{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:HYG5ZPMCIN5VWFEFZVI2YF2D2W","short_pith_number":"pith:HYG5ZPMC","canonical_record":{"source":{"id":"2010.09117","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-18T21:58:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8c5817fc16f8971e8f2c49d7b14bbdcb6816cce998bcaf61aa92355823516582","abstract_canon_sha256":"143f1faacde6a51339d09d72d360c04495e5fa10d57734ceffb07e79241d758e"},"schema_version":"1.0"},"canonical_sha256":"3e0ddcbd82437b5b1485cd51ac1743d5b21a5d30288a6e205f5685dda6e836ac","source":{"kind":"arxiv","id":"2010.09117","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09117","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09117v2","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09117","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"pith_short_12","alias_value":"HYG5ZPMCIN5V","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"HYG5ZPMCIN5VWFEF","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"HYG5ZPMC","created_at":"2026-07-05T02:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:HYG5ZPMCIN5VWFEFZVI2YF2D2W","target":"record","payload":{"canonical_record":{"source":{"id":"2010.09117","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-18T21:58:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8c5817fc16f8971e8f2c49d7b14bbdcb6816cce998bcaf61aa92355823516582","abstract_canon_sha256":"143f1faacde6a51339d09d72d360c04495e5fa10d57734ceffb07e79241d758e"},"schema_version":"1.0"},"canonical_sha256":"3e0ddcbd82437b5b1485cd51ac1743d5b21a5d30288a6e205f5685dda6e836ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:33:21.163831Z","signature_b64":"OmClpUxGM76O6Ay/XUmtPbMXNxDxfubZyIhTkTBCAmEi1qaWmkQ84tc3/Q0x1qy5ndqUHcueMX60VrcwpNOnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e0ddcbd82437b5b1485cd51ac1743d5b21a5d30288a6e205f5685dda6e836ac","last_reissued_at":"2026-07-05T02:33:21.163353Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:33:21.163353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.09117","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:33:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAkMT19dIqxtv4Knz2G8P3bWX4cqkbOud2nnJo9012ZpXuXN8DviFUP4+nqeXoJlexzsi7QQ376Rimu1/q/kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:07:29.015958Z"},"content_sha256":"0eccc7258c356dda9d75fc44141367b71e014ecf31006de5a70480422750e482","schema_version":"1.0","event_id":"sha256:0eccc7258c356dda9d75fc44141367b71e014ecf31006de5a70480422750e482"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:HYG5ZPMCIN5VWFEFZVI2YF2D2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The quartic integrability and long time existence of steep water waves in 2D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Sijue Wu","submitted_at":"2020-10-18T21:58:59Z","abstract_excerpt":"It is known since the work of Dyachenko \\& Zakharov \\cite{zd} that for the weakly nonlinear 2d infinite depth water waves, there are no 3-wave interactions and all of the 4-wave interaction coefficients vanish on the non-trivial resonant manifold. In this paper we study this partial integrability from a different point of view.\n  We construct, directly in the physical space, a sequence of energy functionals $\\mathfrak E_j(t)$ which are explicit in the Riemann mapping variable and involve material derivatives of order $j$ of the solutions for the 2d water wave equation, so that $\\frac d{dt} \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09117","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.09117/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:33:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aHPf34lh1n9z0vHQkK5tYOGtKXPS68HY0tPw85YIYkVFFUvji5WDX9TABa5o86ZLy88MYdks87izmqDARNmWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:07:29.016691Z"},"content_sha256":"20961b1ccd14ae2a3ffbdcef9253f08186ae8d4b4ed4b7d3cafe966a3eaee9dc","schema_version":"1.0","event_id":"sha256:20961b1ccd14ae2a3ffbdcef9253f08186ae8d4b4ed4b7d3cafe966a3eaee9dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYG5ZPMCIN5VWFEFZVI2YF2D2W/bundle.json","state_url":"https://pith.science/pith/HYG5ZPMCIN5VWFEFZVI2YF2D2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYG5ZPMCIN5VWFEFZVI2YF2D2W/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":"2026-08-09T14:07:29Z","links":{"resolver":"https://pith.science/pith/HYG5ZPMCIN5VWFEFZVI2YF2D2W","bundle":"https://pith.science/pith/HYG5ZPMCIN5VWFEFZVI2YF2D2W/bundle.json","state":"https://pith.science/pith/HYG5ZPMCIN5VWFEFZVI2YF2D2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYG5ZPMCIN5VWFEFZVI2YF2D2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HYG5ZPMCIN5VWFEFZVI2YF2D2W","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":"143f1faacde6a51339d09d72d360c04495e5fa10d57734ceffb07e79241d758e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-18T21:58:59Z","title_canon_sha256":"8c5817fc16f8971e8f2c49d7b14bbdcb6816cce998bcaf61aa92355823516582"},"schema_version":"1.0","source":{"id":"2010.09117","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09117","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09117v2","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09117","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"pith_short_12","alias_value":"HYG5ZPMCIN5V","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"HYG5ZPMCIN5VWFEF","created_at":"2026-07-05T02:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"HYG5ZPMC","created_at":"2026-07-05T02:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:20961b1ccd14ae2a3ffbdcef9253f08186ae8d4b4ed4b7d3cafe966a3eaee9dc","target":"graph","created_at":"2026-07-05T02:33:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.09117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is known since the work of Dyachenko \\& Zakharov \\cite{zd} that for the weakly nonlinear 2d infinite depth water waves, there are no 3-wave interactions and all of the 4-wave interaction coefficients vanish on the non-trivial resonant manifold. In this paper we study this partial integrability from a different point of view.\n  We construct, directly in the physical space, a sequence of energy functionals $\\mathfrak E_j(t)$ which are explicit in the Riemann mapping variable and involve material derivatives of order $j$ of the solutions for the 2d water wave equation, so that $\\frac d{dt} \\ma","authors_text":"Sijue Wu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-18T21:58:59Z","title":"The quartic integrability and long time existence of steep water waves in 2D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09117","kind":"arxiv","version":2},"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":"sha256:0eccc7258c356dda9d75fc44141367b71e014ecf31006de5a70480422750e482","target":"record","created_at":"2026-07-05T02:33:21Z","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":"143f1faacde6a51339d09d72d360c04495e5fa10d57734ceffb07e79241d758e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-18T21:58:59Z","title_canon_sha256":"8c5817fc16f8971e8f2c49d7b14bbdcb6816cce998bcaf61aa92355823516582"},"schema_version":"1.0","source":{"id":"2010.09117","kind":"arxiv","version":2}},"canonical_sha256":"3e0ddcbd82437b5b1485cd51ac1743d5b21a5d30288a6e205f5685dda6e836ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0ddcbd82437b5b1485cd51ac1743d5b21a5d30288a6e205f5685dda6e836ac","first_computed_at":"2026-07-05T02:33:21.163353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:33:21.163353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OmClpUxGM76O6Ay/XUmtPbMXNxDxfubZyIhTkTBCAmEi1qaWmkQ84tc3/Q0x1qy5ndqUHcueMX60VrcwpNOnBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:33:21.163831Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.09117","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eccc7258c356dda9d75fc44141367b71e014ecf31006de5a70480422750e482","sha256:20961b1ccd14ae2a3ffbdcef9253f08186ae8d4b4ed4b7d3cafe966a3eaee9dc"],"state_sha256":"8d26a0db14df50442eacf4f8308e441fdbf1d0af450756bde1947daa14694d2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6hPeRhv84Sm8VSyQbV2y7AOvyhVXX0Migvz+qlf6Tv84o6y7+gn4CXekJEDSzb4cId+kXPk6EVk/boVEON2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T14:07:29.022433Z","bundle_sha256":"1efc0824ab03c795fab2fe9e16f702a78e7be1b32ec75b053e252c612b831120"}}