{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QAM7G6KWUOIL2NHEO66TP4VTPF","short_pith_number":"pith:QAM7G6KW","canonical_record":{"source":{"id":"1602.00913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-02T13:10:15Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6fde2bd23e8014362ee82badadb858a752b204f293993d1345016abb4ba0cdc4","abstract_canon_sha256":"67c4214366e1eb1fc4aeec97a2341c4f5577603b23fd128935d33019c2eb7af7"},"schema_version":"1.0"},"canonical_sha256":"8019f37956a390bd34e477bd37f2b3794f448e36346d9209a1737f1190cc6033","source":{"kind":"arxiv","id":"1602.00913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00913","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00913v1","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00913","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"QAM7G6KWUOIL","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QAM7G6KWUOIL2NHE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QAM7G6KW","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QAM7G6KWUOIL2NHEO66TP4VTPF","target":"record","payload":{"canonical_record":{"source":{"id":"1602.00913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-02T13:10:15Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"6fde2bd23e8014362ee82badadb858a752b204f293993d1345016abb4ba0cdc4","abstract_canon_sha256":"67c4214366e1eb1fc4aeec97a2341c4f5577603b23fd128935d33019c2eb7af7"},"schema_version":"1.0"},"canonical_sha256":"8019f37956a390bd34e477bd37f2b3794f448e36346d9209a1737f1190cc6033","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:24.320442Z","signature_b64":"N6q5sUN1fjzC7xwtTPWpSyH69QgNup0vk1U70f0dhW0nrd0+MAJOLD0pnROZd7y+yATKvjCIPyxy09p2BquQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8019f37956a390bd34e477bd37f2b3794f448e36346d9209a1737f1190cc6033","last_reissued_at":"2026-05-18T01:21:24.319899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:24.319899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.00913","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":"2026-05-18T01:21:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/YHpHvTtntwrU4eVUjiB+wNkXKPc69pLuvN/Wrs58s0rdt8M4oPdk/Q53kV5bZWpo5Dkmp8AeVBj2++mPylMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:39:03.661651Z"},"content_sha256":"faae0c168fce9596eb2ebc57b91bf8718873be69295f66dd28244fcc97db9363","schema_version":"1.0","event_id":"sha256:faae0c168fce9596eb2ebc57b91bf8718873be69295f66dd28244fcc97db9363"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QAM7G6KWUOIL2NHEO66TP4VTPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometry of second-order ordinary differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Boris Doubrov, Boris Komrakov","submitted_at":"2016-02-02T13:10:15Z","abstract_excerpt":"These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan connection, techniques for computing invariants of differential equations starting from the Cartan connection, recognition of symmetric 2nd order ODEs by their differential invariants and the constructive aspects of the local equivalence problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00913","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":"2026-05-18T01:21:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vFvQ+oKhlaKfh5dHVw0x9SRJeQ3dU3CE/FGKJjD/c3ne+X06oAFRy5aSA4zzZCHSZSeYI6SNjtCczTO6GwYQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:39:03.662248Z"},"content_sha256":"b0d7e2ccb0df6e36e986138eb20d97ca13423fc5ecc6e664d48462c138ef77de","schema_version":"1.0","event_id":"sha256:b0d7e2ccb0df6e36e986138eb20d97ca13423fc5ecc6e664d48462c138ef77de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QAM7G6KWUOIL2NHEO66TP4VTPF/bundle.json","state_url":"https://pith.science/pith/QAM7G6KWUOIL2NHEO66TP4VTPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QAM7G6KWUOIL2NHEO66TP4VTPF/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":"2026-06-05T22:39:03Z","links":{"resolver":"https://pith.science/pith/QAM7G6KWUOIL2NHEO66TP4VTPF","bundle":"https://pith.science/pith/QAM7G6KWUOIL2NHEO66TP4VTPF/bundle.json","state":"https://pith.science/pith/QAM7G6KWUOIL2NHEO66TP4VTPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QAM7G6KWUOIL2NHEO66TP4VTPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QAM7G6KWUOIL2NHEO66TP4VTPF","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":"67c4214366e1eb1fc4aeec97a2341c4f5577603b23fd128935d33019c2eb7af7","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-02T13:10:15Z","title_canon_sha256":"6fde2bd23e8014362ee82badadb858a752b204f293993d1345016abb4ba0cdc4"},"schema_version":"1.0","source":{"id":"1602.00913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00913","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00913v1","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00913","created_at":"2026-05-18T01:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"QAM7G6KWUOIL","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QAM7G6KWUOIL2NHE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QAM7G6KW","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:b0d7e2ccb0df6e36e986138eb20d97ca13423fc5ecc6e664d48462c138ef77de","target":"graph","created_at":"2026-05-18T01:21:24Z","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":"These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan connection, techniques for computing invariants of differential equations starting from the Cartan connection, recognition of symmetric 2nd order ODEs by their differential invariants and the constructive aspects of the local equivalence problem.","authors_text":"Boris Doubrov, Boris Komrakov","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-02T13:10:15Z","title":"The geometry of second-order ordinary differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00913","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:faae0c168fce9596eb2ebc57b91bf8718873be69295f66dd28244fcc97db9363","target":"record","created_at":"2026-05-18T01:21:24Z","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":"67c4214366e1eb1fc4aeec97a2341c4f5577603b23fd128935d33019c2eb7af7","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-02T13:10:15Z","title_canon_sha256":"6fde2bd23e8014362ee82badadb858a752b204f293993d1345016abb4ba0cdc4"},"schema_version":"1.0","source":{"id":"1602.00913","kind":"arxiv","version":1}},"canonical_sha256":"8019f37956a390bd34e477bd37f2b3794f448e36346d9209a1737f1190cc6033","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8019f37956a390bd34e477bd37f2b3794f448e36346d9209a1737f1190cc6033","first_computed_at":"2026-05-18T01:21:24.319899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:24.319899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N6q5sUN1fjzC7xwtTPWpSyH69QgNup0vk1U70f0dhW0nrd0+MAJOLD0pnROZd7y+yATKvjCIPyxy09p2BquQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:24.320442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faae0c168fce9596eb2ebc57b91bf8718873be69295f66dd28244fcc97db9363","sha256:b0d7e2ccb0df6e36e986138eb20d97ca13423fc5ecc6e664d48462c138ef77de"],"state_sha256":"c1be4f47b373d66faa35bb267fd4a505f98ec6fa96267be42fb874306a632ea6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NPhM75laP/jIn9HeqBjb495THVFiVVozzHEO9rHRhQpPl37CpxB5bLJSS2t3jJV9qMnTFVqgESAj8wzKixRMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:39:03.666775Z","bundle_sha256":"75641dc80eb0396a901ef460a818520094054d8a94a82b46c7addcd33b9e69b5"}}