{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:OFCAFE6K5GD7PDK3QIC5K4UK4X","short_pith_number":"pith:OFCAFE6K","schema_version":"1.0","canonical_sha256":"71440293cae987f78d5b8205d5728ae5cae2f0e6f301ab1f365ca5e1d06205ad","source":{"kind":"arxiv","id":"2308.00673","version":2},"attestation_state":"computed","paper":{"title":"Orthonormal eigenfunction expansions for sixth-order boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"I C Christov, N C Papanicolaou","submitted_at":"2023-08-01T17:20:21Z","abstract_excerpt":"Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions -- resembling trigonometric sines and cosines, as well as the so-called ``beam'' functions. These functions intrinsically satisfy boundary conditions (BCs) of relevance to thin-film flows, since they are the solutions of a self-adjoint sixth-order Sturm--Liouville BVP with the same BCs. Next, we propose a Galerkin spectral approach for sixth-order problems; namely the sought func"},"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":"2308.00673","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-01T17:20:21Z","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"title_canon_sha256":"c9f98f61c9e3ebe092aa1d336b87a7886a94b93561b698716157419f41592c75","abstract_canon_sha256":"1afaa1ba8e3c2bff7dbecd63ee8444f983ee24eeb1887d65cceb573157995390"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:27:26.212781Z","signature_b64":"ney0BiUB4IAp72QfFYADiCZ+1StFUkZnB0EMrv5YlwzQ8zxNqDBXIIZ3ybVM5/3FLE+VHyY8APbEZPXl1OhUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71440293cae987f78d5b8205d5728ae5cae2f0e6f301ab1f365ca5e1d06205ad","last_reissued_at":"2026-07-05T07:27:26.212279Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:27:26.212279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orthonormal eigenfunction expansions for sixth-order boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"I C Christov, N C Papanicolaou","submitted_at":"2023-08-01T17:20:21Z","abstract_excerpt":"Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions -- resembling trigonometric sines and cosines, as well as the so-called ``beam'' functions. These functions intrinsically satisfy boundary conditions (BCs) of relevance to thin-film flows, since they are the solutions of a self-adjoint sixth-order Sturm--Liouville BVP with the same BCs. Next, we propose a Galerkin spectral approach for sixth-order problems; namely the sought func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.00673","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.00673/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2308.00673","created_at":"2026-07-05T07:27:26.212343+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.00673v2","created_at":"2026-07-05T07:27:26.212343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.00673","created_at":"2026-07-05T07:27:26.212343+00:00"},{"alias_kind":"pith_short_12","alias_value":"OFCAFE6K5GD7","created_at":"2026-07-05T07:27:26.212343+00:00"},{"alias_kind":"pith_short_16","alias_value":"OFCAFE6K5GD7PDK3","created_at":"2026-07-05T07:27:26.212343+00:00"},{"alias_kind":"pith_short_8","alias_value":"OFCAFE6K","created_at":"2026-07-05T07:27:26.212343+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.09702","citing_title":"Series solutions for clamped peridynamic beams using fourth-order eigenfunctions","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X","json":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X.json","graph_json":"https://pith.science/api/pith-number/OFCAFE6K5GD7PDK3QIC5K4UK4X/graph.json","events_json":"https://pith.science/api/pith-number/OFCAFE6K5GD7PDK3QIC5K4UK4X/events.json","paper":"https://pith.science/paper/OFCAFE6K"},"agent_actions":{"view_html":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X","download_json":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X.json","view_paper":"https://pith.science/paper/OFCAFE6K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.00673&json=true","fetch_graph":"https://pith.science/api/pith-number/OFCAFE6K5GD7PDK3QIC5K4UK4X/graph.json","fetch_events":"https://pith.science/api/pith-number/OFCAFE6K5GD7PDK3QIC5K4UK4X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X/action/storage_attestation","attest_author":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X/action/author_attestation","sign_citation":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X/action/citation_signature","submit_replication":"https://pith.science/pith/OFCAFE6K5GD7PDK3QIC5K4UK4X/action/replication_record"}},"created_at":"2026-07-05T07:27:26.212343+00:00","updated_at":"2026-07-05T07:27:26.212343+00:00"}