{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5HISGSPE4IO7ENFX5RFERSWYOR","short_pith_number":"pith:5HISGSPE","canonical_record":{"source":{"id":"1608.02811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-09T14:21:14Z","cross_cats_sorted":[],"title_canon_sha256":"bfe921a5b1e2a04072802af5e4161c26c48199eb74e97a65e115e4316982e3e7","abstract_canon_sha256":"f9b662bcf5319c2b1940131bf1ff716290893c57d3e62f03c0390925109e1a1f"},"schema_version":"1.0"},"canonical_sha256":"e9d12349e4e21df234b7ec4a48cad8746c195e5b4465aac4354aad4c3044a2b9","source":{"kind":"arxiv","id":"1608.02811","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02811","created_at":"2026-05-18T00:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02811v1","created_at":"2026-05-18T00:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02811","created_at":"2026-05-18T00:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"5HISGSPE4IO7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5HISGSPE4IO7ENFX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5HISGSPE","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5HISGSPE4IO7ENFX5RFERSWYOR","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-09T14:21:14Z","cross_cats_sorted":[],"title_canon_sha256":"bfe921a5b1e2a04072802af5e4161c26c48199eb74e97a65e115e4316982e3e7","abstract_canon_sha256":"f9b662bcf5319c2b1940131bf1ff716290893c57d3e62f03c0390925109e1a1f"},"schema_version":"1.0"},"canonical_sha256":"e9d12349e4e21df234b7ec4a48cad8746c195e5b4465aac4354aad4c3044a2b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:41.427642Z","signature_b64":"pt+x56JVy41PJ8VzNipEAYr0XzWyJ9KlyNI0yNcH+2VnD35ZV5JhU2Ybitsy9XEDKxP/MiyiT1aIBWz+bNX1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9d12349e4e21df234b7ec4a48cad8746c195e5b4465aac4354aad4c3044a2b9","last_reissued_at":"2026-05-18T00:41:41.427146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:41.427146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02811","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":"2026-05-18T00:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uCQy9WuK3xgw0f/BIFWrx3L2n1LoRQIXVDSW1R9cpkC7P6CJixwJvGP9SzSlTamGSsp2jt82uCh4FeSInqh6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:57:27.642360Z"},"content_sha256":"8eab152b8a49136d0e24478d7b3d42686c2506c953bd80d64b52c710ca4b3309","schema_version":"1.0","event_id":"sha256:8eab152b8a49136d0e24478d7b3d42686c2506c953bd80d64b52c710ca4b3309"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5HISGSPE4IO7ENFX5RFERSWYOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of $L^\\infty$-entropy solutions to scalar conservation laws in one-space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elio Marconi, Stefano Bianchini","submitted_at":"2016-08-09T14:21:14Z","abstract_excerpt":"We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. \\\\ In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f\"=0$.\n  We prove also that the initial data is taken in a suitably strong sense and we give some counterex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02811","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":"2026-05-18T00:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TMiap8Q5r3AwI82LQxHEcBz924uE9ok2LqzoqC+1gcr8lz4VJ4ZHUp8Ki/RT/NurfiNJlZnlssZAqBWMwC8nAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:57:27.643041Z"},"content_sha256":"d676382ebc78811406742ee79f8a76053b9c6041e0150702b6b73cb10a21dc04","schema_version":"1.0","event_id":"sha256:d676382ebc78811406742ee79f8a76053b9c6041e0150702b6b73cb10a21dc04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HISGSPE4IO7ENFX5RFERSWYOR/bundle.json","state_url":"https://pith.science/pith/5HISGSPE4IO7ENFX5RFERSWYOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HISGSPE4IO7ENFX5RFERSWYOR/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":"2026-06-06T06:57:27Z","links":{"resolver":"https://pith.science/pith/5HISGSPE4IO7ENFX5RFERSWYOR","bundle":"https://pith.science/pith/5HISGSPE4IO7ENFX5RFERSWYOR/bundle.json","state":"https://pith.science/pith/5HISGSPE4IO7ENFX5RFERSWYOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HISGSPE4IO7ENFX5RFERSWYOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5HISGSPE4IO7ENFX5RFERSWYOR","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":"f9b662bcf5319c2b1940131bf1ff716290893c57d3e62f03c0390925109e1a1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-09T14:21:14Z","title_canon_sha256":"bfe921a5b1e2a04072802af5e4161c26c48199eb74e97a65e115e4316982e3e7"},"schema_version":"1.0","source":{"id":"1608.02811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02811","created_at":"2026-05-18T00:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02811v1","created_at":"2026-05-18T00:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02811","created_at":"2026-05-18T00:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"5HISGSPE4IO7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5HISGSPE4IO7ENFX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5HISGSPE","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:d676382ebc78811406742ee79f8a76053b9c6041e0150702b6b73cb10a21dc04","target":"graph","created_at":"2026-05-18T00:41:41Z","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":"We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. \\\\ In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f\"=0$.\n  We prove also that the initial data is taken in a suitably strong sense and we give some counterex","authors_text":"Elio Marconi, Stefano Bianchini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-09T14:21:14Z","title":"On the structure of $L^\\infty$-entropy solutions to scalar conservation laws in one-space dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02811","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":"sha256:8eab152b8a49136d0e24478d7b3d42686c2506c953bd80d64b52c710ca4b3309","target":"record","created_at":"2026-05-18T00:41:41Z","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":"f9b662bcf5319c2b1940131bf1ff716290893c57d3e62f03c0390925109e1a1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-09T14:21:14Z","title_canon_sha256":"bfe921a5b1e2a04072802af5e4161c26c48199eb74e97a65e115e4316982e3e7"},"schema_version":"1.0","source":{"id":"1608.02811","kind":"arxiv","version":1}},"canonical_sha256":"e9d12349e4e21df234b7ec4a48cad8746c195e5b4465aac4354aad4c3044a2b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9d12349e4e21df234b7ec4a48cad8746c195e5b4465aac4354aad4c3044a2b9","first_computed_at":"2026-05-18T00:41:41.427146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:41.427146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pt+x56JVy41PJ8VzNipEAYr0XzWyJ9KlyNI0yNcH+2VnD35ZV5JhU2Ybitsy9XEDKxP/MiyiT1aIBWz+bNX1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:41.427642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8eab152b8a49136d0e24478d7b3d42686c2506c953bd80d64b52c710ca4b3309","sha256:d676382ebc78811406742ee79f8a76053b9c6041e0150702b6b73cb10a21dc04"],"state_sha256":"c600098a5b7a4cc59908eaf1436c5692bfb0b15b785d8483c80143c34be32766"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iSC4iX27FCpoc8Ki6l9ZqSkhN6WUGKrIzp0D5vc+JQ74c9rTSoKvZZQOQeKKubod3/SSum1HSgUmaUrkLdmGCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:57:27.647072Z","bundle_sha256":"305064760d8e76364bdf684c3e16488a619c2a4c6e66d753b0420199b905ac09"}}