27919774f62aa5c9f42bbd303e37a5e27f400beabc2512f3"},"schema_version":"1.0","source":{"id":"1108.5854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5854","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5854v1","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5854","created_at":"2026-05-18T04:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"XPROSMFQXIFZ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XPROSMFQXIFZKZ7P","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XPROSMFQ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:1a8c09f01123d24a45eea7dd8f0f46c71ca216d5f1d1bd8edf9b1601920a702d","target":"graph","created_at":"2026-05-18T04:14:28Z","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 investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we relate this to the geometry of rank 2 distributions. We find a criterion for integration in quadratures and in closed form, as in the method of Darboux, and discuss nonlinear Laplace transformations and symmetric PDE models.","authors_text":"Boris Kruglikov","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-30T07:27:49Z","title":"Lie theorem via rank 2 distributions (integration of PDE of class \\omega=1)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5854","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":"sha256:527d27d0cb211c7500546bdb065874d7ce2de1ee85f1203d9ca4c1bc072016f8","target":"record","created_at":"2026-05-18T04:14:28Z","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":"709469def37f9828d217cddceb5566a9db684b7d83b4b516a871d974de185aa3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-30T07:27:49Z","title_canon_sha256":"b9a7ec0d16e0de6f27919774f62aa5c9f42bbd303e37a5e27f400beabc2512f3"},"schema_version":"1.0","source":{"id":"1108.5854","kind":"arxiv","version":1}},"canonical_sha256":"bbe2e930b0ba0b9567ef8fd238154a1c786cfdea44a0be09919e5787d0f2e5d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbe2e930b0ba0b9567ef8fd238154a1c786cfdea44a0be09919e5787d0f2e5d9","first_computed_at":"2026-05-18T04:14:28.405954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:28.405954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9vmTAZlUGdxsb0+qmf57RHFm2Tow04q4b4uR1wNnj77WPfXGqdQqaZnDeZoSOvI1si9xUIWkBmMugTIMKYoZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:28.406434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:527d27d0cb211c7500546bdb065874d7ce2de1ee85f1203d9ca4c1bc072016f8","sha256:1a8c09f01123d24a45eea7dd8f0f46c71ca216d5f1d1bd8edf9b1601920a702d"],"state_sha256":"910aad4f1b0d2635e56f2ee5d83b678c2066f7d8441b308e08bbd7d01052b2f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dNyxhlbjuK5DvLkG5p1R0miLZC7OjUAx4DvC6BXVrVzZV22/1zXtvLnrLJypify2/C65xCIuPvhtAtKPkS8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:18:03.002201Z","bundle_sha256":"b6c8ff4c17c2b39e06afe67c21e60185c389888acc39ec512ecd4e1ec45fc7dd"}}