{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:B4JG62DF6QI27R2PCSJUY2DEUS","short_pith_number":"pith:B4JG62DF","canonical_record":{"source":{"id":"1212.0280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-03T04:02:59Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"df8cee5688ff174ea9dcbd27e7006edc03aa330ed23492e6c19acb00c44b9ebb","abstract_canon_sha256":"fe55b8d714848fa740336a978fc2b3b36ffdfb45f07f8ff30e1779968d368d5e"},"schema_version":"1.0"},"canonical_sha256":"0f126f6865f411afc74f14934c6864a4944823b26d6a82884f69e31c58cdc10b","source":{"kind":"arxiv","id":"1212.0280","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0280","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0280v1","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0280","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"pith_short_12","alias_value":"B4JG62DF6QI2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B4JG62DF6QI27R2P","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B4JG62DF","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:B4JG62DF6QI27R2PCSJUY2DEUS","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-03T04:02:59Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"df8cee5688ff174ea9dcbd27e7006edc03aa330ed23492e6c19acb00c44b9ebb","abstract_canon_sha256":"fe55b8d714848fa740336a978fc2b3b36ffdfb45f07f8ff30e1779968d368d5e"},"schema_version":"1.0"},"canonical_sha256":"0f126f6865f411afc74f14934c6864a4944823b26d6a82884f69e31c58cdc10b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:26.569183Z","signature_b64":"ehW7U3gHoHB89oqSE7IIEO34GD+/VK6Ztpmc7CLXTYOr1PfCJM+pG7uLdMXzt2TyI1jBCznqdUo+0Sht3Yw2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f126f6865f411afc74f14934c6864a4944823b26d6a82884f69e31c58cdc10b","last_reissued_at":"2026-05-18T03:39:26.568427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:26.568427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0280","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":"2026-05-18T03:39:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1WsbsaitDFct0pNlrc1V27UwdxKfKh96EaYSZ6SJNBPMUSSaJznNzz9KOTK4pQDIcT7aWkLGU5LxYPbGKtPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:59:39.765651Z"},"content_sha256":"8da311b024c423268f9b42aa7f1383f55f2e984e31b4219466c36663caedd50e","schema_version":"1.0","event_id":"sha256:8da311b024c423268f9b42aa7f1383f55f2e984e31b4219466c36663caedd50e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:B4JG62DF6QI27R2PCSJUY2DEUS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error Bounds on Derivatives during Simulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE"],"primary_cat":"math.NA","authors_text":"Alexander Basyrov, Gregory Bard","submitted_at":"2012-12-03T04:02:59Z","abstract_excerpt":"The methods commonly used for numerical differentiation, such as the \"center-difference formula\" and \"four-points formula\" are unusable in simulations or real-time data analysis because they require knowledge of the future. In Bard'11, an algorithm was shown that generates formulas that require knowledge only of the past and present values of $f(t)$ to estimate $f'(t)$. Furthermore, the algorithm can handle irregularly spaced data and higher-order derivatives. That work did not include a rigorous proof of correctness nor the error bounds. In this paper, the correctness and error bounds of that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0280","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":"2026-05-18T03:39:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C5HAJv0317EokI8ab6MisSgTHqoHQMB/sZrHWusrqNM6OFAqS5DWedW0sbNgyyJwSlPhFGIvWN737NtQfhhOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:59:39.765989Z"},"content_sha256":"09b7c59f2d1027e0b23a4b347e23bf72f064bb00c7f1a55d13e6655600b32048","schema_version":"1.0","event_id":"sha256:09b7c59f2d1027e0b23a4b347e23bf72f064bb00c7f1a55d13e6655600b32048"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4JG62DF6QI27R2PCSJUY2DEUS/bundle.json","state_url":"https://pith.science/pith/B4JG62DF6QI27R2PCSJUY2DEUS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4JG62DF6QI27R2PCSJUY2DEUS/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":"2026-06-08T14:59:39Z","links":{"resolver":"https://pith.science/pith/B4JG62DF6QI27R2PCSJUY2DEUS","bundle":"https://pith.science/pith/B4JG62DF6QI27R2PCSJUY2DEUS/bundle.json","state":"https://pith.science/pith/B4JG62DF6QI27R2PCSJUY2DEUS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4JG62DF6QI27R2PCSJUY2DEUS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B4JG62DF6QI27R2PCSJUY2DEUS","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":"fe55b8d714848fa740336a978fc2b3b36ffdfb45f07f8ff30e1779968d368d5e","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-03T04:02:59Z","title_canon_sha256":"df8cee5688ff174ea9dcbd27e7006edc03aa330ed23492e6c19acb00c44b9ebb"},"schema_version":"1.0","source":{"id":"1212.0280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0280","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0280v1","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0280","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"pith_short_12","alias_value":"B4JG62DF6QI2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B4JG62DF6QI27R2P","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B4JG62DF","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:09b7c59f2d1027e0b23a4b347e23bf72f064bb00c7f1a55d13e6655600b32048","target":"graph","created_at":"2026-05-18T03:39:26Z","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 methods commonly used for numerical differentiation, such as the \"center-difference formula\" and \"four-points formula\" are unusable in simulations or real-time data analysis because they require knowledge of the future. In Bard'11, an algorithm was shown that generates formulas that require knowledge only of the past and present values of $f(t)$ to estimate $f'(t)$. Furthermore, the algorithm can handle irregularly spaced data and higher-order derivatives. That work did not include a rigorous proof of correctness nor the error bounds. In this paper, the correctness and error bounds of that","authors_text":"Alexander Basyrov, Gregory Bard","cross_cats":["cs.CE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-03T04:02:59Z","title":"Error Bounds on Derivatives during Simulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0280","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":"sha256:8da311b024c423268f9b42aa7f1383f55f2e984e31b4219466c36663caedd50e","target":"record","created_at":"2026-05-18T03:39:26Z","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":"fe55b8d714848fa740336a978fc2b3b36ffdfb45f07f8ff30e1779968d368d5e","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-03T04:02:59Z","title_canon_sha256":"df8cee5688ff174ea9dcbd27e7006edc03aa330ed23492e6c19acb00c44b9ebb"},"schema_version":"1.0","source":{"id":"1212.0280","kind":"arxiv","version":1}},"canonical_sha256":"0f126f6865f411afc74f14934c6864a4944823b26d6a82884f69e31c58cdc10b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f126f6865f411afc74f14934c6864a4944823b26d6a82884f69e31c58cdc10b","first_computed_at":"2026-05-18T03:39:26.568427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:26.568427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ehW7U3gHoHB89oqSE7IIEO34GD+/VK6Ztpmc7CLXTYOr1PfCJM+pG7uLdMXzt2TyI1jBCznqdUo+0Sht3Yw2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:26.569183Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da311b024c423268f9b42aa7f1383f55f2e984e31b4219466c36663caedd50e","sha256:09b7c59f2d1027e0b23a4b347e23bf72f064bb00c7f1a55d13e6655600b32048"],"state_sha256":"ae4387ddf44b98aadeb0970e1304e74b21f2aed197d4e499a5fb158cf7cb4f6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vkYGzAwtOq59i+51F8ZDu+qYGMuNbnIF2L2R+1qbK3mo2kKDlpjJhDtJnTzrfuEnrN5Er9vFjT267mrNduDoDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:59:39.767792Z","bundle_sha256":"21171ecd6456f0182a49e911d355777a1f9b3dc48ba4aa4bbf9797b4bc0fc928"}}