{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XNDQS76FH4KSKB74LXBNNZ2EMI","short_pith_number":"pith:XNDQS76F","canonical_record":{"source":{"id":"1202.1236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-06T18:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"e5fb9ecad1f46d1989a36baf16086de2209659030d5a7ae3f3131434221a6f9d","abstract_canon_sha256":"a0d53768febb74fcb341678b288374b5db02963e8f30444c6355e9169f6f83d0"},"schema_version":"1.0"},"canonical_sha256":"bb47097fc53f152507fc5dc2d6e744623327b9709c188fd4823625ea2546c240","source":{"kind":"arxiv","id":"1202.1236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1236","created_at":"2026-05-18T04:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1236v1","created_at":"2026-05-18T04:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1236","created_at":"2026-05-18T04:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"XNDQS76FH4KS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XNDQS76FH4KSKB74","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XNDQS76F","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XNDQS76FH4KSKB74LXBNNZ2EMI","target":"record","payload":{"canonical_record":{"source":{"id":"1202.1236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-06T18:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"e5fb9ecad1f46d1989a36baf16086de2209659030d5a7ae3f3131434221a6f9d","abstract_canon_sha256":"a0d53768febb74fcb341678b288374b5db02963e8f30444c6355e9169f6f83d0"},"schema_version":"1.0"},"canonical_sha256":"bb47097fc53f152507fc5dc2d6e744623327b9709c188fd4823625ea2546c240","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:54.795905Z","signature_b64":"WGPTfn7Unn3o884lG2xOkk1RbouZPjUwzW36dAOTIPQKpEbIlUgrTtt0CQkydofasbz9i8pftEIrl4xv45vHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb47097fc53f152507fc5dc2d6e744623327b9709c188fd4823625ea2546c240","last_reissued_at":"2026-05-18T04:02:54.795204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:54.795204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.1236","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":"2026-05-18T04:02:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zK9xQhKQoMHovMEMH5jFCqMXcHi/no3SDUVR24FXFrm9lf6tJR2xgKx+x05Da2Rz/dinWsqrGyfDeeOxTQGaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:42:08.691102Z"},"content_sha256":"d00c655229a0a6c34aa97ea9577d2866e305b4e52ea717028bc53bdbad0deaec","schema_version":"1.0","event_id":"sha256:d00c655229a0a6c34aa97ea9577d2866e305b4e52ea717028bc53bdbad0deaec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XNDQS76FH4KSKB74LXBNNZ2EMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a nonlocal hyperbolic conservation law arising from a gradient constraint problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paulo Amorim","submitted_at":"2012-02-06T18:38:18Z","abstract_excerpt":"In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by studying a related conservation law with a spatial nonlocal term. We prove existence, uniqueness and stability of solution of the Cauchy problem for this nonlocal conservation law. In turn, this allows us to provide a notion of solution to the conservation law with a gradient constraint. The proof of existence is based on a time-stepping technique, and an $L^1$-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1236","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":"2026-05-18T04:02:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"89CC9pgFR/BZGyXnvQp3zNTyHrVfw5epOfdGSDzABBog3uTjRng5Mv28d9AQYZkLinakrkDgN+5tI1Vnp0ZBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:42:08.691466Z"},"content_sha256":"e0b1e577e7ab682f70b9662ec3e7e07cd1fe454e682b6288689d525af600cda1","schema_version":"1.0","event_id":"sha256:e0b1e577e7ab682f70b9662ec3e7e07cd1fe454e682b6288689d525af600cda1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNDQS76FH4KSKB74LXBNNZ2EMI/bundle.json","state_url":"https://pith.science/pith/XNDQS76FH4KSKB74LXBNNZ2EMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNDQS76FH4KSKB74LXBNNZ2EMI/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":"2026-06-20T08:42:08Z","links":{"resolver":"https://pith.science/pith/XNDQS76FH4KSKB74LXBNNZ2EMI","bundle":"https://pith.science/pith/XNDQS76FH4KSKB74LXBNNZ2EMI/bundle.json","state":"https://pith.science/pith/XNDQS76FH4KSKB74LXBNNZ2EMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNDQS76FH4KSKB74LXBNNZ2EMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XNDQS76FH4KSKB74LXBNNZ2EMI","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":"a0d53768febb74fcb341678b288374b5db02963e8f30444c6355e9169f6f83d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-06T18:38:18Z","title_canon_sha256":"e5fb9ecad1f46d1989a36baf16086de2209659030d5a7ae3f3131434221a6f9d"},"schema_version":"1.0","source":{"id":"1202.1236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1236","created_at":"2026-05-18T04:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1236v1","created_at":"2026-05-18T04:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1236","created_at":"2026-05-18T04:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"XNDQS76FH4KS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XNDQS76FH4KSKB74","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XNDQS76F","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:e0b1e577e7ab682f70b9662ec3e7e07cd1fe454e682b6288689d525af600cda1","target":"graph","created_at":"2026-05-18T04:02:54Z","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":"In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by studying a related conservation law with a spatial nonlocal term. We prove existence, uniqueness and stability of solution of the Cauchy problem for this nonlocal conservation law. In turn, this allows us to provide a notion of solution to the conservation law with a gradient constraint. The proof of existence is based on a time-stepping technique, and an $L^1$-c","authors_text":"Paulo Amorim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-06T18:38:18Z","title":"On a nonlocal hyperbolic conservation law arising from a gradient constraint problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1236","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:d00c655229a0a6c34aa97ea9577d2866e305b4e52ea717028bc53bdbad0deaec","target":"record","created_at":"2026-05-18T04:02:54Z","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":"a0d53768febb74fcb341678b288374b5db02963e8f30444c6355e9169f6f83d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-06T18:38:18Z","title_canon_sha256":"e5fb9ecad1f46d1989a36baf16086de2209659030d5a7ae3f3131434221a6f9d"},"schema_version":"1.0","source":{"id":"1202.1236","kind":"arxiv","version":1}},"canonical_sha256":"bb47097fc53f152507fc5dc2d6e744623327b9709c188fd4823625ea2546c240","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb47097fc53f152507fc5dc2d6e744623327b9709c188fd4823625ea2546c240","first_computed_at":"2026-05-18T04:02:54.795204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:54.795204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WGPTfn7Unn3o884lG2xOkk1RbouZPjUwzW36dAOTIPQKpEbIlUgrTtt0CQkydofasbz9i8pftEIrl4xv45vHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:54.795905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d00c655229a0a6c34aa97ea9577d2866e305b4e52ea717028bc53bdbad0deaec","sha256:e0b1e577e7ab682f70b9662ec3e7e07cd1fe454e682b6288689d525af600cda1"],"state_sha256":"73eb723d7f7dfd69bd3da305011a496ab51d08697c6af7b12e5f8e0dc6573861"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/7IeOIh9hN7UfE6N2rtimPBQhrrvE41VKUj7BmG/YI5uflui/n6DtKYVBXwS/115Ehk4kEZbpwNM+t/6/OYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:42:08.693349Z","bundle_sha256":"d6e8ad625e11142e160a5d1bbfc8b6d2d72cc681b527c0a4f628e63ec5c1f663"}}