{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:L5KRVBSAN7AT2DJWDLKTTL34YQ","short_pith_number":"pith:L5KRVBSA","canonical_record":{"source":{"id":"2008.00895","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-08-03T14:22:37Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"df4705bee9f2de3256bedee0eb46172bd9d730769db2a00d304e11340c8728b7","abstract_canon_sha256":"a95b0ffac594d88bbd8d53a7b98862350aa8f4e0419e95aa58db64f6f822a38a"},"schema_version":"1.0"},"canonical_sha256":"5f551a86406fc13d0d361ad539af7cc406f7f3f76d363c58d81edd8126132600","source":{"kind":"arxiv","id":"2008.00895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.00895","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"arxiv_version","alias_value":"2008.00895v2","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.00895","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"pith_short_12","alias_value":"L5KRVBSAN7AT","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"L5KRVBSAN7AT2DJW","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"L5KRVBSA","created_at":"2026-07-05T03:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:L5KRVBSAN7AT2DJWDLKTTL34YQ","target":"record","payload":{"canonical_record":{"source":{"id":"2008.00895","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-08-03T14:22:37Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"df4705bee9f2de3256bedee0eb46172bd9d730769db2a00d304e11340c8728b7","abstract_canon_sha256":"a95b0ffac594d88bbd8d53a7b98862350aa8f4e0419e95aa58db64f6f822a38a"},"schema_version":"1.0"},"canonical_sha256":"5f551a86406fc13d0d361ad539af7cc406f7f3f76d363c58d81edd8126132600","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:29:27.428409Z","signature_b64":"QR1awzSS4vm2b565Ca9J63cWQK9CUKUR4bAUZVpowLGNWYut/vBvcKETx7K8mG0QbHSmAmp2X9/X27+/QtrbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f551a86406fc13d0d361ad539af7cc406f7f3f76d363c58d81edd8126132600","last_reissued_at":"2026-07-05T03:29:27.427984Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:29:27.427984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.00895","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:29:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AvTNksgdWhmYV80HvYORDOVzq+YYVIvzD7qygxgeNS3dCI4p2b84dUpZDyLZ3li58EAT2HFPEayIP5RsWAbICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:44:09.261968Z"},"content_sha256":"223f65e9e8310f5f991545d863e83b54e53abe07c8f3c3b1d6df7634de17176c","schema_version":"1.0","event_id":"sha256:223f65e9e8310f5f991545d863e83b54e53abe07c8f3c3b1d6df7634de17176c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:L5KRVBSAN7AT2DJWDLKTTL34YQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Chun Liu, Patrik Knopf","submitted_at":"2020-08-03T14:22:37Z","abstract_excerpt":"In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace--Beltrami equation on the boundary of the domain. The bulk and the surface PDE are coupled by a boundary condition that is either of Dirichlet or Robin type. We point out that both the Dirichlet and the Robin type boundary condition can be handled simultaneously through our formalism without having to change the framework. Moreover, we investigate the eigenvalue problems associated with these second-order and fourth-order elliptic syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.00895","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/2008.00895/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:29:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRC5ME/szSq6WzQuBhRm6s4WHWDmZKD3ssSa3hIVw3aIGGaDnWeUSSrFakkrsB21G9RoFw+87fL0bVWkxNtaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:44:09.262481Z"},"content_sha256":"322aa3e34f44f1bfa6456ce9927af8c34de02207ec92e2fcdbde4309aecd42ab","schema_version":"1.0","event_id":"sha256:322aa3e34f44f1bfa6456ce9927af8c34de02207ec92e2fcdbde4309aecd42ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5KRVBSAN7AT2DJWDLKTTL34YQ/bundle.json","state_url":"https://pith.science/pith/L5KRVBSAN7AT2DJWDLKTTL34YQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5KRVBSAN7AT2DJWDLKTTL34YQ/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":"2026-08-03T21:44:09Z","links":{"resolver":"https://pith.science/pith/L5KRVBSAN7AT2DJWDLKTTL34YQ","bundle":"https://pith.science/pith/L5KRVBSAN7AT2DJWDLKTTL34YQ/bundle.json","state":"https://pith.science/pith/L5KRVBSAN7AT2DJWDLKTTL34YQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5KRVBSAN7AT2DJWDLKTTL34YQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:L5KRVBSAN7AT2DJWDLKTTL34YQ","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":"a95b0ffac594d88bbd8d53a7b98862350aa8f4e0419e95aa58db64f6f822a38a","cross_cats_sorted":["math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-08-03T14:22:37Z","title_canon_sha256":"df4705bee9f2de3256bedee0eb46172bd9d730769db2a00d304e11340c8728b7"},"schema_version":"1.0","source":{"id":"2008.00895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.00895","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"arxiv_version","alias_value":"2008.00895v2","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.00895","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"pith_short_12","alias_value":"L5KRVBSAN7AT","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"L5KRVBSAN7AT2DJW","created_at":"2026-07-05T03:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"L5KRVBSA","created_at":"2026-07-05T03:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:322aa3e34f44f1bfa6456ce9927af8c34de02207ec92e2fcdbde4309aecd42ab","target":"graph","created_at":"2026-07-05T03:29:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.00895/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace--Beltrami equation on the boundary of the domain. The bulk and the surface PDE are coupled by a boundary condition that is either of Dirichlet or Robin type. We point out that both the Dirichlet and the Robin type boundary condition can be handled simultaneously through our formalism without having to change the framework. Moreover, we investigate the eigenvalue problems associated with these second-order and fourth-order elliptic syste","authors_text":"Chun Liu, Patrik Knopf","cross_cats":["math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-08-03T14:22:37Z","title":"On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.00895","kind":"arxiv","version":2},"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":"sha256:223f65e9e8310f5f991545d863e83b54e53abe07c8f3c3b1d6df7634de17176c","target":"record","created_at":"2026-07-05T03:29:27Z","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":"a95b0ffac594d88bbd8d53a7b98862350aa8f4e0419e95aa58db64f6f822a38a","cross_cats_sorted":["math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-08-03T14:22:37Z","title_canon_sha256":"df4705bee9f2de3256bedee0eb46172bd9d730769db2a00d304e11340c8728b7"},"schema_version":"1.0","source":{"id":"2008.00895","kind":"arxiv","version":2}},"canonical_sha256":"5f551a86406fc13d0d361ad539af7cc406f7f3f76d363c58d81edd8126132600","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f551a86406fc13d0d361ad539af7cc406f7f3f76d363c58d81edd8126132600","first_computed_at":"2026-07-05T03:29:27.427984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:29:27.427984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QR1awzSS4vm2b565Ca9J63cWQK9CUKUR4bAUZVpowLGNWYut/vBvcKETx7K8mG0QbHSmAmp2X9/X27+/QtrbCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:29:27.428409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.00895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:223f65e9e8310f5f991545d863e83b54e53abe07c8f3c3b1d6df7634de17176c","sha256:322aa3e34f44f1bfa6456ce9927af8c34de02207ec92e2fcdbde4309aecd42ab"],"state_sha256":"2d212ad1cd94285aa0f245c3b0920031e38b7809e773ce8b1953991e54065477"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBqTN4Z+8gfK5OuVZSZ4pPO/5Spm76adS+j2+92L+4VtE8tWN5Ehi2iTJoBbge2oHduhfL0CAdxPtGMezWV2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:44:09.265792Z","bundle_sha256":"ae35d74bbc934b3f21075861aa4222a0419e55ae23f1272c1945589c6e0a14eb"}}