{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YHHJLTO6HXWAVJ4O7TDIN3PGHL","short_pith_number":"pith:YHHJLTO6","canonical_record":{"source":{"id":"1505.04115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T16:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"c76c31346a2b975e9d306e3a8fb2a9e24ba257804c851aaefd7631bcbce4758b","abstract_canon_sha256":"b78e82a19ebd8bab2f98c382e27cafd5cef9732e7aa685f87d07d27dc72383ba"},"schema_version":"1.0"},"canonical_sha256":"c1ce95cdde3dec0aa78efcc686ede63af42e4523fb21b020312eae223b73ca77","source":{"kind":"arxiv","id":"1505.04115","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04115","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04115v2","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04115","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"YHHJLTO6HXWA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YHHJLTO6HXWAVJ4O","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YHHJLTO6","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YHHJLTO6HXWAVJ4O7TDIN3PGHL","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T16:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"c76c31346a2b975e9d306e3a8fb2a9e24ba257804c851aaefd7631bcbce4758b","abstract_canon_sha256":"b78e82a19ebd8bab2f98c382e27cafd5cef9732e7aa685f87d07d27dc72383ba"},"schema_version":"1.0"},"canonical_sha256":"c1ce95cdde3dec0aa78efcc686ede63af42e4523fb21b020312eae223b73ca77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:14.257180Z","signature_b64":"zC5l/u+RmIv7PpmXayOYsGA7wo/xwe8AC4qz4/wAPl16RJHrtsCnNm4nqIGHsUEA1QUJ2Ky5Ek629IL16quBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1ce95cdde3dec0aa78efcc686ede63af42e4523fb21b020312eae223b73ca77","last_reissued_at":"2026-05-18T01:28:14.256471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:14.256471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04115","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":"2026-05-18T01:28:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFFnLrLR7j1ehNuvIe2ua6d/adoSk/ViaYmf4D7XrLEawD+BL2dmmCGL3t73q4oFE8CPpRPwYtzYG7e39S5aCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:39:55.372936Z"},"content_sha256":"f92275612a4f6ea7941a5e8249696021ccf1b9a5cca685029f8ef60d8a6bc905","schema_version":"1.0","event_id":"sha256:f92275612a4f6ea7941a5e8249696021ccf1b9a5cca685029f8ef60d8a6bc905"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YHHJLTO6HXWAVJ4O7TDIN3PGHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A fundamental solution to the time-periodic Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mads Kyed","submitted_at":"2015-05-15T16:41:00Z","abstract_excerpt":"The concept of a fundamental solution to the time-periodic Stokes equations in dimension $n\\geq 2$ is introduced. A fundamental solution is then identified and analyzed. Integrability and pointwise estimates are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04115","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":"2026-05-18T01:28:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NUkzc6Lu3WoySwxgT0kAwnT28guomQ3rmb9t9AmpYdgAlSVzj4YPWBp8rvFaaXDOqvI9qubRdtZu5RPQip5oAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:39:55.373646Z"},"content_sha256":"e4961401a14bbbb0b4ce9e9d2d3bcf1ad189b1b6fd827e6170937000d905ce53","schema_version":"1.0","event_id":"sha256:e4961401a14bbbb0b4ce9e9d2d3bcf1ad189b1b6fd827e6170937000d905ce53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YHHJLTO6HXWAVJ4O7TDIN3PGHL/bundle.json","state_url":"https://pith.science/pith/YHHJLTO6HXWAVJ4O7TDIN3PGHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YHHJLTO6HXWAVJ4O7TDIN3PGHL/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":"2026-06-08T18:39:55Z","links":{"resolver":"https://pith.science/pith/YHHJLTO6HXWAVJ4O7TDIN3PGHL","bundle":"https://pith.science/pith/YHHJLTO6HXWAVJ4O7TDIN3PGHL/bundle.json","state":"https://pith.science/pith/YHHJLTO6HXWAVJ4O7TDIN3PGHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YHHJLTO6HXWAVJ4O7TDIN3PGHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YHHJLTO6HXWAVJ4O7TDIN3PGHL","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":"b78e82a19ebd8bab2f98c382e27cafd5cef9732e7aa685f87d07d27dc72383ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T16:41:00Z","title_canon_sha256":"c76c31346a2b975e9d306e3a8fb2a9e24ba257804c851aaefd7631bcbce4758b"},"schema_version":"1.0","source":{"id":"1505.04115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04115","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04115v2","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04115","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"YHHJLTO6HXWA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YHHJLTO6HXWAVJ4O","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YHHJLTO6","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:e4961401a14bbbb0b4ce9e9d2d3bcf1ad189b1b6fd827e6170937000d905ce53","target":"graph","created_at":"2026-05-18T01:28:14Z","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 concept of a fundamental solution to the time-periodic Stokes equations in dimension $n\\geq 2$ is introduced. A fundamental solution is then identified and analyzed. Integrability and pointwise estimates are established.","authors_text":"Mads Kyed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T16:41:00Z","title":"A fundamental solution to the time-periodic Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04115","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:f92275612a4f6ea7941a5e8249696021ccf1b9a5cca685029f8ef60d8a6bc905","target":"record","created_at":"2026-05-18T01:28:14Z","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":"b78e82a19ebd8bab2f98c382e27cafd5cef9732e7aa685f87d07d27dc72383ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T16:41:00Z","title_canon_sha256":"c76c31346a2b975e9d306e3a8fb2a9e24ba257804c851aaefd7631bcbce4758b"},"schema_version":"1.0","source":{"id":"1505.04115","kind":"arxiv","version":2}},"canonical_sha256":"c1ce95cdde3dec0aa78efcc686ede63af42e4523fb21b020312eae223b73ca77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1ce95cdde3dec0aa78efcc686ede63af42e4523fb21b020312eae223b73ca77","first_computed_at":"2026-05-18T01:28:14.256471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:14.256471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zC5l/u+RmIv7PpmXayOYsGA7wo/xwe8AC4qz4/wAPl16RJHrtsCnNm4nqIGHsUEA1QUJ2Ky5Ek629IL16quBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:14.257180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f92275612a4f6ea7941a5e8249696021ccf1b9a5cca685029f8ef60d8a6bc905","sha256:e4961401a14bbbb0b4ce9e9d2d3bcf1ad189b1b6fd827e6170937000d905ce53"],"state_sha256":"17ad1c3649f84dd3c5bb3fb8297c244d979702b8ceca221a01bd5459771f7539"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vtsc2bq8xx9SOdWO8+9z0/7jKLGKZJVgM9X414+yR17nmKuXuzcCNGqXFFcyqwzxP3veAWkWGgRXjQoVxY9fCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:39:55.377373Z","bundle_sha256":"7cba5c32c1b061064e79bfaa0d2c324af295b97326b09ba0b10dc21463616b02"}}