{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:J2WIA5KBAC2OD5GHJASSRQRQ5D","short_pith_number":"pith:J2WIA5KB","canonical_record":{"source":{"id":"1105.1653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T12:16:33Z","cross_cats_sorted":[],"title_canon_sha256":"10a69b248fd207403ccd33d61c77a26f96960179d44eac208212b78a7b59c35b","abstract_canon_sha256":"8f04ffc21996dc2bee02118cc30366e298e5ed95bd7d368e52a97eb947883596"},"schema_version":"1.0"},"canonical_sha256":"4eac80754100b4e1f4c7482528c230e8d1088b999671964f14d3d83a99733d09","source":{"kind":"arxiv","id":"1105.1653","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1653","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1653v1","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1653","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"J2WIA5KBAC2O","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J2WIA5KBAC2OD5GH","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J2WIA5KB","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:J2WIA5KBAC2OD5GHJASSRQRQ5D","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T12:16:33Z","cross_cats_sorted":[],"title_canon_sha256":"10a69b248fd207403ccd33d61c77a26f96960179d44eac208212b78a7b59c35b","abstract_canon_sha256":"8f04ffc21996dc2bee02118cc30366e298e5ed95bd7d368e52a97eb947883596"},"schema_version":"1.0"},"canonical_sha256":"4eac80754100b4e1f4c7482528c230e8d1088b999671964f14d3d83a99733d09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:02.587160Z","signature_b64":"aWOJivX0fOF3wNeJpT5qXhxC+QrHNUb2g/QC52Zf+xPPhSekxdQLwoGPbXe8biaWmk9PMYxpovMmLICZ4z6zAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eac80754100b4e1f4c7482528c230e8d1088b999671964f14d3d83a99733d09","last_reissued_at":"2026-05-18T02:02:02.586503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:02.586503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1653","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":"2026-05-18T02:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWjAy5t2cF840nWPMH+v2Bgw09zQQZGmYd8BE4XZpZTzmz53wLieBOP8QyrgzPGlgEkcX03XAlBShiXm1J2uAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:46:06.029162Z"},"content_sha256":"93be13efb7ec6b8cd85a54a96c5ca1e44363089186adb501f8c25f3baaaaa91e","schema_version":"1.0","event_id":"sha256:93be13efb7ec6b8cd85a54a96c5ca1e44363089186adb501f8c25f3baaaaa91e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:J2WIA5KBAC2OD5GHJASSRQRQ5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivalence of weak formulations of the steady water waves equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arghir Zarnescu, Eugen Varvaruca","submitted_at":"2011-05-09T12:16:33Z","abstract_excerpt":"We prove the equivalence of three weak formulations of the steady water waves equations, namely the velocity formulation, the stream function formulation, and the Dubreil-Jacotin formulation, under weak Holder regularity assumptions on their solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1653","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":"2026-05-18T02:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KtFSNhfgin1EFUjnngSGsbGIXicqlXbloB9mVZhpnLKIxgejL31U7ED5jYz00wPUsykwaIk490fHzK/IhIzJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:46:06.029520Z"},"content_sha256":"9592df5110e0d12b130ee974b9fb4f28d4e67a7f61015e1e76d73ca3eb84f168","schema_version":"1.0","event_id":"sha256:9592df5110e0d12b130ee974b9fb4f28d4e67a7f61015e1e76d73ca3eb84f168"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J2WIA5KBAC2OD5GHJASSRQRQ5D/bundle.json","state_url":"https://pith.science/pith/J2WIA5KBAC2OD5GHJASSRQRQ5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J2WIA5KBAC2OD5GHJASSRQRQ5D/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":"2026-06-21T21:46:06Z","links":{"resolver":"https://pith.science/pith/J2WIA5KBAC2OD5GHJASSRQRQ5D","bundle":"https://pith.science/pith/J2WIA5KBAC2OD5GHJASSRQRQ5D/bundle.json","state":"https://pith.science/pith/J2WIA5KBAC2OD5GHJASSRQRQ5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J2WIA5KBAC2OD5GHJASSRQRQ5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J2WIA5KBAC2OD5GHJASSRQRQ5D","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":"8f04ffc21996dc2bee02118cc30366e298e5ed95bd7d368e52a97eb947883596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T12:16:33Z","title_canon_sha256":"10a69b248fd207403ccd33d61c77a26f96960179d44eac208212b78a7b59c35b"},"schema_version":"1.0","source":{"id":"1105.1653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1653","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1653v1","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1653","created_at":"2026-05-18T02:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"J2WIA5KBAC2O","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J2WIA5KBAC2OD5GH","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J2WIA5KB","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:9592df5110e0d12b130ee974b9fb4f28d4e67a7f61015e1e76d73ca3eb84f168","target":"graph","created_at":"2026-05-18T02:02:02Z","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":"We prove the equivalence of three weak formulations of the steady water waves equations, namely the velocity formulation, the stream function formulation, and the Dubreil-Jacotin formulation, under weak Holder regularity assumptions on their solutions.","authors_text":"Arghir Zarnescu, Eugen Varvaruca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T12:16:33Z","title":"Equivalence of weak formulations of the steady water waves equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1653","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":"sha256:93be13efb7ec6b8cd85a54a96c5ca1e44363089186adb501f8c25f3baaaaa91e","target":"record","created_at":"2026-05-18T02:02:02Z","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":"8f04ffc21996dc2bee02118cc30366e298e5ed95bd7d368e52a97eb947883596","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-09T12:16:33Z","title_canon_sha256":"10a69b248fd207403ccd33d61c77a26f96960179d44eac208212b78a7b59c35b"},"schema_version":"1.0","source":{"id":"1105.1653","kind":"arxiv","version":1}},"canonical_sha256":"4eac80754100b4e1f4c7482528c230e8d1088b999671964f14d3d83a99733d09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eac80754100b4e1f4c7482528c230e8d1088b999671964f14d3d83a99733d09","first_computed_at":"2026-05-18T02:02:02.586503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:02.586503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aWOJivX0fOF3wNeJpT5qXhxC+QrHNUb2g/QC52Zf+xPPhSekxdQLwoGPbXe8biaWmk9PMYxpovMmLICZ4z6zAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:02.587160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93be13efb7ec6b8cd85a54a96c5ca1e44363089186adb501f8c25f3baaaaa91e","sha256:9592df5110e0d12b130ee974b9fb4f28d4e67a7f61015e1e76d73ca3eb84f168"],"state_sha256":"4ce2d19a26fbb954477f9b080d078d885a965db4c23067ce2b6201f739fd8a1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cj9KERbtRMr1UrQkJ5kOcBrYMA3o3MTJmBD0gfSXNKE/8sRAl2zHRd55ASu+wk0OWGwkM5B44drvHRSaRkpECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:46:06.031455Z","bundle_sha256":"e3ebad5eeeae9e60c6e9c8006bb50f192a13a9b546b05a686786ccaf853e1b4a"}}