{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QAMRIP3Z6GTD3STIN7N4PNIDL4","short_pith_number":"pith:QAMRIP3Z","canonical_record":{"source":{"id":"1507.02478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-09T12:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"2b3dddd491f520fadc828d87bc405edbc454ff709c4fdf7efc0f35c03b053372","abstract_canon_sha256":"9f32f5cd4cfafbc9453fc39bd92853e65aa9dd085d74cfe8d1692bf8541657a3"},"schema_version":"1.0"},"canonical_sha256":"8019143f79f1a63dca686fdbc7b5035f1019b617344a57410921d873b64fe84b","source":{"kind":"arxiv","id":"1507.02478","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02478","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02478v1","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02478","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"QAMRIP3Z6GTD","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QAMRIP3Z6GTD3STI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QAMRIP3Z","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QAMRIP3Z6GTD3STIN7N4PNIDL4","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-09T12:23:57Z","cross_cats_sorted":[],"title_canon_sha256":"2b3dddd491f520fadc828d87bc405edbc454ff709c4fdf7efc0f35c03b053372","abstract_canon_sha256":"9f32f5cd4cfafbc9453fc39bd92853e65aa9dd085d74cfe8d1692bf8541657a3"},"schema_version":"1.0"},"canonical_sha256":"8019143f79f1a63dca686fdbc7b5035f1019b617344a57410921d873b64fe84b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:06.606819Z","signature_b64":"m1TKATx5WZ5YlrUtRI+qDT8wuliXeV2pn5WTL4UkutBmm1GsVsTWan0sowoUKebC3Y7AD0autUDRh9DDL6F9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8019143f79f1a63dca686fdbc7b5035f1019b617344a57410921d873b64fe84b","last_reissued_at":"2026-05-18T01:37:06.606298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:06.606298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02478","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":"2026-05-18T01:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64rdNEmLQFq0cSWCOef2GhdcE9+AYdAIZxLnaOro7eh/RF2O6rzNl64/XN4+Iti6B2zeROPsZUhGjBAQQ5OMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:26:55.458063Z"},"content_sha256":"1c451488668a5af0eaa57909aaf074023d539b6a32a9cf7d1d238103b37dfc0d","schema_version":"1.0","event_id":"sha256:1c451488668a5af0eaa57909aaf074023d539b6a32a9cf7d1d238103b37dfc0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QAMRIP3Z6GTD3STIN7N4PNIDL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Wang, Weiren Zhao, Yunrui Zheng, Zhifei Zhang","submitted_at":"2015-07-09T12:23:57Z","abstract_excerpt":"In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschtiz function and the free surface belongs to $C^{\\f32+\\varepsilon}$. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02478","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":"2026-05-18T01:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1HAlCIezq3zXDCDiYLQYLkG3I4bDUDCU4KeScKhStjNOfV20md6CxL7iWdalX0LOA4Q8AMs9JGdri0Id8gC2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:26:55.458769Z"},"content_sha256":"b7e9d647c9f206eea46bac2036512a3d119cddce4f4b21df63bb1f8ef58c7c4d","schema_version":"1.0","event_id":"sha256:b7e9d647c9f206eea46bac2036512a3d119cddce4f4b21df63bb1f8ef58c7c4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QAMRIP3Z6GTD3STIN7N4PNIDL4/bundle.json","state_url":"https://pith.science/pith/QAMRIP3Z6GTD3STIN7N4PNIDL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QAMRIP3Z6GTD3STIN7N4PNIDL4/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":"2026-05-31T15:26:55Z","links":{"resolver":"https://pith.science/pith/QAMRIP3Z6GTD3STIN7N4PNIDL4","bundle":"https://pith.science/pith/QAMRIP3Z6GTD3STIN7N4PNIDL4/bundle.json","state":"https://pith.science/pith/QAMRIP3Z6GTD3STIN7N4PNIDL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QAMRIP3Z6GTD3STIN7N4PNIDL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QAMRIP3Z6GTD3STIN7N4PNIDL4","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":"9f32f5cd4cfafbc9453fc39bd92853e65aa9dd085d74cfe8d1692bf8541657a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-09T12:23:57Z","title_canon_sha256":"2b3dddd491f520fadc828d87bc405edbc454ff709c4fdf7efc0f35c03b053372"},"schema_version":"1.0","source":{"id":"1507.02478","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02478","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02478v1","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02478","created_at":"2026-05-18T01:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"QAMRIP3Z6GTD","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QAMRIP3Z6GTD3STI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QAMRIP3Z","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:b7e9d647c9f206eea46bac2036512a3d119cddce4f4b21df63bb1f8ef58c7c4d","target":"graph","created_at":"2026-05-18T01:37:06Z","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":"In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschtiz function and the free surface belongs to $C^{\\f32+\\varepsilon}$. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.","authors_text":"Chao Wang, Weiren Zhao, Yunrui Zheng, Zhifei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-09T12:23:57Z","title":"Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02478","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":"sha256:1c451488668a5af0eaa57909aaf074023d539b6a32a9cf7d1d238103b37dfc0d","target":"record","created_at":"2026-05-18T01:37:06Z","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":"9f32f5cd4cfafbc9453fc39bd92853e65aa9dd085d74cfe8d1692bf8541657a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-09T12:23:57Z","title_canon_sha256":"2b3dddd491f520fadc828d87bc405edbc454ff709c4fdf7efc0f35c03b053372"},"schema_version":"1.0","source":{"id":"1507.02478","kind":"arxiv","version":1}},"canonical_sha256":"8019143f79f1a63dca686fdbc7b5035f1019b617344a57410921d873b64fe84b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8019143f79f1a63dca686fdbc7b5035f1019b617344a57410921d873b64fe84b","first_computed_at":"2026-05-18T01:37:06.606298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:06.606298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m1TKATx5WZ5YlrUtRI+qDT8wuliXeV2pn5WTL4UkutBmm1GsVsTWan0sowoUKebC3Y7AD0autUDRh9DDL6F9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:06.606819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02478","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c451488668a5af0eaa57909aaf074023d539b6a32a9cf7d1d238103b37dfc0d","sha256:b7e9d647c9f206eea46bac2036512a3d119cddce4f4b21df63bb1f8ef58c7c4d"],"state_sha256":"3e8c46d1072ed79dae20ef261d857727e948b36d961840bec40fd2a1d47ee795"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6YXzKJHqYhAtGU+xSa1c5qMp0UZM9dUJgPPliYNl/+crRdvSuGym2sMbBTcXd0Bv1An+JkguSk/5q9jvNCGJCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:26:55.462661Z","bundle_sha256":"9ac9364e94740498c62bc085205cae2877c6657e3b5cc082f4a5c6a78585d562"}}