{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QLDNZXWCVG4KZLOR3YGZLCBT5P","short_pith_number":"pith:QLDNZXWC","canonical_record":{"source":{"id":"1608.04681","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-16T17:38:35Z","cross_cats_sorted":[],"title_canon_sha256":"790477d0a8ec122472257105ae0ce3e159af6676723dd228fdde05e18e42626f","abstract_canon_sha256":"7a4f64b43daf45e6473b0cf4a45d92e6a6a21a9bebad76c510fa23f26a9ffc04"},"schema_version":"1.0"},"canonical_sha256":"82c6dcdec2a9b8acadd1de0d958833ebf7f1c7de58ae19b613737dc12193fa81","source":{"kind":"arxiv","id":"1608.04681","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04681","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04681v2","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04681","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"QLDNZXWCVG4K","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QLDNZXWCVG4KZLOR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QLDNZXWC","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QLDNZXWCVG4KZLOR3YGZLCBT5P","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04681","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-16T17:38:35Z","cross_cats_sorted":[],"title_canon_sha256":"790477d0a8ec122472257105ae0ce3e159af6676723dd228fdde05e18e42626f","abstract_canon_sha256":"7a4f64b43daf45e6473b0cf4a45d92e6a6a21a9bebad76c510fa23f26a9ffc04"},"schema_version":"1.0"},"canonical_sha256":"82c6dcdec2a9b8acadd1de0d958833ebf7f1c7de58ae19b613737dc12193fa81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:02.277255Z","signature_b64":"fCbW4T0Bwqmjfw316M5qElTrQUpQa+4c0Ry2JR/cBBsGHGr4EEuKYtFx3Up5wLfgjzSBm9YZyHe6KDcVffoLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82c6dcdec2a9b8acadd1de0d958833ebf7f1c7de58ae19b613737dc12193fa81","last_reissued_at":"2026-05-18T01:04:02.276525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:02.276525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04681","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":"2026-05-18T01:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+0tIhtfvMO6R0oqyihyBT2Aslo9o9nqLwT9WQ0XPNzubVgJW/jJyH1g0TgdIMUzfl9E25bbE4R7J8BMDiwpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:29:11.122108Z"},"content_sha256":"b0b66726463ffb267a974c66f3a247f56ba22795da2ee0c5049eacc79835f5fa","schema_version":"1.0","event_id":"sha256:b0b66726463ffb267a974c66f3a247f56ba22795da2ee0c5049eacc79835f5fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QLDNZXWCVG4KZLOR3YGZLCBT5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wave breaking in a shallow water model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lizheng Tao, Vera Mikyoung Hur","submitted_at":"2016-08-16T17:38:35Z","abstract_excerpt":"We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham equation to permit bidirectional wave propagation, provided that the slope of the initial data is sufficiently negative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04681","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":""},"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":"2026-05-18T01:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PaoIvCmR+E3INGa5tJBeUi5J2KzpIO9lk4TemBZxveGAKKxBBXMJeIAfxhBzDeBYy1pH0oIA2e9/xxWDkMk5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:29:11.122453Z"},"content_sha256":"f321e6676335c0265482c8cc1d56e178152a49fdd4623cbbb0b66743df707547","schema_version":"1.0","event_id":"sha256:f321e6676335c0265482c8cc1d56e178152a49fdd4623cbbb0b66743df707547"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QLDNZXWCVG4KZLOR3YGZLCBT5P/bundle.json","state_url":"https://pith.science/pith/QLDNZXWCVG4KZLOR3YGZLCBT5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QLDNZXWCVG4KZLOR3YGZLCBT5P/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":"2026-06-21T20:29:11Z","links":{"resolver":"https://pith.science/pith/QLDNZXWCVG4KZLOR3YGZLCBT5P","bundle":"https://pith.science/pith/QLDNZXWCVG4KZLOR3YGZLCBT5P/bundle.json","state":"https://pith.science/pith/QLDNZXWCVG4KZLOR3YGZLCBT5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QLDNZXWCVG4KZLOR3YGZLCBT5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QLDNZXWCVG4KZLOR3YGZLCBT5P","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":"7a4f64b43daf45e6473b0cf4a45d92e6a6a21a9bebad76c510fa23f26a9ffc04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-16T17:38:35Z","title_canon_sha256":"790477d0a8ec122472257105ae0ce3e159af6676723dd228fdde05e18e42626f"},"schema_version":"1.0","source":{"id":"1608.04681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04681","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04681v2","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04681","created_at":"2026-05-18T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"QLDNZXWCVG4K","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QLDNZXWCVG4KZLOR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QLDNZXWC","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:f321e6676335c0265482c8cc1d56e178152a49fdd4623cbbb0b66743df707547","target":"graph","created_at":"2026-05-18T01:04:02Z","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 wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham equation to permit bidirectional wave propagation, provided that the slope of the initial data is sufficiently negative.","authors_text":"Lizheng Tao, Vera Mikyoung Hur","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-16T17:38:35Z","title":"Wave breaking in a shallow water model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04681","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:b0b66726463ffb267a974c66f3a247f56ba22795da2ee0c5049eacc79835f5fa","target":"record","created_at":"2026-05-18T01:04:02Z","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":"7a4f64b43daf45e6473b0cf4a45d92e6a6a21a9bebad76c510fa23f26a9ffc04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-16T17:38:35Z","title_canon_sha256":"790477d0a8ec122472257105ae0ce3e159af6676723dd228fdde05e18e42626f"},"schema_version":"1.0","source":{"id":"1608.04681","kind":"arxiv","version":2}},"canonical_sha256":"82c6dcdec2a9b8acadd1de0d958833ebf7f1c7de58ae19b613737dc12193fa81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82c6dcdec2a9b8acadd1de0d958833ebf7f1c7de58ae19b613737dc12193fa81","first_computed_at":"2026-05-18T01:04:02.276525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:02.276525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCbW4T0Bwqmjfw316M5qElTrQUpQa+4c0Ry2JR/cBBsGHGr4EEuKYtFx3Up5wLfgjzSBm9YZyHe6KDcVffoLCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:02.277255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0b66726463ffb267a974c66f3a247f56ba22795da2ee0c5049eacc79835f5fa","sha256:f321e6676335c0265482c8cc1d56e178152a49fdd4623cbbb0b66743df707547"],"state_sha256":"07e95aaf84f63ba25bf3cde0c0d66206249ac4fd60a11e3807372960e8e5c4c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GFbzs5nYXKViJvqi7M0J0PSNOAK/09kCj7jHp6ZpT1MuLNG8UtNonxN3YKW//BKjEAdhLManh9pN6o9r3FaQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:29:11.124307Z","bundle_sha256":"4cab9ba654d821950ea0b69e9a872a632787d4144e703dc64ad0f22566d4da82"}}