{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NTMC6MN2MYHQM5EKTZFBBCXCQ7","short_pith_number":"pith:NTMC6MN2","canonical_record":{"source":{"id":"1308.1423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T21:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"dcfbf5e0b5e6559484f9546b92ee1138d2acfe41b1931d38d5eebcdb0e590c29","abstract_canon_sha256":"dcd7bb16fb9f855384db72041aeb174473cf4cff3616bcfc6063a30d0a49ef88"},"schema_version":"1.0"},"canonical_sha256":"6cd82f31ba660f06748a9e4a108ae287c87d56fa6dd940b33116ec8225e91cc3","source":{"kind":"arxiv","id":"1308.1423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1423","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1423v1","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1423","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"NTMC6MN2MYHQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NTMC6MN2MYHQM5EK","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NTMC6MN2","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NTMC6MN2MYHQM5EKTZFBBCXCQ7","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T21:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"dcfbf5e0b5e6559484f9546b92ee1138d2acfe41b1931d38d5eebcdb0e590c29","abstract_canon_sha256":"dcd7bb16fb9f855384db72041aeb174473cf4cff3616bcfc6063a30d0a49ef88"},"schema_version":"1.0"},"canonical_sha256":"6cd82f31ba660f06748a9e4a108ae287c87d56fa6dd940b33116ec8225e91cc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:38.062890Z","signature_b64":"Nx6xd/4hTi2FZZt/ZckLpqRDssaHh9K1b4FW9JVBZHg7iavt0+mYVSKZx/tKyrjso3BGE5segYcf/qtdhvqxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cd82f31ba660f06748a9e4a108ae287c87d56fa6dd940b33116ec8225e91cc3","last_reissued_at":"2026-05-18T03:16:38.062370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:38.062370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1423","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":"2026-05-18T03:16:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjL9EHXp/j09gxbXaNGBRZKelSc3zJCv8sjJOY9ZmBlR60if5q4OoF0wW1GOn5AUcTItJ6ThmbnnrY9WLmKSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:51:58.487436Z"},"content_sha256":"87009d85b56262efcefd3dc09737119dd363b3b8a2a78af0ab754b82ad07db86","schema_version":"1.0","event_id":"sha256:87009d85b56262efcefd3dc09737119dd363b3b8a2a78af0ab754b82ad07db86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NTMC6MN2MYHQM5EKTZFBBCXCQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strichartz estimates for gravity water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claude Zuily, Nicolas Burq, Thomas Alazard","submitted_at":"2013-08-06T21:02:44Z","abstract_excerpt":"We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled in $L^\\infty$-norm, or the initial free surface has a curvature not controlled in $L^2$-norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1423","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":"2026-05-18T03:16:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2I9FiAEyKUxSNQ0LJjtAg0MKcCJifvwkjv48cWVb+QyGPMmQtKPDpCOSeHjzLPpM9sej4ruBIIpPeWb/r/xDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:51:58.487783Z"},"content_sha256":"8d5f9ce90240f75f503fe46aa93cf3503a6afddea938e63e3b9e7003139e4855","schema_version":"1.0","event_id":"sha256:8d5f9ce90240f75f503fe46aa93cf3503a6afddea938e63e3b9e7003139e4855"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTMC6MN2MYHQM5EKTZFBBCXCQ7/bundle.json","state_url":"https://pith.science/pith/NTMC6MN2MYHQM5EKTZFBBCXCQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTMC6MN2MYHQM5EKTZFBBCXCQ7/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":"2026-06-21T08:51:58Z","links":{"resolver":"https://pith.science/pith/NTMC6MN2MYHQM5EKTZFBBCXCQ7","bundle":"https://pith.science/pith/NTMC6MN2MYHQM5EKTZFBBCXCQ7/bundle.json","state":"https://pith.science/pith/NTMC6MN2MYHQM5EKTZFBBCXCQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTMC6MN2MYHQM5EKTZFBBCXCQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NTMC6MN2MYHQM5EKTZFBBCXCQ7","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":"dcd7bb16fb9f855384db72041aeb174473cf4cff3616bcfc6063a30d0a49ef88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T21:02:44Z","title_canon_sha256":"dcfbf5e0b5e6559484f9546b92ee1138d2acfe41b1931d38d5eebcdb0e590c29"},"schema_version":"1.0","source":{"id":"1308.1423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1423","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1423v1","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1423","created_at":"2026-05-18T03:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"NTMC6MN2MYHQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NTMC6MN2MYHQM5EK","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NTMC6MN2","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:8d5f9ce90240f75f503fe46aa93cf3503a6afddea938e63e3b9e7003139e4855","target":"graph","created_at":"2026-05-18T03:16:38Z","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 Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled in $L^\\infty$-norm, or the initial free surface has a curvature not controlled in $L^2$-norm.","authors_text":"Claude Zuily, Nicolas Burq, Thomas Alazard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T21:02:44Z","title":"Strichartz estimates for gravity water waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1423","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":"sha256:87009d85b56262efcefd3dc09737119dd363b3b8a2a78af0ab754b82ad07db86","target":"record","created_at":"2026-05-18T03:16:38Z","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":"dcd7bb16fb9f855384db72041aeb174473cf4cff3616bcfc6063a30d0a49ef88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T21:02:44Z","title_canon_sha256":"dcfbf5e0b5e6559484f9546b92ee1138d2acfe41b1931d38d5eebcdb0e590c29"},"schema_version":"1.0","source":{"id":"1308.1423","kind":"arxiv","version":1}},"canonical_sha256":"6cd82f31ba660f06748a9e4a108ae287c87d56fa6dd940b33116ec8225e91cc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cd82f31ba660f06748a9e4a108ae287c87d56fa6dd940b33116ec8225e91cc3","first_computed_at":"2026-05-18T03:16:38.062370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:38.062370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nx6xd/4hTi2FZZt/ZckLpqRDssaHh9K1b4FW9JVBZHg7iavt0+mYVSKZx/tKyrjso3BGE5segYcf/qtdhvqxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:38.062890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87009d85b56262efcefd3dc09737119dd363b3b8a2a78af0ab754b82ad07db86","sha256:8d5f9ce90240f75f503fe46aa93cf3503a6afddea938e63e3b9e7003139e4855"],"state_sha256":"90c767ab5cacc473da46c90dba4c11b5385d5f8a7775b3f7e7ee5be26a41fa03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOrVVRgrZwBx8lyGK5w6bFk3nqASYoKCA3uapD3/NT6o5weHcHG4DJ1YraGoAgVytbOOsqR2GFQG5KqOooXXDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:51:58.489714Z","bundle_sha256":"f5588ec589049fdc1635de2b486c291cf1e954801a1faab38379ec35e66ce6fd"}}