{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AMEAHOBAHMUJWQ7NSL7MDEVPD7","short_pith_number":"pith:AMEAHOBA","canonical_record":{"source":{"id":"1001.0509","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-04T13:31:16Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"2b42996eb7f405391703235c690a000eabc241eec3f7f438c080c5c1a762be86","abstract_canon_sha256":"1a2ed99e667bc85f64ce83b47a351e9d60311e0c0f69b6dd6771b89857898032"},"schema_version":"1.0"},"canonical_sha256":"030803b8203b289b43ed92fec192af1fe0e49273013bdb23a80e569b4fdefdd9","source":{"kind":"arxiv","id":"1001.0509","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0509","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0509v3","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0509","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"AMEAHOBAHMUJ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AMEAHOBAHMUJWQ7N","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AMEAHOBA","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AMEAHOBAHMUJWQ7NSL7MDEVPD7","target":"record","payload":{"canonical_record":{"source":{"id":"1001.0509","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-04T13:31:16Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"2b42996eb7f405391703235c690a000eabc241eec3f7f438c080c5c1a762be86","abstract_canon_sha256":"1a2ed99e667bc85f64ce83b47a351e9d60311e0c0f69b6dd6771b89857898032"},"schema_version":"1.0"},"canonical_sha256":"030803b8203b289b43ed92fec192af1fe0e49273013bdb23a80e569b4fdefdd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:41.383890Z","signature_b64":"/RE+kxG2jFl3BMJDQ4xGf5mwmWzmrjHLdK0NS8oHFvYk/gSVyvWPbCVASYOJyNV6g5YUddcoF8o/hYCaD6lHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"030803b8203b289b43ed92fec192af1fe0e49273013bdb23a80e569b4fdefdd9","last_reissued_at":"2026-05-18T04:31:41.383213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:41.383213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.0509","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5ZqSKmZ2NYH4QSmFWzmeKXu8eG8erRxT+Kp6bNFGQ5TS0yeZTi6ntPhxfs9n7C3vm19PRZUR+p6iGQcCILmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:29:30.817197Z"},"content_sha256":"4e4c0488954ac44ae31fd757088570a8ea7de181e60f6233339e5e49aa446ca9","schema_version":"1.0","event_id":"sha256:4e4c0488954ac44ae31fd757088570a8ea7de181e60f6233339e5e49aa446ca9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AMEAHOBAHMUJWQ7NSL7MDEVPD7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation error of the Lagrange reconstructing polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"G.A. Gerolymos","submitted_at":"2010-01-04T13:31:16Z","abstract_excerpt":"The reconstruction approach [Shu C.W.: {\\em SIAM Rev.} {\\bf 51} (2009) 82--126] for the numerical approximation of $f'(x)$ is based on the construction of a dual function $h(x)$ whose sliding averages over the interval $[x-\\tfrac{1}{2}\\Delta x,x+\\tfrac{1}{2}\\Delta x]$ are equal to $f(x)$ (assuming an homogeneous grid of cell-size $\\Delta x$). We study the deconvolution problem [Harten A., Engquist B., Osher S., Chakravarthy S.R.: {\\em J. Comp. Phys.} {\\bf 71} (1987) 231--303] which relates the Taylor polynomials of $h(x)$ and $f(x)$, and obtain its explicit solution, by introducing rational nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0509","kind":"arxiv","version":3},"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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C4gmkWc24+F0s1vpCSYyQUFiwCLERdklPd3XVBRlEt+NKV5aXXKQ4kiMwdEudEnW2GYXn/NHdOcWFL5cOENqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:29:30.817569Z"},"content_sha256":"49a84510ce4e76fafded31690512866e7b808858c415fde2747560c92425f687","schema_version":"1.0","event_id":"sha256:49a84510ce4e76fafded31690512866e7b808858c415fde2747560c92425f687"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMEAHOBAHMUJWQ7NSL7MDEVPD7/bundle.json","state_url":"https://pith.science/pith/AMEAHOBAHMUJWQ7NSL7MDEVPD7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMEAHOBAHMUJWQ7NSL7MDEVPD7/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":"2026-05-30T09:29:30Z","links":{"resolver":"https://pith.science/pith/AMEAHOBAHMUJWQ7NSL7MDEVPD7","bundle":"https://pith.science/pith/AMEAHOBAHMUJWQ7NSL7MDEVPD7/bundle.json","state":"https://pith.science/pith/AMEAHOBAHMUJWQ7NSL7MDEVPD7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMEAHOBAHMUJWQ7NSL7MDEVPD7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AMEAHOBAHMUJWQ7NSL7MDEVPD7","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":"1a2ed99e667bc85f64ce83b47a351e9d60311e0c0f69b6dd6771b89857898032","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-04T13:31:16Z","title_canon_sha256":"2b42996eb7f405391703235c690a000eabc241eec3f7f438c080c5c1a762be86"},"schema_version":"1.0","source":{"id":"1001.0509","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0509","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0509v3","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0509","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"AMEAHOBAHMUJ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AMEAHOBAHMUJWQ7N","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AMEAHOBA","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:49a84510ce4e76fafded31690512866e7b808858c415fde2747560c92425f687","target":"graph","created_at":"2026-05-18T04:31:41Z","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 reconstruction approach [Shu C.W.: {\\em SIAM Rev.} {\\bf 51} (2009) 82--126] for the numerical approximation of $f'(x)$ is based on the construction of a dual function $h(x)$ whose sliding averages over the interval $[x-\\tfrac{1}{2}\\Delta x,x+\\tfrac{1}{2}\\Delta x]$ are equal to $f(x)$ (assuming an homogeneous grid of cell-size $\\Delta x$). We study the deconvolution problem [Harten A., Engquist B., Osher S., Chakravarthy S.R.: {\\em J. Comp. Phys.} {\\bf 71} (1987) 231--303] which relates the Taylor polynomials of $h(x)$ and $f(x)$, and obtain its explicit solution, by introducing rational nu","authors_text":"G.A. Gerolymos","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-04T13:31:16Z","title":"Approximation error of the Lagrange reconstructing polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0509","kind":"arxiv","version":3},"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":"sha256:4e4c0488954ac44ae31fd757088570a8ea7de181e60f6233339e5e49aa446ca9","target":"record","created_at":"2026-05-18T04:31:41Z","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":"1a2ed99e667bc85f64ce83b47a351e9d60311e0c0f69b6dd6771b89857898032","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-04T13:31:16Z","title_canon_sha256":"2b42996eb7f405391703235c690a000eabc241eec3f7f438c080c5c1a762be86"},"schema_version":"1.0","source":{"id":"1001.0509","kind":"arxiv","version":3}},"canonical_sha256":"030803b8203b289b43ed92fec192af1fe0e49273013bdb23a80e569b4fdefdd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"030803b8203b289b43ed92fec192af1fe0e49273013bdb23a80e569b4fdefdd9","first_computed_at":"2026-05-18T04:31:41.383213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:41.383213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/RE+kxG2jFl3BMJDQ4xGf5mwmWzmrjHLdK0NS8oHFvYk/gSVyvWPbCVASYOJyNV6g5YUddcoF8o/hYCaD6lHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:41.383890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0509","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e4c0488954ac44ae31fd757088570a8ea7de181e60f6233339e5e49aa446ca9","sha256:49a84510ce4e76fafded31690512866e7b808858c415fde2747560c92425f687"],"state_sha256":"6ba5ae492423b6efe73e4e3c924de5bcca138eb007065dbdadf5036c53d46a16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5Q6uIaZsK6Zn5TDvL7Py0ESoxx0NK+sBrVtzU9J9eGqiA/BIfVrTdQRMSHHQZVEXhWnlgMm4qpoA3+pyNepCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:29:30.819828Z","bundle_sha256":"ec8e5f95dcc049836c8db04b4e169c271fa91df6f3cd8272d0abf6c2ad3a7454"}}