{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NFQCSNLPQX5HBWZ6BEXIX3C2JB","short_pith_number":"pith:NFQCSNLP","canonical_record":{"source":{"id":"1401.5139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-21T01:24:16Z","cross_cats_sorted":[],"title_canon_sha256":"2edec7109822295b4e142280368968c633ff1a2c9f812230a7f78325ceb1fcb5","abstract_canon_sha256":"e7cd8a9f0ae7f5b38e6d8552acb73b136992cbc6b7d81c8d052651ecc524fd3a"},"schema_version":"1.0"},"canonical_sha256":"696029356f85fa70db3e092e8bec5a4840ed044ce7d5dc86b2b3585e0d89c762","source":{"kind":"arxiv","id":"1401.5139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5139","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5139v1","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5139","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"NFQCSNLPQX5H","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFQCSNLPQX5HBWZ6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFQCSNLP","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NFQCSNLPQX5HBWZ6BEXIX3C2JB","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-21T01:24:16Z","cross_cats_sorted":[],"title_canon_sha256":"2edec7109822295b4e142280368968c633ff1a2c9f812230a7f78325ceb1fcb5","abstract_canon_sha256":"e7cd8a9f0ae7f5b38e6d8552acb73b136992cbc6b7d81c8d052651ecc524fd3a"},"schema_version":"1.0"},"canonical_sha256":"696029356f85fa70db3e092e8bec5a4840ed044ce7d5dc86b2b3585e0d89c762","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:34.792103Z","signature_b64":"M2Kne3QMIs1XuzBM9vDjjJCJwLpp3GPz+U0plpz/DIwe+4s9ol13r5Amqjae1DqZmjo6/f7mIIpx2fmny8uSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"696029356f85fa70db3e092e8bec5a4840ed044ce7d5dc86b2b3585e0d89c762","last_reissued_at":"2026-05-18T03:01:34.791611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:34.791611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5139","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":"2026-05-18T03:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CnuAfGxxceifdzLQwHkB17TTDBevy8ohItfgbUmZCJ+AOORJ4txO4MIcSaGPPv1nTpNQAdeqM/MCKAufS/GCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:17:48.579787Z"},"content_sha256":"6d395c6012be9194577723d1efb6231feb1265eb2112ebfcc1e282b30c2391dc","schema_version":"1.0","event_id":"sha256:6d395c6012be9194577723d1efb6231feb1265eb2112ebfcc1e282b30c2391dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NFQCSNLPQX5HBWZ6BEXIX3C2JB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Amiya K. Pani, Samir Karaa","submitted_at":"2014-01-21T01:24:16Z","abstract_excerpt":"In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal domain. The effect of numerical quadrature is also examined. In the semidiscrete case, optimal error estimates in L^{\\infty}(L2) and L^{\\infty}(H1)- norms are shown to hold with minimal regularity assumptions on the initial data, whereas quasi-optimal estimate in derived in L^{\\infty}(L^{\\infty})-norm under higher regularity on the data. Based on a second orde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5139","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":"2026-05-18T03:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OeRl/taGTtcEetunUptUDvUHmCKzKupFcWCIB1WVoNi78YtjR/aKCgHJx8fXXiTZwmPCPzG2g+HIhDgaxXswBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:17:48.580134Z"},"content_sha256":"ba5b012beed571c4cdbff2d2d08191d236daca8996bbab99b26b1956183cf5b2","schema_version":"1.0","event_id":"sha256:ba5b012beed571c4cdbff2d2d08191d236daca8996bbab99b26b1956183cf5b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFQCSNLPQX5HBWZ6BEXIX3C2JB/bundle.json","state_url":"https://pith.science/pith/NFQCSNLPQX5HBWZ6BEXIX3C2JB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFQCSNLPQX5HBWZ6BEXIX3C2JB/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":"2026-06-21T04:17:48Z","links":{"resolver":"https://pith.science/pith/NFQCSNLPQX5HBWZ6BEXIX3C2JB","bundle":"https://pith.science/pith/NFQCSNLPQX5HBWZ6BEXIX3C2JB/bundle.json","state":"https://pith.science/pith/NFQCSNLPQX5HBWZ6BEXIX3C2JB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFQCSNLPQX5HBWZ6BEXIX3C2JB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NFQCSNLPQX5HBWZ6BEXIX3C2JB","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":"e7cd8a9f0ae7f5b38e6d8552acb73b136992cbc6b7d81c8d052651ecc524fd3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-21T01:24:16Z","title_canon_sha256":"2edec7109822295b4e142280368968c633ff1a2c9f812230a7f78325ceb1fcb5"},"schema_version":"1.0","source":{"id":"1401.5139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5139","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5139v1","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5139","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"NFQCSNLPQX5H","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFQCSNLPQX5HBWZ6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFQCSNLP","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:ba5b012beed571c4cdbff2d2d08191d236daca8996bbab99b26b1956183cf5b2","target":"graph","created_at":"2026-05-18T03:01:34Z","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":"In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal domain. The effect of numerical quadrature is also examined. In the semidiscrete case, optimal error estimates in L^{\\infty}(L2) and L^{\\infty}(H1)- norms are shown to hold with minimal regularity assumptions on the initial data, whereas quasi-optimal estimate in derived in L^{\\infty}(L^{\\infty})-norm under higher regularity on the data. Based on a second orde","authors_text":"Amiya K. Pani, Samir Karaa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-21T01:24:16Z","title":"A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5139","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":"sha256:6d395c6012be9194577723d1efb6231feb1265eb2112ebfcc1e282b30c2391dc","target":"record","created_at":"2026-05-18T03:01:34Z","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":"e7cd8a9f0ae7f5b38e6d8552acb73b136992cbc6b7d81c8d052651ecc524fd3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-21T01:24:16Z","title_canon_sha256":"2edec7109822295b4e142280368968c633ff1a2c9f812230a7f78325ceb1fcb5"},"schema_version":"1.0","source":{"id":"1401.5139","kind":"arxiv","version":1}},"canonical_sha256":"696029356f85fa70db3e092e8bec5a4840ed044ce7d5dc86b2b3585e0d89c762","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"696029356f85fa70db3e092e8bec5a4840ed044ce7d5dc86b2b3585e0d89c762","first_computed_at":"2026-05-18T03:01:34.791611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:34.791611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2Kne3QMIs1XuzBM9vDjjJCJwLpp3GPz+U0plpz/DIwe+4s9ol13r5Amqjae1DqZmjo6/f7mIIpx2fmny8uSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:34.792103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d395c6012be9194577723d1efb6231feb1265eb2112ebfcc1e282b30c2391dc","sha256:ba5b012beed571c4cdbff2d2d08191d236daca8996bbab99b26b1956183cf5b2"],"state_sha256":"2f043c3151597282843d518997c369198eaf89c771ab33fc58f62a6a5bccf3ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R++t60sCvwItCWcyNVdJ82o9FcmwkxwBzUXjjfGhlN5y9iLD7tBGv5D1RnFYCosKlhhOz3hIGTYj6xAKe+eXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T04:17:48.582093Z","bundle_sha256":"ac237211121cce78bbd1874dce6623fcfffd79964163fd236dbd66ced9ca610b"}}