{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SMOA5QQTMNNYAPDIR3I7QOU6IE","short_pith_number":"pith:SMOA5QQT","canonical_record":{"source":{"id":"1508.05365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-08-20T12:05:25Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"6d07b854773fcbb05258362d871d3d5c25d07cd8111d7eb024c184b17df9d860","abstract_canon_sha256":"0f84d8dcf24a6745199c63b6b17beaef98dcb5dc0824986e24ecf6c97ef73714"},"schema_version":"1.0"},"canonical_sha256":"931c0ec213635b803c688ed1f83a9e4138f70c85589e42a0c2b97f04e5a10e63","source":{"kind":"arxiv","id":"1508.05365","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05365","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05365v1","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05365","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"pith_short_12","alias_value":"SMOA5QQTMNNY","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SMOA5QQTMNNYAPDI","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SMOA5QQT","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SMOA5QQTMNNYAPDIR3I7QOU6IE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.05365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-08-20T12:05:25Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"6d07b854773fcbb05258362d871d3d5c25d07cd8111d7eb024c184b17df9d860","abstract_canon_sha256":"0f84d8dcf24a6745199c63b6b17beaef98dcb5dc0824986e24ecf6c97ef73714"},"schema_version":"1.0"},"canonical_sha256":"931c0ec213635b803c688ed1f83a9e4138f70c85589e42a0c2b97f04e5a10e63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:13.102691Z","signature_b64":"MAi0Jbq5GxV/PyyQtm43oyLDLyVoD+5IrUkIM/l10qXHdEFIkKuhAorkBq+eaZ1r9/XqXM8+sIvhC/CK+rdZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"931c0ec213635b803c688ed1f83a9e4138f70c85589e42a0c2b97f04e5a10e63","last_reissued_at":"2026-05-18T01:08:13.102166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:13.102166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.05365","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":"2026-05-18T01:08:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1knWUINxkcGPSLM4LbldO452JAyA0TlL7sfsGHfQVMnZsRijrubNCsl4hsRT6TjWkE2i3m3bAfS7lOpTtt2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:23:44.962299Z"},"content_sha256":"6ea457342ac3f89aeaeaf95f47bae90d9d731dc2f6ed15150feeffb9031bec58","schema_version":"1.0","event_id":"sha256:6ea457342ac3f89aeaeaf95f47bae90d9d731dc2f6ed15150feeffb9031bec58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SMOA5QQTMNNYAPDIR3I7QOU6IE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mechanical balance laws for fully nonlinear and weakly dispersive water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"physics.flu-dyn","authors_text":"Dimitrios Mitsotakis, Henrik Kalisch, Zahra Khorsand","submitted_at":"2015-08-20T12:05:25Z","abstract_excerpt":"The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected.\n  In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05365","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":"2026-05-18T01:08:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4nFUQqVcOVomipzk2Dk7arGp05jMQBffrorGhNoxd71VbA2tOFc+pSR4s7Y1f+xIubLnbyOilE2Xu3phWv8GCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:23:44.962731Z"},"content_sha256":"28ea6b86b6131c065b466675a7ff6b399ba4e65b8a4bc49e10fec937fd5e7c53","schema_version":"1.0","event_id":"sha256:28ea6b86b6131c065b466675a7ff6b399ba4e65b8a4bc49e10fec937fd5e7c53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMOA5QQTMNNYAPDIR3I7QOU6IE/bundle.json","state_url":"https://pith.science/pith/SMOA5QQTMNNYAPDIR3I7QOU6IE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMOA5QQTMNNYAPDIR3I7QOU6IE/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":"2026-06-11T02:23:44Z","links":{"resolver":"https://pith.science/pith/SMOA5QQTMNNYAPDIR3I7QOU6IE","bundle":"https://pith.science/pith/SMOA5QQTMNNYAPDIR3I7QOU6IE/bundle.json","state":"https://pith.science/pith/SMOA5QQTMNNYAPDIR3I7QOU6IE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMOA5QQTMNNYAPDIR3I7QOU6IE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SMOA5QQTMNNYAPDIR3I7QOU6IE","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":"0f84d8dcf24a6745199c63b6b17beaef98dcb5dc0824986e24ecf6c97ef73714","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-08-20T12:05:25Z","title_canon_sha256":"6d07b854773fcbb05258362d871d3d5c25d07cd8111d7eb024c184b17df9d860"},"schema_version":"1.0","source":{"id":"1508.05365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05365","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05365v1","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05365","created_at":"2026-05-18T01:08:13Z"},{"alias_kind":"pith_short_12","alias_value":"SMOA5QQTMNNY","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SMOA5QQTMNNYAPDI","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SMOA5QQT","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:28ea6b86b6131c065b466675a7ff6b399ba4e65b8a4bc49e10fec937fd5e7c53","target":"graph","created_at":"2026-05-18T01:08:13Z","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":"The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected.\n  In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, th","authors_text":"Dimitrios Mitsotakis, Henrik Kalisch, Zahra Khorsand","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-08-20T12:05:25Z","title":"Mechanical balance laws for fully nonlinear and weakly dispersive water waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05365","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":"sha256:6ea457342ac3f89aeaeaf95f47bae90d9d731dc2f6ed15150feeffb9031bec58","target":"record","created_at":"2026-05-18T01:08:13Z","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":"0f84d8dcf24a6745199c63b6b17beaef98dcb5dc0824986e24ecf6c97ef73714","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-08-20T12:05:25Z","title_canon_sha256":"6d07b854773fcbb05258362d871d3d5c25d07cd8111d7eb024c184b17df9d860"},"schema_version":"1.0","source":{"id":"1508.05365","kind":"arxiv","version":1}},"canonical_sha256":"931c0ec213635b803c688ed1f83a9e4138f70c85589e42a0c2b97f04e5a10e63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"931c0ec213635b803c688ed1f83a9e4138f70c85589e42a0c2b97f04e5a10e63","first_computed_at":"2026-05-18T01:08:13.102166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:13.102166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MAi0Jbq5GxV/PyyQtm43oyLDLyVoD+5IrUkIM/l10qXHdEFIkKuhAorkBq+eaZ1r9/XqXM8+sIvhC/CK+rdZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:13.102691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ea457342ac3f89aeaeaf95f47bae90d9d731dc2f6ed15150feeffb9031bec58","sha256:28ea6b86b6131c065b466675a7ff6b399ba4e65b8a4bc49e10fec937fd5e7c53"],"state_sha256":"5fced346bee401ddcd65c3dca1a9ff4473671fcf6de7b42b4b21ee1bea38d9dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/vdgg3rnEyoDiJgaeLsqsCRFtPzkI7Lt0m3eZ8oNoB83bSTqqVJQhP1YpmLkJP/LQOwdo/d3eFtFGnuqpGGoAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:23:44.966292Z","bundle_sha256":"c68148d6f7c41989fc53be49f4890540a0ddccd8e7017bf99ca728341f7bf146"}}