{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:65QPHTV3XONXUONXB4MPDHPQG2","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":"9e761bcf624c3914a032e0f2ed8236beb0684ced25372068637c26aa29adaffc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-08T10:47:06Z","title_canon_sha256":"d5d077331265106e9e8f4c6369c713cf06f94d975a59acc0791e7a7de02660cd"},"schema_version":"1.0","source":{"id":"1504.01907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01907","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01907v1","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01907","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"65QPHTV3XONX","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"65QPHTV3XONXUONX","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"65QPHTV3","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:e39fd832f9efd0246e3c2a215737eb9c1540a3e85e336fa784a2fe1059e05a54","target":"graph","created_at":"2026-05-18T02:19:17Z","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":"The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in Bardos, Leroux and N\\'ed\\'elec (1979), striving to provide a rigorous treatment and detailed references.","authors_text":"Elena Rossi, Rinaldo M. Colombo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-08T10:47:06Z","title":"Rigorous Estimates on Balance Laws in Bounded Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01907","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:d400f5b2ec4e11b7e70659f8dbc5460e7c3a54e26badbe4fd7820de7f9bfbe9f","target":"record","created_at":"2026-05-18T02:19:17Z","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":"9e761bcf624c3914a032e0f2ed8236beb0684ced25372068637c26aa29adaffc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-08T10:47:06Z","title_canon_sha256":"d5d077331265106e9e8f4c6369c713cf06f94d975a59acc0791e7a7de02660cd"},"schema_version":"1.0","source":{"id":"1504.01907","kind":"arxiv","version":1}},"canonical_sha256":"f760f3cebbbb9b7a39b70f18f19df03684f9ee99b5262f15c058cbbc2b9f039f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f760f3cebbbb9b7a39b70f18f19df03684f9ee99b5262f15c058cbbc2b9f039f","first_computed_at":"2026-05-18T02:19:17.849403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:17.849403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xWhxrwlzDJWxsHcVh4CAf3uECPCsn3Mhsd0HrxQa2kAsW6OLkNkMw8HYHBfLrQD/Wz3TBWZ9U1RmwA1CgYx3Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:17.850063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d400f5b2ec4e11b7e70659f8dbc5460e7c3a54e26badbe4fd7820de7f9bfbe9f","sha256:e39fd832f9efd0246e3c2a215737eb9c1540a3e85e336fa784a2fe1059e05a54"],"state_sha256":"8433bdc54ddb24e720d45838e99d7f20de9cd82f7b4d461cc88f2b7d872d4c28"}