{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PEJ3FTLJUVSTXFCTZXQALLBZEN","short_pith_number":"pith:PEJ3FTLJ","canonical_record":{"source":{"id":"1303.4249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2013-03-18T13:46:32Z","cross_cats_sorted":["math.DS","math.NA","nlin.CD"],"title_canon_sha256":"4941139c58a5ff7ea6b0d16ea0fca0284d63234cbedb7a2eba0f6600e2eadc42","abstract_canon_sha256":"436627b069977f2fd8ed39f17723bd3120d607b79e653fd61399be447a9aaa3b"},"schema_version":"1.0"},"canonical_sha256":"7913b2cd69a5653b9453cde005ac392341196bb715008f5ebeade99bc529b22e","source":{"kind":"arxiv","id":"1303.4249","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4249","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4249v2","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4249","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"PEJ3FTLJUVST","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PEJ3FTLJUVSTXFCT","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PEJ3FTLJ","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PEJ3FTLJUVSTXFCTZXQALLBZEN","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4249","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2013-03-18T13:46:32Z","cross_cats_sorted":["math.DS","math.NA","nlin.CD"],"title_canon_sha256":"4941139c58a5ff7ea6b0d16ea0fca0284d63234cbedb7a2eba0f6600e2eadc42","abstract_canon_sha256":"436627b069977f2fd8ed39f17723bd3120d607b79e653fd61399be447a9aaa3b"},"schema_version":"1.0"},"canonical_sha256":"7913b2cd69a5653b9453cde005ac392341196bb715008f5ebeade99bc529b22e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:32.127512Z","signature_b64":"4smnaOSsYHp2nOTjAJHLxjR5lStp78hbQOA7UoOKZo5xt/PN3bkO8x194zTGfWi5jKhO1wjrKLsoQKhcqmeTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7913b2cd69a5653b9453cde005ac392341196bb715008f5ebeade99bc529b22e","last_reissued_at":"2026-05-18T02:45:32.126806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:32.126806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4249","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":"2026-05-18T02:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4UdXxEfSJoCpYRMUHUzvXOOep8l1580ZJXtbEUzAkLHgfhxmcA2MzYNmKWtc6s7amGOzNWmA8hCGnae8C8ndAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:44:44.827020Z"},"content_sha256":"1691b90e2afefd24868203f88c1f978b198322da85468da0e541fb8f4b944a9f","schema_version":"1.0","event_id":"sha256:1691b90e2afefd24868203f88c1f978b198322da85468da0e541fb8f4b944a9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PEJ3FTLJUVSTXFCTZXQALLBZEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete flow mapping: transport of phase space densities on triangulated surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NA","nlin.CD"],"primary_cat":"physics.comp-ph","authors_text":"David Chappell, Dominik Loechel, Gregor Tanner, Niels Sondergaard","submitted_at":"2013-03-18T13:46:32Z","abstract_excerpt":"Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation meth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4249","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":"2026-05-18T02:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MRYqdKZcN3saV8adg0Cb2Rt1OXSjAOL9om7xlkUgJ8QyP0pDGFvZ7+aIVRnl7A6OFhDQ8HL2yQIfrgTm0nSFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:44:44.827384Z"},"content_sha256":"745204aeebbe1c4754bfc195951136911bbb3c6821cd33431b91700b5ec4af79","schema_version":"1.0","event_id":"sha256:745204aeebbe1c4754bfc195951136911bbb3c6821cd33431b91700b5ec4af79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PEJ3FTLJUVSTXFCTZXQALLBZEN/bundle.json","state_url":"https://pith.science/pith/PEJ3FTLJUVSTXFCTZXQALLBZEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PEJ3FTLJUVSTXFCTZXQALLBZEN/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":"2026-06-25T19:44:44Z","links":{"resolver":"https://pith.science/pith/PEJ3FTLJUVSTXFCTZXQALLBZEN","bundle":"https://pith.science/pith/PEJ3FTLJUVSTXFCTZXQALLBZEN/bundle.json","state":"https://pith.science/pith/PEJ3FTLJUVSTXFCTZXQALLBZEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PEJ3FTLJUVSTXFCTZXQALLBZEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PEJ3FTLJUVSTXFCTZXQALLBZEN","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":"436627b069977f2fd8ed39f17723bd3120d607b79e653fd61399be447a9aaa3b","cross_cats_sorted":["math.DS","math.NA","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2013-03-18T13:46:32Z","title_canon_sha256":"4941139c58a5ff7ea6b0d16ea0fca0284d63234cbedb7a2eba0f6600e2eadc42"},"schema_version":"1.0","source":{"id":"1303.4249","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4249","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4249v2","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4249","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"PEJ3FTLJUVST","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PEJ3FTLJUVSTXFCT","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PEJ3FTLJ","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:745204aeebbe1c4754bfc195951136911bbb3c6821cd33431b91700b5ec4af79","target":"graph","created_at":"2026-05-18T02:45:32Z","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":"Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation meth","authors_text":"David Chappell, Dominik Loechel, Gregor Tanner, Niels Sondergaard","cross_cats":["math.DS","math.NA","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2013-03-18T13:46:32Z","title":"Discrete flow mapping: transport of phase space densities on triangulated surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4249","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":"sha256:1691b90e2afefd24868203f88c1f978b198322da85468da0e541fb8f4b944a9f","target":"record","created_at":"2026-05-18T02:45:32Z","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":"436627b069977f2fd8ed39f17723bd3120d607b79e653fd61399be447a9aaa3b","cross_cats_sorted":["math.DS","math.NA","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2013-03-18T13:46:32Z","title_canon_sha256":"4941139c58a5ff7ea6b0d16ea0fca0284d63234cbedb7a2eba0f6600e2eadc42"},"schema_version":"1.0","source":{"id":"1303.4249","kind":"arxiv","version":2}},"canonical_sha256":"7913b2cd69a5653b9453cde005ac392341196bb715008f5ebeade99bc529b22e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7913b2cd69a5653b9453cde005ac392341196bb715008f5ebeade99bc529b22e","first_computed_at":"2026-05-18T02:45:32.126806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:32.126806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4smnaOSsYHp2nOTjAJHLxjR5lStp78hbQOA7UoOKZo5xt/PN3bkO8x194zTGfWi5jKhO1wjrKLsoQKhcqmeTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:32.127512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4249","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1691b90e2afefd24868203f88c1f978b198322da85468da0e541fb8f4b944a9f","sha256:745204aeebbe1c4754bfc195951136911bbb3c6821cd33431b91700b5ec4af79"],"state_sha256":"abcc58dcfba41091d2291626d4f4a73511115e2e1170440274eac816390e139f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQiyb3l9cu4oCvSKyHqCvLH/cSZAq5NXWF35pCp7QjokHT5QLRo2GUUJtr7CWDzN7vECtiEXbJH0lrywSaUzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:44:44.829414Z","bundle_sha256":"12c73686fa3b4014453b35f361224d829c04bee0b73b53fb3cdb37ae5ae72b12"}}