{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HXIGF65TZRYCCHOGOPR4PJBC7K","short_pith_number":"pith:HXIGF65T","canonical_record":{"source":{"id":"1812.01583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T18:40:13Z","cross_cats_sorted":[],"title_canon_sha256":"5580d6b8fa915391788ec75a73f7ceaf8f427f9fe112638d270258af5078b11e","abstract_canon_sha256":"f6d6fdb97e814df8d13028c14eee8ebf23c81b4b841dd6959adc3aaacaa4e7cb"},"schema_version":"1.0"},"canonical_sha256":"3dd062fbb3cc70211dc673e3c7a422faac674d4290a0c075e9df1bc92d207032","source":{"kind":"arxiv","id":"1812.01583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01583","created_at":"2026-05-17T23:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01583v1","created_at":"2026-05-17T23:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01583","created_at":"2026-05-17T23:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"HXIGF65TZRYC","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HXIGF65TZRYCCHOG","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HXIGF65T","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HXIGF65TZRYCCHOGOPR4PJBC7K","target":"record","payload":{"canonical_record":{"source":{"id":"1812.01583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T18:40:13Z","cross_cats_sorted":[],"title_canon_sha256":"5580d6b8fa915391788ec75a73f7ceaf8f427f9fe112638d270258af5078b11e","abstract_canon_sha256":"f6d6fdb97e814df8d13028c14eee8ebf23c81b4b841dd6959adc3aaacaa4e7cb"},"schema_version":"1.0"},"canonical_sha256":"3dd062fbb3cc70211dc673e3c7a422faac674d4290a0c075e9df1bc92d207032","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:10.447619Z","signature_b64":"n4PYc9KehT+d7SqHDb8Fu7ZvM9fBDxTiuTE/whl7SlyHHs3RzB/hbebF1yiImZUmj6b0rGO6B5NUm9UnjSy1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dd062fbb3cc70211dc673e3c7a422faac674d4290a0c075e9df1bc92d207032","last_reissued_at":"2026-05-17T23:59:10.446981Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:10.446981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.01583","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":"2026-05-17T23:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVdrYBZqRXWSKc7OgjpAeao31L8AMPfAelrFtNIA5xNw2rNaNnIFzl9jbAQXp2rjn5I1f6PIXXDOz6Ny8ESIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T13:17:45.669229Z"},"content_sha256":"be3db255782cc83bac6831177a85cf74281a8b716bec0efaec4d292d751602a4","schema_version":"1.0","event_id":"sha256:be3db255782cc83bac6831177a85cf74281a8b716bec0efaec4d292d751602a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HXIGF65TZRYCCHOGOPR4PJBC7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the lifespan of three-dimensional gravity water waves with vorticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Ginsberg","submitted_at":"2018-12-04T18:40:13Z","abstract_excerpt":"We prove a long-term regularity result for three-dimensional gravity water waves with small initial data but nonzero initial vorticity. We consider solutions whose vorticity vanishes on the free boundary and use this to derive a system for the evolution of the free boundary which reduces to the Zakharov/Craig-Sulem formulation in the irrotational case. We are able to continue the solution until a time determined by the size of the initial vorticity in such a way that if the vorticity is zero, one recovers a lifespan $T\\sim \\epsilon^{-N}$ where $N$ can be taken arbitrarily large if the initial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01583","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":"2026-05-17T23:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4gZugTTrt59pYh67JcG8BEbZVGv2iMhoKi/pFY49yL5g5jS5mJAva+xfzzz3Rm981y7CIxOj0wDSVcCzUy7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T13:17:45.669573Z"},"content_sha256":"7f314769c39b921cab85fc73f3ddab8d7b40d0807c336bfb517bfc98228afa43","schema_version":"1.0","event_id":"sha256:7f314769c39b921cab85fc73f3ddab8d7b40d0807c336bfb517bfc98228afa43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXIGF65TZRYCCHOGOPR4PJBC7K/bundle.json","state_url":"https://pith.science/pith/HXIGF65TZRYCCHOGOPR4PJBC7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXIGF65TZRYCCHOGOPR4PJBC7K/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":"2026-06-28T13:17:45Z","links":{"resolver":"https://pith.science/pith/HXIGF65TZRYCCHOGOPR4PJBC7K","bundle":"https://pith.science/pith/HXIGF65TZRYCCHOGOPR4PJBC7K/bundle.json","state":"https://pith.science/pith/HXIGF65TZRYCCHOGOPR4PJBC7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXIGF65TZRYCCHOGOPR4PJBC7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HXIGF65TZRYCCHOGOPR4PJBC7K","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":"f6d6fdb97e814df8d13028c14eee8ebf23c81b4b841dd6959adc3aaacaa4e7cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T18:40:13Z","title_canon_sha256":"5580d6b8fa915391788ec75a73f7ceaf8f427f9fe112638d270258af5078b11e"},"schema_version":"1.0","source":{"id":"1812.01583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01583","created_at":"2026-05-17T23:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01583v1","created_at":"2026-05-17T23:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01583","created_at":"2026-05-17T23:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"HXIGF65TZRYC","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HXIGF65TZRYCCHOG","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HXIGF65T","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:7f314769c39b921cab85fc73f3ddab8d7b40d0807c336bfb517bfc98228afa43","target":"graph","created_at":"2026-05-17T23:59:10Z","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 a long-term regularity result for three-dimensional gravity water waves with small initial data but nonzero initial vorticity. We consider solutions whose vorticity vanishes on the free boundary and use this to derive a system for the evolution of the free boundary which reduces to the Zakharov/Craig-Sulem formulation in the irrotational case. We are able to continue the solution until a time determined by the size of the initial vorticity in such a way that if the vorticity is zero, one recovers a lifespan $T\\sim \\epsilon^{-N}$ where $N$ can be taken arbitrarily large if the initial ","authors_text":"Daniel Ginsberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T18:40:13Z","title":"On the lifespan of three-dimensional gravity water waves with vorticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01583","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:be3db255782cc83bac6831177a85cf74281a8b716bec0efaec4d292d751602a4","target":"record","created_at":"2026-05-17T23:59:10Z","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":"f6d6fdb97e814df8d13028c14eee8ebf23c81b4b841dd6959adc3aaacaa4e7cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-04T18:40:13Z","title_canon_sha256":"5580d6b8fa915391788ec75a73f7ceaf8f427f9fe112638d270258af5078b11e"},"schema_version":"1.0","source":{"id":"1812.01583","kind":"arxiv","version":1}},"canonical_sha256":"3dd062fbb3cc70211dc673e3c7a422faac674d4290a0c075e9df1bc92d207032","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dd062fbb3cc70211dc673e3c7a422faac674d4290a0c075e9df1bc92d207032","first_computed_at":"2026-05-17T23:59:10.446981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:10.446981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n4PYc9KehT+d7SqHDb8Fu7ZvM9fBDxTiuTE/whl7SlyHHs3RzB/hbebF1yiImZUmj6b0rGO6B5NUm9UnjSy1Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:10.447619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be3db255782cc83bac6831177a85cf74281a8b716bec0efaec4d292d751602a4","sha256:7f314769c39b921cab85fc73f3ddab8d7b40d0807c336bfb517bfc98228afa43"],"state_sha256":"5b7087931f0edfe74ebb868d1c3e4832d1fa85d5f57b2982d4397bdacd98b54e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6YrXz4jVlTL+gKw7sJ2KXPn3UNSH6OXzuYVJCLePziI88H+QGV0uIj+c9MkWe8442jDmsTR8iwldrW0JsXqRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T13:17:45.671608Z","bundle_sha256":"3f0869faa17a7ac620374d89b51dbc9036e075d02e0433e41921f7e42d7307f3"}}