{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:J22HDBQ2SU26M73KK5UVXCUGYS","short_pith_number":"pith:J22HDBQ2","canonical_record":{"source":{"id":"1804.04172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T19:06:35Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"516ba071813b27868a08383e7693392634b95e389a9d7fe35bfe4407cf786c7c","abstract_canon_sha256":"ec0e142b0f7894a22c80163677f2256053d5cc73ec45a558f8888065e861c702"},"schema_version":"1.0"},"canonical_sha256":"4eb471861a9535e67f6a57695b8a86c48b49994dae45764af1033cd3198eaed5","source":{"kind":"arxiv","id":"1804.04172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04172","created_at":"2026-05-18T00:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04172v1","created_at":"2026-05-18T00:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04172","created_at":"2026-05-18T00:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"J22HDBQ2SU26","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J22HDBQ2SU26M73K","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J22HDBQ2","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:J22HDBQ2SU26M73KK5UVXCUGYS","target":"record","payload":{"canonical_record":{"source":{"id":"1804.04172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T19:06:35Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"516ba071813b27868a08383e7693392634b95e389a9d7fe35bfe4407cf786c7c","abstract_canon_sha256":"ec0e142b0f7894a22c80163677f2256053d5cc73ec45a558f8888065e861c702"},"schema_version":"1.0"},"canonical_sha256":"4eb471861a9535e67f6a57695b8a86c48b49994dae45764af1033cd3198eaed5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:40.574068Z","signature_b64":"ViusdQ0ucuYdWwDB1bWsVhDRNj+mXngTJyHquF44iS7cyahORfEj76UJqf39ctI+8wbRb5RgqQUXJ0Lpd6fhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eb471861a9535e67f6a57695b8a86c48b49994dae45764af1033cd3198eaed5","last_reissued_at":"2026-05-18T00:18:40.573388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:40.573388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.04172","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":"2026-05-18T00:18:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+RsJvSdZTc2UALpZNx4a+oKGvC5M7zOjWA4JfCsaO7fz2W4LwccEwQHDlaMFkHo+UUEJjYxC4VkV+0SmbdmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:29:46.344045Z"},"content_sha256":"16d6a76c4d4254271cb7a3e086e025d8272c28de69583b4658c7cd4929abdf68","schema_version":"1.0","event_id":"sha256:16d6a76c4d4254271cb7a3e086e025d8272c28de69583b4658c7cd4929abdf68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:J22HDBQ2SU26M73KK5UVXCUGYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variational principle for three-dimensional water waves over Beltrami flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Erik Wahl\\'en, Evgeniy Lokharu","submitted_at":"2018-04-11T19:06:35Z","abstract_excerpt":"We consider steady three-dimensional gravity-capillary water waves with vorticity propagating on water of finite depth. We prove a variational principle for doubly periodic waves with relative velocities given by Beltrami vector fields, under general assumptions on the wave profile."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04172","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":"2026-05-18T00:18:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j59Yk8kA9viTHG4eNPKRliOmcMYZSv+tpGSIOHiuvUqqdigyjxzJwGTwy5jNgGtcuvdWX8ocTxaxkXhHT+f4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:29:46.344446Z"},"content_sha256":"218cd56e38e3801cca32db17222323abac78d992e7e8da6ebac2d2514dc5775d","schema_version":"1.0","event_id":"sha256:218cd56e38e3801cca32db17222323abac78d992e7e8da6ebac2d2514dc5775d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J22HDBQ2SU26M73KK5UVXCUGYS/bundle.json","state_url":"https://pith.science/pith/J22HDBQ2SU26M73KK5UVXCUGYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J22HDBQ2SU26M73KK5UVXCUGYS/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":"2026-05-31T21:29:46Z","links":{"resolver":"https://pith.science/pith/J22HDBQ2SU26M73KK5UVXCUGYS","bundle":"https://pith.science/pith/J22HDBQ2SU26M73KK5UVXCUGYS/bundle.json","state":"https://pith.science/pith/J22HDBQ2SU26M73KK5UVXCUGYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J22HDBQ2SU26M73KK5UVXCUGYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J22HDBQ2SU26M73KK5UVXCUGYS","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":"ec0e142b0f7894a22c80163677f2256053d5cc73ec45a558f8888065e861c702","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T19:06:35Z","title_canon_sha256":"516ba071813b27868a08383e7693392634b95e389a9d7fe35bfe4407cf786c7c"},"schema_version":"1.0","source":{"id":"1804.04172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.04172","created_at":"2026-05-18T00:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.04172v1","created_at":"2026-05-18T00:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04172","created_at":"2026-05-18T00:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"J22HDBQ2SU26","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J22HDBQ2SU26M73K","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J22HDBQ2","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:218cd56e38e3801cca32db17222323abac78d992e7e8da6ebac2d2514dc5775d","target":"graph","created_at":"2026-05-18T00:18:40Z","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 consider steady three-dimensional gravity-capillary water waves with vorticity propagating on water of finite depth. We prove a variational principle for doubly periodic waves with relative velocities given by Beltrami vector fields, under general assumptions on the wave profile.","authors_text":"Erik Wahl\\'en, Evgeniy Lokharu","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T19:06:35Z","title":"A variational principle for three-dimensional water waves over Beltrami flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04172","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":"sha256:16d6a76c4d4254271cb7a3e086e025d8272c28de69583b4658c7cd4929abdf68","target":"record","created_at":"2026-05-18T00:18:40Z","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":"ec0e142b0f7894a22c80163677f2256053d5cc73ec45a558f8888065e861c702","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T19:06:35Z","title_canon_sha256":"516ba071813b27868a08383e7693392634b95e389a9d7fe35bfe4407cf786c7c"},"schema_version":"1.0","source":{"id":"1804.04172","kind":"arxiv","version":1}},"canonical_sha256":"4eb471861a9535e67f6a57695b8a86c48b49994dae45764af1033cd3198eaed5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eb471861a9535e67f6a57695b8a86c48b49994dae45764af1033cd3198eaed5","first_computed_at":"2026-05-18T00:18:40.573388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:40.573388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ViusdQ0ucuYdWwDB1bWsVhDRNj+mXngTJyHquF44iS7cyahORfEj76UJqf39ctI+8wbRb5RgqQUXJ0Lpd6fhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:40.574068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.04172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16d6a76c4d4254271cb7a3e086e025d8272c28de69583b4658c7cd4929abdf68","sha256:218cd56e38e3801cca32db17222323abac78d992e7e8da6ebac2d2514dc5775d"],"state_sha256":"7679e5165d84877ca11cbefd4a3f13b932c5ea8e24f3b6fe65580f96b7db2a2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DohrlvtbW5bPNv3up0vd5eSHiSHPs1ZDkOFlLot/i631x3Q94BBlayP7GOtR+osw2Wc4Rd/thpMtSgJjTCMQCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:29:46.346521Z","bundle_sha256":"e77d861996afd913781e9132c018e5777707444927d2fad4266252ba2a855639"}}