{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:GWBJGGZ4FBKGVGRNPJKXEDVRXP","short_pith_number":"pith:GWBJGGZ4","canonical_record":{"source":{"id":"0810.0255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-10-01T18:51:59Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"e5a2a636ab684bce3d2ac055c6675fb5de2d6df6782d197d4403f745805751e7","abstract_canon_sha256":"dfbc714029941a234d499e05d8ca17bcacc3aafb810deac5c719f4595beb5570"},"schema_version":"1.0"},"canonical_sha256":"3582931b3c28546a9a2d7a55720eb1bbf4df2deeebd338a2ccd6a7aaaed6d672","source":{"kind":"arxiv","id":"0810.0255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0255","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0255v1","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0255","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"GWBJGGZ4FBKG","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_16","alias_value":"GWBJGGZ4FBKGVGRN","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_8","alias_value":"GWBJGGZ4","created_at":"2026-06-03T22:06:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:GWBJGGZ4FBKGVGRNPJKXEDVRXP","target":"record","payload":{"canonical_record":{"source":{"id":"0810.0255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-10-01T18:51:59Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"e5a2a636ab684bce3d2ac055c6675fb5de2d6df6782d197d4403f745805751e7","abstract_canon_sha256":"dfbc714029941a234d499e05d8ca17bcacc3aafb810deac5c719f4595beb5570"},"schema_version":"1.0"},"canonical_sha256":"3582931b3c28546a9a2d7a55720eb1bbf4df2deeebd338a2ccd6a7aaaed6d672","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:10.439672Z","signature_b64":"VGWoxiew6nYAXG0setZ2CrLxjCd8FOfJQaUb/pJ2P5/qpYxISnQU90S/xIZA7Kc4PvPd2NGJkM6Bcct8Q+fNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3582931b3c28546a9a2d7a55720eb1bbf4df2deeebd338a2ccd6a7aaaed6d672","last_reissued_at":"2026-06-03T22:06:10.439102Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:10.439102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.0255","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":"2026-06-03T22:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LprHR0gr2Ppz7rtgq/ScLSmCqgNUA1j7yXgBl07p8bTSxUhHyr4CRaUX0PgrKQMnhhqo+50vpk8CvRb1VR1jDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:47:37.785189Z"},"content_sha256":"9d772ad289ed36a8611be94b48205b2b520f833333cee0daf3ad753e074e0006","schema_version":"1.0","event_id":"sha256:9d772ad289ed36a8611be94b48205b2b520f833333cee0daf3ad753e074e0006"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:GWBJGGZ4FBKGVGRNPJKXEDVRXP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Baver Okutmustur, Philippe G. LeFloch","submitted_at":"2008-10-01T18:51:59Z","abstract_excerpt":"We consider nonlinear hyperbolic conservation laws, posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and in which the \"flux\" is defined as a flux field of n-forms depending on a parameter (the unknown variable). We introduce a formulation of the initial and boundary value problem which is geometric in nature and is more natural than the vector field approach recently developed for Riemannian manifolds. Our main assumption on the manifold and the flux field is a global hyperbolicity condition, which provides a global time-orientation as is standard in Lorentzian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0810.0255/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":"2026-06-03T22:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfGoH3496Of9z9y5PaDWyNz8YF2RsOLL+CY5SXx0gB/xTLHN5M/4wSGeoYFrBu2rPv65pCcL26cjuAzdckqjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:47:37.785946Z"},"content_sha256":"dfe66d34eadb17711cedca768a38b4905b75f85b63e0698497883771059c334d","schema_version":"1.0","event_id":"sha256:dfe66d34eadb17711cedca768a38b4905b75f85b63e0698497883771059c334d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWBJGGZ4FBKGVGRNPJKXEDVRXP/bundle.json","state_url":"https://pith.science/pith/GWBJGGZ4FBKGVGRNPJKXEDVRXP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWBJGGZ4FBKGVGRNPJKXEDVRXP/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":"2026-06-06T14:47:37Z","links":{"resolver":"https://pith.science/pith/GWBJGGZ4FBKGVGRNPJKXEDVRXP","bundle":"https://pith.science/pith/GWBJGGZ4FBKGVGRNPJKXEDVRXP/bundle.json","state":"https://pith.science/pith/GWBJGGZ4FBKGVGRNPJKXEDVRXP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWBJGGZ4FBKGVGRNPJKXEDVRXP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GWBJGGZ4FBKGVGRNPJKXEDVRXP","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":"dfbc714029941a234d499e05d8ca17bcacc3aafb810deac5c719f4595beb5570","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-10-01T18:51:59Z","title_canon_sha256":"e5a2a636ab684bce3d2ac055c6675fb5de2d6df6782d197d4403f745805751e7"},"schema_version":"1.0","source":{"id":"0810.0255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.0255","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"0810.0255v1","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.0255","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"GWBJGGZ4FBKG","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_16","alias_value":"GWBJGGZ4FBKGVGRN","created_at":"2026-06-03T22:06:10Z"},{"alias_kind":"pith_short_8","alias_value":"GWBJGGZ4","created_at":"2026-06-03T22:06:10Z"}],"graph_snapshots":[{"event_id":"sha256:dfe66d34eadb17711cedca768a38b4905b75f85b63e0698497883771059c334d","target":"graph","created_at":"2026-06-03T22:06:10Z","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/0810.0255/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider nonlinear hyperbolic conservation laws, posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and in which the \"flux\" is defined as a flux field of n-forms depending on a parameter (the unknown variable). We introduce a formulation of the initial and boundary value problem which is geometric in nature and is more natural than the vector field approach recently developed for Riemannian manifolds. Our main assumption on the manifold and the flux field is a global hyperbolicity condition, which provides a global time-orientation as is standard in Lorentzian ","authors_text":"Baver Okutmustur, Philippe G. LeFloch","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-10-01T18:51:59Z","title":"Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0255","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":"sha256:9d772ad289ed36a8611be94b48205b2b520f833333cee0daf3ad753e074e0006","target":"record","created_at":"2026-06-03T22:06:10Z","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":"dfbc714029941a234d499e05d8ca17bcacc3aafb810deac5c719f4595beb5570","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-10-01T18:51:59Z","title_canon_sha256":"e5a2a636ab684bce3d2ac055c6675fb5de2d6df6782d197d4403f745805751e7"},"schema_version":"1.0","source":{"id":"0810.0255","kind":"arxiv","version":1}},"canonical_sha256":"3582931b3c28546a9a2d7a55720eb1bbf4df2deeebd338a2ccd6a7aaaed6d672","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3582931b3c28546a9a2d7a55720eb1bbf4df2deeebd338a2ccd6a7aaaed6d672","first_computed_at":"2026-06-03T22:06:10.439102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:10.439102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VGWoxiew6nYAXG0setZ2CrLxjCd8FOfJQaUb/pJ2P5/qpYxISnQU90S/xIZA7Kc4PvPd2NGJkM6Bcct8Q+fNAA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:10.439672Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.0255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d772ad289ed36a8611be94b48205b2b520f833333cee0daf3ad753e074e0006","sha256:dfe66d34eadb17711cedca768a38b4905b75f85b63e0698497883771059c334d"],"state_sha256":"ecc8aed286c940e2c0cff5bc8b5e5685c3a0befab3f938f7bebbf40e33ff6cc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XrhCwODEOE7faymIPaOjWhDEjKU8zAkdkUtGHwOVcNpGt0+Sdj5lcn33f75jHZwAAc49ts2mLsFk9MwzFf5xCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:47:37.789502Z","bundle_sha256":"310d7a60f1ef7237e3bdbd1bdc84445b085ce50ae6cc443d9d58eb2b6aeb1a8e"}}