{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ELJORC2WFOVCQMAHJYR3SPSXQ5","short_pith_number":"pith:ELJORC2W","canonical_record":{"source":{"id":"1809.02424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-07T12:02:23Z","cross_cats_sorted":[],"title_canon_sha256":"a613b63f308d1b80b95ed1161c0fe6aad811beeb98b7d5c25fcb0fab6a4862df","abstract_canon_sha256":"146cf9250cea70548e13e746bc30b83101542ed56d96b8340b8ea37eb3ce036c"},"schema_version":"1.0"},"canonical_sha256":"22d2e88b562baa2830074e23b93e57875ba5fc126566f4f808311e546a4e427b","source":{"kind":"arxiv","id":"1809.02424","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02424","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02424v2","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02424","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"ELJORC2WFOVC","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ELJORC2WFOVCQMAH","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ELJORC2W","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ELJORC2WFOVCQMAHJYR3SPSXQ5","target":"record","payload":{"canonical_record":{"source":{"id":"1809.02424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-07T12:02:23Z","cross_cats_sorted":[],"title_canon_sha256":"a613b63f308d1b80b95ed1161c0fe6aad811beeb98b7d5c25fcb0fab6a4862df","abstract_canon_sha256":"146cf9250cea70548e13e746bc30b83101542ed56d96b8340b8ea37eb3ce036c"},"schema_version":"1.0"},"canonical_sha256":"22d2e88b562baa2830074e23b93e57875ba5fc126566f4f808311e546a4e427b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:55.396207Z","signature_b64":"Ht+DQuwK5DONAQosDoxw2loA7pXTFUjrqmKNS0lZmgAFD2hZrd7As54LGiwg3mKKibdiKKLCWv7PqKddxSL1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22d2e88b562baa2830074e23b93e57875ba5fc126566f4f808311e546a4e427b","last_reissued_at":"2026-05-18T00:03:55.395612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:55.395612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.02424","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":"2026-05-18T00:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6vo2EP3c2jhcyg4jLUKRMyv588p8t63zMHRbEgWDkHYYKjM7O6vwvHqq4dPsQSHW68M82gR77QRfAUV5oxtgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:40:42.325878Z"},"content_sha256":"5b1a9b88e18fbaf84bfb38f9f4960e9d1f1bc82db6db617cb53584e944ef9a08","schema_version":"1.0","event_id":"sha256:5b1a9b88e18fbaf84bfb38f9f4960e9d1f1bc82db6db617cb53584e944ef9a08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ELJORC2WFOVCQMAHJYR3SPSXQ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-periodic Stokes equations with inhomogeneous Dirichlet boundary conditions in a half-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aday Celik, Mads Kyed","submitted_at":"2018-09-07T12:02:23Z","abstract_excerpt":"The time-periodic Stokes problem in a half-space with fully inhomogeneous right-hand side is investigated. Maximal regularity in a time-periodic Lp setting is established. A method based on Fourier multipliers is employed that leads to a decomposition of the solution into a steady-state and a purely oscillatory part in order to identify the optimal function spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02424","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":""},"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":"2026-05-18T00:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSDd+FXwgIeBxWQrwIZ9dc8ZEESfT6RXBWZn24FKkHW9V1aavCghMaUrrX/NMHF6BK0AEL6CuRWIzNly8yXHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:40:42.326215Z"},"content_sha256":"9e43a1bd0fb12fcb0ba63b6abba589535d59742d49c11163794a4218209b4b74","schema_version":"1.0","event_id":"sha256:9e43a1bd0fb12fcb0ba63b6abba589535d59742d49c11163794a4218209b4b74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELJORC2WFOVCQMAHJYR3SPSXQ5/bundle.json","state_url":"https://pith.science/pith/ELJORC2WFOVCQMAHJYR3SPSXQ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELJORC2WFOVCQMAHJYR3SPSXQ5/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":"2026-06-21T08:40:42Z","links":{"resolver":"https://pith.science/pith/ELJORC2WFOVCQMAHJYR3SPSXQ5","bundle":"https://pith.science/pith/ELJORC2WFOVCQMAHJYR3SPSXQ5/bundle.json","state":"https://pith.science/pith/ELJORC2WFOVCQMAHJYR3SPSXQ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELJORC2WFOVCQMAHJYR3SPSXQ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ELJORC2WFOVCQMAHJYR3SPSXQ5","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":"146cf9250cea70548e13e746bc30b83101542ed56d96b8340b8ea37eb3ce036c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-07T12:02:23Z","title_canon_sha256":"a613b63f308d1b80b95ed1161c0fe6aad811beeb98b7d5c25fcb0fab6a4862df"},"schema_version":"1.0","source":{"id":"1809.02424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02424","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02424v2","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02424","created_at":"2026-05-18T00:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"ELJORC2WFOVC","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ELJORC2WFOVCQMAH","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ELJORC2W","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:9e43a1bd0fb12fcb0ba63b6abba589535d59742d49c11163794a4218209b4b74","target":"graph","created_at":"2026-05-18T00:03:55Z","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 time-periodic Stokes problem in a half-space with fully inhomogeneous right-hand side is investigated. Maximal regularity in a time-periodic Lp setting is established. A method based on Fourier multipliers is employed that leads to a decomposition of the solution into a steady-state and a purely oscillatory part in order to identify the optimal function spaces.","authors_text":"Aday Celik, Mads Kyed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-07T12:02:23Z","title":"Time-periodic Stokes equations with inhomogeneous Dirichlet boundary conditions in a half-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02424","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":"sha256:5b1a9b88e18fbaf84bfb38f9f4960e9d1f1bc82db6db617cb53584e944ef9a08","target":"record","created_at":"2026-05-18T00:03:55Z","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":"146cf9250cea70548e13e746bc30b83101542ed56d96b8340b8ea37eb3ce036c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-07T12:02:23Z","title_canon_sha256":"a613b63f308d1b80b95ed1161c0fe6aad811beeb98b7d5c25fcb0fab6a4862df"},"schema_version":"1.0","source":{"id":"1809.02424","kind":"arxiv","version":2}},"canonical_sha256":"22d2e88b562baa2830074e23b93e57875ba5fc126566f4f808311e546a4e427b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22d2e88b562baa2830074e23b93e57875ba5fc126566f4f808311e546a4e427b","first_computed_at":"2026-05-18T00:03:55.395612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:55.395612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ht+DQuwK5DONAQosDoxw2loA7pXTFUjrqmKNS0lZmgAFD2hZrd7As54LGiwg3mKKibdiKKLCWv7PqKddxSL1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:55.396207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b1a9b88e18fbaf84bfb38f9f4960e9d1f1bc82db6db617cb53584e944ef9a08","sha256:9e43a1bd0fb12fcb0ba63b6abba589535d59742d49c11163794a4218209b4b74"],"state_sha256":"91e7af7a69fed54c85d9b5a4327b8bc9e715d04e092e24be7675a7781a56801f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ialxRbwYxB+ZYzjSNAmx+BT5mDUScGGvmY0gd1Ou76/xIFjxjYiLCUtL+bGgz19n7Ch137+Ttue8tfUoHuA6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:40:42.328191Z","bundle_sha256":"9cdeef68039f9a0be4913f2e94e5a105e149ddaebc6dbd6ba4e85be66512c135"}}