{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:46O2IBJULLULAZCK3BE2NYGR6S","short_pith_number":"pith:46O2IBJU","canonical_record":{"source":{"id":"math/0612846","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-12-29T08:20:46Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"494e50a7083d1bb07338e1dfa29c59782056ab658dca4d33c7302e5e81a1b996","abstract_canon_sha256":"b41a3a5192148cd6bcd64e30c6c557ec51f3ebd176077c54fb2e21aa6b40697d"},"schema_version":"1.0"},"canonical_sha256":"e79da405345ae8b0644ad849a6e0d1f4a075357b98f37847e9d7a242f87043bf","source":{"kind":"arxiv","id":"math/0612846","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612846","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612846v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612846","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"46O2IBJULLUL","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"46O2IBJULLULAZCK","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"46O2IBJU","created_at":"2026-06-03T22:06:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:46O2IBJULLULAZCK3BE2NYGR6S","target":"record","payload":{"canonical_record":{"source":{"id":"math/0612846","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-12-29T08:20:46Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"494e50a7083d1bb07338e1dfa29c59782056ab658dca4d33c7302e5e81a1b996","abstract_canon_sha256":"b41a3a5192148cd6bcd64e30c6c557ec51f3ebd176077c54fb2e21aa6b40697d"},"schema_version":"1.0"},"canonical_sha256":"e79da405345ae8b0644ad849a6e0d1f4a075357b98f37847e9d7a242f87043bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:21.620792Z","signature_b64":"IFJeitjtlX/9dfCXm3+zDjkJOehcmDtIqlleD2W/go6T0USUGMFCfxPJkFO7syIgQDvmgpRHnejrYAlD11c6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e79da405345ae8b0644ad849a6e0d1f4a075357b98f37847e9d7a242f87043bf","last_reissued_at":"2026-06-03T22:06:21.620405Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:21.620405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0612846","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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CAY3DUT9f703DJVC1E6SZxwv+1E5a0alMEw/SIvrw48B7mE+GD0Rh8xV5JhlFOG1/BkhxHlovqFGNWm5YHz2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:40:07.507426Z"},"content_sha256":"2848f5737609b1a3489873b01b57504632a2b41312eacd5aed23f4082b7bc6ff","schema_version":"1.0","event_id":"sha256:2848f5737609b1a3489873b01b57504632a2b41312eacd5aed23f4082b7bc6ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:46O2IBJULLULAZCK3BE2NYGR6S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness theory for geometry compatible hyperbolic conservation laws on manifolds","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Matania Ben-Artzi, Philippe G. LeFloch","submitted_at":"2006-12-29T08:20:46Z","abstract_excerpt":"Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of the conservation laws is viewed as a vector-field on the manifold and depends on the unknown function as a parameter. We introduce notions of entropy solutions in the class of bounded measurable functions and in the class of measure-valued mappings. We establish the well-posedness theory for conservation laws on a manifold, by generalizing both Kruzkov's an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612846","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/math/0612846/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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"znTBKBq3FNBhfypm/S5szARu/k5dUgY63Y/lY5KL/pALjop1oUw2Lxmzsto6A3CjHPMi7L4vZwayXES5mCz/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:40:07.508128Z"},"content_sha256":"2e5378c37190e3ab5b52ec0892098b4703e3147d2039e93b3c51193cb4d8d0ef","schema_version":"1.0","event_id":"sha256:2e5378c37190e3ab5b52ec0892098b4703e3147d2039e93b3c51193cb4d8d0ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46O2IBJULLULAZCK3BE2NYGR6S/bundle.json","state_url":"https://pith.science/pith/46O2IBJULLULAZCK3BE2NYGR6S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46O2IBJULLULAZCK3BE2NYGR6S/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":"2026-06-11T20:40:07Z","links":{"resolver":"https://pith.science/pith/46O2IBJULLULAZCK3BE2NYGR6S","bundle":"https://pith.science/pith/46O2IBJULLULAZCK3BE2NYGR6S/bundle.json","state":"https://pith.science/pith/46O2IBJULLULAZCK3BE2NYGR6S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46O2IBJULLULAZCK3BE2NYGR6S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:46O2IBJULLULAZCK3BE2NYGR6S","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":"b41a3a5192148cd6bcd64e30c6c557ec51f3ebd176077c54fb2e21aa6b40697d","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AP","submitted_at":"2006-12-29T08:20:46Z","title_canon_sha256":"494e50a7083d1bb07338e1dfa29c59782056ab658dca4d33c7302e5e81a1b996"},"schema_version":"1.0","source":{"id":"math/0612846","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612846","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612846v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612846","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"46O2IBJULLUL","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"46O2IBJULLULAZCK","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"46O2IBJU","created_at":"2026-06-03T22:06:21Z"}],"graph_snapshots":[{"event_id":"sha256:2e5378c37190e3ab5b52ec0892098b4703e3147d2039e93b3c51193cb4d8d0ef","target":"graph","created_at":"2026-06-03T22:06:21Z","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/math/0612846/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of the conservation laws is viewed as a vector-field on the manifold and depends on the unknown function as a parameter. We introduce notions of entropy solutions in the class of bounded measurable functions and in the class of measure-valued mappings. We establish the well-posedness theory for conservation laws on a manifold, by generalizing both Kruzkov's an","authors_text":"Matania Ben-Artzi, Philippe G. LeFloch","cross_cats":["cs.NA","math.NA"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-12-29T08:20:46Z","title":"Well-posedness theory for geometry compatible hyperbolic conservation laws on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612846","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":"sha256:2848f5737609b1a3489873b01b57504632a2b41312eacd5aed23f4082b7bc6ff","target":"record","created_at":"2026-06-03T22:06:21Z","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":"b41a3a5192148cd6bcd64e30c6c557ec51f3ebd176077c54fb2e21aa6b40697d","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AP","submitted_at":"2006-12-29T08:20:46Z","title_canon_sha256":"494e50a7083d1bb07338e1dfa29c59782056ab658dca4d33c7302e5e81a1b996"},"schema_version":"1.0","source":{"id":"math/0612846","kind":"arxiv","version":1}},"canonical_sha256":"e79da405345ae8b0644ad849a6e0d1f4a075357b98f37847e9d7a242f87043bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e79da405345ae8b0644ad849a6e0d1f4a075357b98f37847e9d7a242f87043bf","first_computed_at":"2026-06-03T22:06:21.620405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:21.620405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IFJeitjtlX/9dfCXm3+zDjkJOehcmDtIqlleD2W/go6T0USUGMFCfxPJkFO7syIgQDvmgpRHnejrYAlD11c6Bw==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:21.620792Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612846","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2848f5737609b1a3489873b01b57504632a2b41312eacd5aed23f4082b7bc6ff","sha256:2e5378c37190e3ab5b52ec0892098b4703e3147d2039e93b3c51193cb4d8d0ef"],"state_sha256":"431d5116935b8a735deb12a8652f95f93e1cccb6f1db67121a69cf4895f96ce0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJwMMsDewJHaIfjPpWcBuWxw0mO4clBjx0G6XYInV4ZKtUbFQP7AqxCU0eovTmqmROOeZz5JKqjC1vRVwU0LCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:40:07.512100Z","bundle_sha256":"d5315a6111aa3c6e591e742be230a6e09c510d98a7343c7a3f0603e0bc2e0df8"}}