{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LKRZGGKGV6USPHBBYM5SJXL6A7","short_pith_number":"pith:LKRZGGKG","canonical_record":{"source":{"id":"1602.06163","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-02-19T14:27:59Z","cross_cats_sorted":["nlin.SI","physics.flu-dyn"],"title_canon_sha256":"13cd88769d86651a901daabebe44a75654f693581b50771b33081ad3f6495dd0","abstract_canon_sha256":"1201e4b16253b07fc28cdc3ec3abf709f47397eed28688cf641db003f3bcb969"},"schema_version":"1.0"},"canonical_sha256":"5aa3931946afa9279c21c33b24dd7e07d32dfe67194d109dea2d54ed0fe34cb1","source":{"kind":"arxiv","id":"1602.06163","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06163","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06163v2","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06163","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"LKRZGGKGV6US","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LKRZGGKGV6USPHBB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LKRZGGKG","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LKRZGGKGV6USPHBBYM5SJXL6A7","target":"record","payload":{"canonical_record":{"source":{"id":"1602.06163","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-02-19T14:27:59Z","cross_cats_sorted":["nlin.SI","physics.flu-dyn"],"title_canon_sha256":"13cd88769d86651a901daabebe44a75654f693581b50771b33081ad3f6495dd0","abstract_canon_sha256":"1201e4b16253b07fc28cdc3ec3abf709f47397eed28688cf641db003f3bcb969"},"schema_version":"1.0"},"canonical_sha256":"5aa3931946afa9279c21c33b24dd7e07d32dfe67194d109dea2d54ed0fe34cb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:14.711474Z","signature_b64":"8RLRVEofYllcYMsQTTSgDzICMSazd3PoNyRHv06s73p8xvNu4Dslwq41I3WTHXeBzPzsb8/NwvVgYxjIn86pDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5aa3931946afa9279c21c33b24dd7e07d32dfe67194d109dea2d54ed0fe34cb1","last_reissued_at":"2026-05-18T01:10:14.710947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:14.710947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.06163","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":"2026-05-18T01:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+0wqnN0tKaG1BNHNlr3FOr3Fw/uTvT+5Chz993CiHWOTMBFz41IKWeq7dlCWVJY62scnWHwVOnUUZHRRS8vDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:25:24.650923Z"},"content_sha256":"9a4d850efb0abacab3402aae8490bc73cda5d3d7b61847202cba61bc9b083b10","schema_version":"1.0","event_id":"sha256:9a4d850efb0abacab3402aae8490bc73cda5d3d7b61847202cba61bc9b083b10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LKRZGGKGV6USPHBBYM5SJXL6A7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersive shock waves and modulation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI","physics.flu-dyn"],"primary_cat":"nlin.PS","authors_text":"G. A. El, M. A. Hoefer","submitted_at":"2016-02-19T14:27:59Z","abstract_excerpt":"There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.~B.~Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06163","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":"2026-05-18T01:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sGGpTHVASfA25Jzi8dya/fI5cozVV92l1zEnGa+/TEbuh4+RxNVpRU+y9t3OU+F/BZDhFSWPvdO+hA1P+aTfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:25:24.651648Z"},"content_sha256":"e5e41bcbad4a03ca093da071d4fd38f534b76c76193df2a4e0afab3770bbde46","schema_version":"1.0","event_id":"sha256:e5e41bcbad4a03ca093da071d4fd38f534b76c76193df2a4e0afab3770bbde46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LKRZGGKGV6USPHBBYM5SJXL6A7/bundle.json","state_url":"https://pith.science/pith/LKRZGGKGV6USPHBBYM5SJXL6A7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LKRZGGKGV6USPHBBYM5SJXL6A7/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":"2026-06-09T08:25:24Z","links":{"resolver":"https://pith.science/pith/LKRZGGKGV6USPHBBYM5SJXL6A7","bundle":"https://pith.science/pith/LKRZGGKGV6USPHBBYM5SJXL6A7/bundle.json","state":"https://pith.science/pith/LKRZGGKGV6USPHBBYM5SJXL6A7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LKRZGGKGV6USPHBBYM5SJXL6A7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LKRZGGKGV6USPHBBYM5SJXL6A7","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":"1201e4b16253b07fc28cdc3ec3abf709f47397eed28688cf641db003f3bcb969","cross_cats_sorted":["nlin.SI","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-02-19T14:27:59Z","title_canon_sha256":"13cd88769d86651a901daabebe44a75654f693581b50771b33081ad3f6495dd0"},"schema_version":"1.0","source":{"id":"1602.06163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06163","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06163v2","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06163","created_at":"2026-05-18T01:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"LKRZGGKGV6US","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LKRZGGKGV6USPHBB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LKRZGGKG","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:e5e41bcbad4a03ca093da071d4fd38f534b76c76193df2a4e0afab3770bbde46","target":"graph","created_at":"2026-05-18T01:10:14Z","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":"There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.~B.~Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coh","authors_text":"G. A. El, M. A. Hoefer","cross_cats":["nlin.SI","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-02-19T14:27:59Z","title":"Dispersive shock waves and modulation theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06163","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":"sha256:9a4d850efb0abacab3402aae8490bc73cda5d3d7b61847202cba61bc9b083b10","target":"record","created_at":"2026-05-18T01:10:14Z","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":"1201e4b16253b07fc28cdc3ec3abf709f47397eed28688cf641db003f3bcb969","cross_cats_sorted":["nlin.SI","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-02-19T14:27:59Z","title_canon_sha256":"13cd88769d86651a901daabebe44a75654f693581b50771b33081ad3f6495dd0"},"schema_version":"1.0","source":{"id":"1602.06163","kind":"arxiv","version":2}},"canonical_sha256":"5aa3931946afa9279c21c33b24dd7e07d32dfe67194d109dea2d54ed0fe34cb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5aa3931946afa9279c21c33b24dd7e07d32dfe67194d109dea2d54ed0fe34cb1","first_computed_at":"2026-05-18T01:10:14.710947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:14.710947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8RLRVEofYllcYMsQTTSgDzICMSazd3PoNyRHv06s73p8xvNu4Dslwq41I3WTHXeBzPzsb8/NwvVgYxjIn86pDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:14.711474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a4d850efb0abacab3402aae8490bc73cda5d3d7b61847202cba61bc9b083b10","sha256:e5e41bcbad4a03ca093da071d4fd38f534b76c76193df2a4e0afab3770bbde46"],"state_sha256":"45815bc17a27c174bdc4c4314e2129765a6b48049cd603495699ffb44ab1d19c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uRWm2IxOWqEAJMDn0zVOW2UmQuNM/m8775O7ubkfA8JY27obbe6Xel6vhqEhtpe5O47c+wbnhnlNs01jvnjZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:25:24.655999Z","bundle_sha256":"c6c14692e73a038677e0a0df991e0ccde69c51faf2d2482f9afc6d2995cd0626"}}