{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:ENVX62HHPRGISMNJG2MBM7WWGG","short_pith_number":"pith:ENVX62HH","canonical_record":{"source":{"id":"math/0401097","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2004-01-09T21:50:09Z","cross_cats_sorted":["math-ph","math.GR","math.MP"],"title_canon_sha256":"093d182e8207e84e143a5e542c68a23917ed4e5340dcf445e3cf64e6ca8e7a2a","abstract_canon_sha256":"e11b4bd7e1639ac152b4e3eea46e09fdbeebd075fa140181865b37f7763a2286"},"schema_version":"1.0"},"canonical_sha256":"236b7f68e77c4c8931a93698167ed63184a0e1b6514ec50af8ea805b8bb015bb","source":{"kind":"arxiv","id":"math/0401097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401097","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401097v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401097","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"ENVX62HHPRGI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ENVX62HHPRGISMNJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ENVX62HH","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:ENVX62HHPRGISMNJG2MBM7WWGG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0401097","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2004-01-09T21:50:09Z","cross_cats_sorted":["math-ph","math.GR","math.MP"],"title_canon_sha256":"093d182e8207e84e143a5e542c68a23917ed4e5340dcf445e3cf64e6ca8e7a2a","abstract_canon_sha256":"e11b4bd7e1639ac152b4e3eea46e09fdbeebd075fa140181865b37f7763a2286"},"schema_version":"1.0"},"canonical_sha256":"236b7f68e77c4c8931a93698167ed63184a0e1b6514ec50af8ea805b8bb015bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:27.354869Z","signature_b64":"i6uFbvd5jNNaAtWUQ+9wtB902cCAi94fY0QsJKMEPBxC/y0z1eGG/3mUYoL4fJA+0mEHNH0NeBfRTvZ+DGqxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"236b7f68e77c4c8931a93698167ed63184a0e1b6514ec50af8ea805b8bb015bb","last_reissued_at":"2026-05-18T03:36:27.354458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:27.354458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0401097","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":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5RG2q2CLByqBKxXUf+MKraRxzm3OqkpCInes7jW2/JvpXnC5c5IDfXRMYbj4DBrLGlxfugtu2LITrf4HnQgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:40:45.299517Z"},"content_sha256":"c04cd4476cbfd5c0e961b0f731514b1d263c6a6b1b0182b6398de1f3ea8e2e01","schema_version":"1.0","event_id":"sha256:c04cd4476cbfd5c0e961b0f731514b1d263c6a6b1b0182b6398de1f3ea8e2e01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:ENVX62HHPRGISMNJG2MBM7WWGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jacobi fields and odular structure of affine manifolds","license":"","headline":"","cross_cats":["math-ph","math.GR","math.MP"],"primary_cat":"math.DG","authors_text":"Alexander I. Nesterov","submitted_at":"2004-01-09T21:50:09Z","abstract_excerpt":"The connection between Jacobi fields and odular structures of affine manifold is established. It is shown that the Jacobi fields generate the natural geoodular structure of affinely connected manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401097","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":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5CEvC4UuW6iLlHh/bR+wxT4OGtiTB6s+8e8LMgM2m+OKA3JCoTPa/mPE6BLTegSZRhgPax90kBUVb0iLW/3lBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:40:45.300184Z"},"content_sha256":"8e31ef340ec7cce2d16cf9ab568de6c87e403c1b2a3d8f77bd10704c8b3243e5","schema_version":"1.0","event_id":"sha256:8e31ef340ec7cce2d16cf9ab568de6c87e403c1b2a3d8f77bd10704c8b3243e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ENVX62HHPRGISMNJG2MBM7WWGG/bundle.json","state_url":"https://pith.science/pith/ENVX62HHPRGISMNJG2MBM7WWGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ENVX62HHPRGISMNJG2MBM7WWGG/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":"2026-05-26T23:40:45Z","links":{"resolver":"https://pith.science/pith/ENVX62HHPRGISMNJG2MBM7WWGG","bundle":"https://pith.science/pith/ENVX62HHPRGISMNJG2MBM7WWGG/bundle.json","state":"https://pith.science/pith/ENVX62HHPRGISMNJG2MBM7WWGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ENVX62HHPRGISMNJG2MBM7WWGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:ENVX62HHPRGISMNJG2MBM7WWGG","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":"e11b4bd7e1639ac152b4e3eea46e09fdbeebd075fa140181865b37f7763a2286","cross_cats_sorted":["math-ph","math.GR","math.MP"],"license":"","primary_cat":"math.DG","submitted_at":"2004-01-09T21:50:09Z","title_canon_sha256":"093d182e8207e84e143a5e542c68a23917ed4e5340dcf445e3cf64e6ca8e7a2a"},"schema_version":"1.0","source":{"id":"math/0401097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401097","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401097v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401097","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"ENVX62HHPRGI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ENVX62HHPRGISMNJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ENVX62HH","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:8e31ef340ec7cce2d16cf9ab568de6c87e403c1b2a3d8f77bd10704c8b3243e5","target":"graph","created_at":"2026-05-18T03:36:27Z","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":"The connection between Jacobi fields and odular structures of affine manifold is established. It is shown that the Jacobi fields generate the natural geoodular structure of affinely connected manifolds.","authors_text":"Alexander I. Nesterov","cross_cats":["math-ph","math.GR","math.MP"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2004-01-09T21:50:09Z","title":"Jacobi fields and odular structure of affine manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401097","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:c04cd4476cbfd5c0e961b0f731514b1d263c6a6b1b0182b6398de1f3ea8e2e01","target":"record","created_at":"2026-05-18T03:36:27Z","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":"e11b4bd7e1639ac152b4e3eea46e09fdbeebd075fa140181865b37f7763a2286","cross_cats_sorted":["math-ph","math.GR","math.MP"],"license":"","primary_cat":"math.DG","submitted_at":"2004-01-09T21:50:09Z","title_canon_sha256":"093d182e8207e84e143a5e542c68a23917ed4e5340dcf445e3cf64e6ca8e7a2a"},"schema_version":"1.0","source":{"id":"math/0401097","kind":"arxiv","version":1}},"canonical_sha256":"236b7f68e77c4c8931a93698167ed63184a0e1b6514ec50af8ea805b8bb015bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"236b7f68e77c4c8931a93698167ed63184a0e1b6514ec50af8ea805b8bb015bb","first_computed_at":"2026-05-18T03:36:27.354458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:27.354458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6uFbvd5jNNaAtWUQ+9wtB902cCAi94fY0QsJKMEPBxC/y0z1eGG/3mUYoL4fJA+0mEHNH0NeBfRTvZ+DGqxBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:27.354869Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c04cd4476cbfd5c0e961b0f731514b1d263c6a6b1b0182b6398de1f3ea8e2e01","sha256:8e31ef340ec7cce2d16cf9ab568de6c87e403c1b2a3d8f77bd10704c8b3243e5"],"state_sha256":"224adeaec75041ee6d08b141fa4450bef91e33f3974ccc20d0ab779d773da612"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtlEqJR05a4m15slhEPu0jpEv5o7Myq5U8QgyAbpPA85r/vtlC4vH/lIMAnvFY188JMovAkNwXSxuVsNS50HCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:40:45.304396Z","bundle_sha256":"6ab1dadd36137d725956c77afb3bbb9339195d22829683c8794eca0884e3c2c7"}}