{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NKYTC3Z3I6WMSAVYRE2XQY6XFC","short_pith_number":"pith:NKYTC3Z3","canonical_record":{"source":{"id":"1904.10941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-24T17:30:17Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"5d2bdb45f184d48c0ffa3272a580a19870b2aaa6ada670a1a03775bd3a85038e","abstract_canon_sha256":"8176ae601accc6a0c6ade56dcc9c07012982561bd4d185beb82ec57e27b3baa2"},"schema_version":"1.0"},"canonical_sha256":"6ab1316f3b47acc902b889357863d72892d55405b0e8337ba65eafa1946c5d30","source":{"kind":"arxiv","id":"1904.10941","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10941","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10941v1","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10941","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"NKYTC3Z3I6WM","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NKYTC3Z3I6WMSAVY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NKYTC3Z3","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NKYTC3Z3I6WMSAVYRE2XQY6XFC","target":"record","payload":{"canonical_record":{"source":{"id":"1904.10941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-24T17:30:17Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"5d2bdb45f184d48c0ffa3272a580a19870b2aaa6ada670a1a03775bd3a85038e","abstract_canon_sha256":"8176ae601accc6a0c6ade56dcc9c07012982561bd4d185beb82ec57e27b3baa2"},"schema_version":"1.0"},"canonical_sha256":"6ab1316f3b47acc902b889357863d72892d55405b0e8337ba65eafa1946c5d30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:49.619383Z","signature_b64":"WxTLZ+cipDtBpqqJDILabAfrvvjrZv8vB//qI2QbFkfW15e5XwgDU5zbwa64RSgGs1dt4hrU6Eh6oZVtsoMsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ab1316f3b47acc902b889357863d72892d55405b0e8337ba65eafa1946c5d30","last_reissued_at":"2026-05-17T23:47:49.618697Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:49.618697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.10941","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":"2026-05-17T23:47:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gTKEVIQ5BvttIBKtPP6q6y90GCqN6CxJiN8oP6VfHEYGWTRuxb0ORnaPquduGnXY/f2CjwMVK6zzvROUIScBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:06:49.971971Z"},"content_sha256":"f6e14f5b660a61bd0f879bfb145bbfef5fd08d3d05077b3f217ef38f7688374d","schema_version":"1.0","event_id":"sha256:f6e14f5b660a61bd0f879bfb145bbfef5fd08d3d05077b3f217ef38f7688374d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NKYTC3Z3I6WMSAVYRE2XQY6XFC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical solutions for two-dimensional singly periodic Stokes flow singularity arrays near walls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CV","authors_text":"Darren Crowdy, Elena Luca","submitted_at":"2019-04-24T17:30:17Z","abstract_excerpt":"New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from a concentric annulus (or a disc) to a rectangle and a complex variable formulation of Stokes flow to derive the solutions. The form of the solutions is amenable to fast and accurate numerical computation without the need for Ewald summation or other fast summation techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10941","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":"2026-05-17T23:47:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmH6opzyu66PzIu81yDj+6Ipsh2IFnCG1sBKMTOvWinX0QvOhG079SskUVS0xLJiAopxRdWa7cy5kJ/Aky0cAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:06:49.972331Z"},"content_sha256":"68b474f5bf09e74df9f12b5717b025c5807569da0f9ea6a810ce69bba8785d78","schema_version":"1.0","event_id":"sha256:68b474f5bf09e74df9f12b5717b025c5807569da0f9ea6a810ce69bba8785d78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKYTC3Z3I6WMSAVYRE2XQY6XFC/bundle.json","state_url":"https://pith.science/pith/NKYTC3Z3I6WMSAVYRE2XQY6XFC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKYTC3Z3I6WMSAVYRE2XQY6XFC/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":"2026-06-25T23:06:49Z","links":{"resolver":"https://pith.science/pith/NKYTC3Z3I6WMSAVYRE2XQY6XFC","bundle":"https://pith.science/pith/NKYTC3Z3I6WMSAVYRE2XQY6XFC/bundle.json","state":"https://pith.science/pith/NKYTC3Z3I6WMSAVYRE2XQY6XFC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKYTC3Z3I6WMSAVYRE2XQY6XFC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NKYTC3Z3I6WMSAVYRE2XQY6XFC","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":"8176ae601accc6a0c6ade56dcc9c07012982561bd4d185beb82ec57e27b3baa2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-24T17:30:17Z","title_canon_sha256":"5d2bdb45f184d48c0ffa3272a580a19870b2aaa6ada670a1a03775bd3a85038e"},"schema_version":"1.0","source":{"id":"1904.10941","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10941","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10941v1","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10941","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"NKYTC3Z3I6WM","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NKYTC3Z3I6WMSAVY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NKYTC3Z3","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:68b474f5bf09e74df9f12b5717b025c5807569da0f9ea6a810ce69bba8785d78","target":"graph","created_at":"2026-05-17T23:47:49Z","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":"New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from a concentric annulus (or a disc) to a rectangle and a complex variable formulation of Stokes flow to derive the solutions. The form of the solutions is amenable to fast and accurate numerical computation without the need for Ewald summation or other fast summation techniques.","authors_text":"Darren Crowdy, Elena Luca","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-24T17:30:17Z","title":"Analytical solutions for two-dimensional singly periodic Stokes flow singularity arrays near walls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10941","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:f6e14f5b660a61bd0f879bfb145bbfef5fd08d3d05077b3f217ef38f7688374d","target":"record","created_at":"2026-05-17T23:47:49Z","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":"8176ae601accc6a0c6ade56dcc9c07012982561bd4d185beb82ec57e27b3baa2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-04-24T17:30:17Z","title_canon_sha256":"5d2bdb45f184d48c0ffa3272a580a19870b2aaa6ada670a1a03775bd3a85038e"},"schema_version":"1.0","source":{"id":"1904.10941","kind":"arxiv","version":1}},"canonical_sha256":"6ab1316f3b47acc902b889357863d72892d55405b0e8337ba65eafa1946c5d30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ab1316f3b47acc902b889357863d72892d55405b0e8337ba65eafa1946c5d30","first_computed_at":"2026-05-17T23:47:49.618697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:49.618697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WxTLZ+cipDtBpqqJDILabAfrvvjrZv8vB//qI2QbFkfW15e5XwgDU5zbwa64RSgGs1dt4hrU6Eh6oZVtsoMsCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:49.619383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.10941","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6e14f5b660a61bd0f879bfb145bbfef5fd08d3d05077b3f217ef38f7688374d","sha256:68b474f5bf09e74df9f12b5717b025c5807569da0f9ea6a810ce69bba8785d78"],"state_sha256":"7e40635008d5c294cbcf9b7bae9e2cff1804275f24d5a86a73a0c10200c7469e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nMlNL2koE4EFJiBMryo/MnXpgS9sVeaTk6yLcNG7k7fXh+84byRHdkCS2R+LReJeib95FqzqFv9jN/jqu9OJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:06:49.974142Z","bundle_sha256":"79d4721c08222533df916f68573fa8ddc8add984432c6e1db370e298371421e9"}}