{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PCLS6HRY4NQST23NS36EQG5EA2","short_pith_number":"pith:PCLS6HRY","canonical_record":{"source":{"id":"1011.0422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-01T19:43:25Z","cross_cats_sorted":[],"title_canon_sha256":"0338a337ad63986240070a304fd8570fc97e9d4817627f8ade9b869fccf7cab7","abstract_canon_sha256":"30a371d4cc4ab808986c305d78fc3a1cdfb1bd9243dbf7912eed525f7f910d1b"},"schema_version":"1.0"},"canonical_sha256":"78972f1e38e36129eb6d96fc481ba4068ac2133572704fdc3f96f2b185d73e8c","source":{"kind":"arxiv","id":"1011.0422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0422","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0422v1","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0422","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"PCLS6HRY4NQS","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PCLS6HRY4NQST23N","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PCLS6HRY","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PCLS6HRY4NQST23NS36EQG5EA2","target":"record","payload":{"canonical_record":{"source":{"id":"1011.0422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-01T19:43:25Z","cross_cats_sorted":[],"title_canon_sha256":"0338a337ad63986240070a304fd8570fc97e9d4817627f8ade9b869fccf7cab7","abstract_canon_sha256":"30a371d4cc4ab808986c305d78fc3a1cdfb1bd9243dbf7912eed525f7f910d1b"},"schema_version":"1.0"},"canonical_sha256":"78972f1e38e36129eb6d96fc481ba4068ac2133572704fdc3f96f2b185d73e8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:23.285499Z","signature_b64":"oLYpYVZrZ5p4iPwZ0U5A3Fa110S2dAbg0MnxycmFIJWz8QuIO7/HhPYc2Qp0iRLx73xF84je+13UTfQ2nT+mDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78972f1e38e36129eb6d96fc481ba4068ac2133572704fdc3f96f2b185d73e8c","last_reissued_at":"2026-05-18T04:37:23.285062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:23.285062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.0422","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":"2026-05-18T04:37:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g96r29zsORAlgsmpDftDyMrdsBJwGaXlrTSXHxPeQlTjBIfSh9HmLd4ykQFxb1+zqP+xQlWDda4iY8BFfas3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:48:34.868115Z"},"content_sha256":"3a9b6ea4564c1c2d1654a03805cefdef634bc70a97683c0802dfce9afb31ae46","schema_version":"1.0","event_id":"sha256:3a9b6ea4564c1c2d1654a03805cefdef634bc70a97683c0802dfce9afb31ae46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PCLS6HRY4NQST23NS36EQG5EA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A finite time blowup result for quadratic ODE's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dennis Sullivan","submitted_at":"2010-11-01T19:43:25Z","abstract_excerpt":"This short paper is dedicated to Mauricio Peixoto who abstracted the practical theory of ODE's and to David Rand who applied the subsequent powerful abstract theory to practical problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0422","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":"2026-05-18T04:37:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a8jbZLZsY8/LgQE2G9YGqf1sua0QKbGhQ4bI8PZVPN1KPTC9l8q12PPkgto0pQHuQmsZljv/dd0SBjS+vkXdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:48:34.868464Z"},"content_sha256":"1fa42f2038aa9779f39155f6b545a661af1023e6606200ad8e1ec75adaa42776","schema_version":"1.0","event_id":"sha256:1fa42f2038aa9779f39155f6b545a661af1023e6606200ad8e1ec75adaa42776"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCLS6HRY4NQST23NS36EQG5EA2/bundle.json","state_url":"https://pith.science/pith/PCLS6HRY4NQST23NS36EQG5EA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCLS6HRY4NQST23NS36EQG5EA2/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":"2026-06-03T19:48:34Z","links":{"resolver":"https://pith.science/pith/PCLS6HRY4NQST23NS36EQG5EA2","bundle":"https://pith.science/pith/PCLS6HRY4NQST23NS36EQG5EA2/bundle.json","state":"https://pith.science/pith/PCLS6HRY4NQST23NS36EQG5EA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCLS6HRY4NQST23NS36EQG5EA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PCLS6HRY4NQST23NS36EQG5EA2","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":"30a371d4cc4ab808986c305d78fc3a1cdfb1bd9243dbf7912eed525f7f910d1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-01T19:43:25Z","title_canon_sha256":"0338a337ad63986240070a304fd8570fc97e9d4817627f8ade9b869fccf7cab7"},"schema_version":"1.0","source":{"id":"1011.0422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0422","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0422v1","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0422","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"PCLS6HRY4NQS","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PCLS6HRY4NQST23N","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PCLS6HRY","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:1fa42f2038aa9779f39155f6b545a661af1023e6606200ad8e1ec75adaa42776","target":"graph","created_at":"2026-05-18T04:37:23Z","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"},"paper":{"abstract_excerpt":"This short paper is dedicated to Mauricio Peixoto who abstracted the practical theory of ODE's and to David Rand who applied the subsequent powerful abstract theory to practical problems.","authors_text":"Dennis Sullivan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-01T19:43:25Z","title":"A finite time blowup result for quadratic ODE's"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0422","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":"sha256:3a9b6ea4564c1c2d1654a03805cefdef634bc70a97683c0802dfce9afb31ae46","target":"record","created_at":"2026-05-18T04:37:23Z","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":"30a371d4cc4ab808986c305d78fc3a1cdfb1bd9243dbf7912eed525f7f910d1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-11-01T19:43:25Z","title_canon_sha256":"0338a337ad63986240070a304fd8570fc97e9d4817627f8ade9b869fccf7cab7"},"schema_version":"1.0","source":{"id":"1011.0422","kind":"arxiv","version":1}},"canonical_sha256":"78972f1e38e36129eb6d96fc481ba4068ac2133572704fdc3f96f2b185d73e8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78972f1e38e36129eb6d96fc481ba4068ac2133572704fdc3f96f2b185d73e8c","first_computed_at":"2026-05-18T04:37:23.285062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:23.285062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oLYpYVZrZ5p4iPwZ0U5A3Fa110S2dAbg0MnxycmFIJWz8QuIO7/HhPYc2Qp0iRLx73xF84je+13UTfQ2nT+mDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:23.285499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a9b6ea4564c1c2d1654a03805cefdef634bc70a97683c0802dfce9afb31ae46","sha256:1fa42f2038aa9779f39155f6b545a661af1023e6606200ad8e1ec75adaa42776"],"state_sha256":"4e46a7c2e8744bc7c93200cc24ed941d7eb9d9b65f923969eec92984614ba373"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7CcWcUHyRjCPIjtdlKeeFqgi5kb9ZRw7czTh9uyUiSEIWq/F4GqDn1GrLcSEyUOyiLUJ0YFDg1dZuX3heafCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:48:34.870672Z","bundle_sha256":"d95966131a1aa088f5f1eb7a120024d6db7a7aef6b0e524846ec485107635a2b"}}