{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:YTW7PNSVBFWHSHAXF3JW326M53","short_pith_number":"pith:YTW7PNSV","schema_version":"1.0","canonical_sha256":"c4edf7b655096c791c172ed36debcceecb9a5dadc8dad3bc8075ceae2d27b42c","source":{"kind":"arxiv","id":"math/0510066","version":3},"attestation_state":"computed","paper":{"title":"Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions","license":"","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.NA","authors_text":"Bruno Lombard (LMA), Jo\\\"el Piraux (LMA)","submitted_at":"2005-10-04T08:55:20Z","abstract_excerpt":"The propagation of elastic waves in a fractured rock is investigated, both theoretically and numerically. Outside the fractures, the propagation of compressional waves is described in the simple framework of one-dimensional linear elastodynamics. The focus here is on the interactions between the waves and fractures: for this purpose, the mechanical behavior of the fractures is modeled using nonlinear jump conditions deduced from the Bandis-Barton model classicaly used in geomechanics. Well-posedness of the initial-boundary value problem thus obtained is proved. Numerical modeling is performed "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0510066","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2005-10-04T08:55:20Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"0f9532b846aba1955dcc47557221681b72aed716e66583a9b4f5aaea13254736","abstract_canon_sha256":"43f5288cb4b9313e46aeb6ad8e17ab2fb7261c4ce13db5f202133be1b5436909"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:50.879644Z","signature_b64":"Ztmeb+mRjwpZOupAwmG5m+E69LwBDDRJrqcWFscxi5KTWrlUAtaV0Ih7rBtaEDTvoqPdfnhdlKQJWguzgPHvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4edf7b655096c791c172ed36debcceecb9a5dadc8dad3bc8075ceae2d27b42c","last_reissued_at":"2026-05-18T01:08:50.879034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:50.879034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions","license":"","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.NA","authors_text":"Bruno Lombard (LMA), Jo\\\"el Piraux (LMA)","submitted_at":"2005-10-04T08:55:20Z","abstract_excerpt":"The propagation of elastic waves in a fractured rock is investigated, both theoretically and numerically. Outside the fractures, the propagation of compressional waves is described in the simple framework of one-dimensional linear elastodynamics. The focus here is on the interactions between the waves and fractures: for this purpose, the mechanical behavior of the fractures is modeled using nonlinear jump conditions deduced from the Bandis-Barton model classicaly used in geomechanics. Well-posedness of the initial-boundary value problem thus obtained is proved. Numerical modeling is performed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510066","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0510066","created_at":"2026-05-18T01:08:50.879138+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0510066v3","created_at":"2026-05-18T01:08:50.879138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510066","created_at":"2026-05-18T01:08:50.879138+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTW7PNSVBFWH","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTW7PNSVBFWHSHAX","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTW7PNSV","created_at":"2026-05-18T12:25:53.939244+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53","json":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53.json","graph_json":"https://pith.science/api/pith-number/YTW7PNSVBFWHSHAXF3JW326M53/graph.json","events_json":"https://pith.science/api/pith-number/YTW7PNSVBFWHSHAXF3JW326M53/events.json","paper":"https://pith.science/paper/YTW7PNSV"},"agent_actions":{"view_html":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53","download_json":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53.json","view_paper":"https://pith.science/paper/YTW7PNSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0510066&json=true","fetch_graph":"https://pith.science/api/pith-number/YTW7PNSVBFWHSHAXF3JW326M53/graph.json","fetch_events":"https://pith.science/api/pith-number/YTW7PNSVBFWHSHAXF3JW326M53/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53/action/storage_attestation","attest_author":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53/action/author_attestation","sign_citation":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53/action/citation_signature","submit_replication":"https://pith.science/pith/YTW7PNSVBFWHSHAXF3JW326M53/action/replication_record"}},"created_at":"2026-05-18T01:08:50.879138+00:00","updated_at":"2026-05-18T01:08:50.879138+00:00"}