{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BS4OO5ZH5Q3KEDQLP3DGC74HHT","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":"30581d6c4d066df13ed793ab6efc3c5fe2baf14f5d0e6d2d6951c5951d3a40ef","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-30T12:50:21Z","title_canon_sha256":"1a3afd261e15a10e5f1350b366b9d8e76a8b77f3f76def6bef3df9f1f58e3515"},"schema_version":"1.0","source":{"id":"1305.7087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7087","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7087v2","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7087","created_at":"2026-05-18T02:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"BS4OO5ZH5Q3K","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BS4OO5ZH5Q3KEDQL","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BS4OO5ZH","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:9bf2568c228296af514eefe41a54a53d6bd70119bf5974edf6c6791b62747c15","target":"graph","created_at":"2026-05-18T02:44:08Z","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":"This article is an attempt to complement some recent developments on conservation laws with stochastic forcing. In a pioneering development, Feng $&$ Nualarthave developed the entropy solution theory for such problems and the presence of stochastic forcing necessitates introduction of {\\it strong entropy condition}. However, the authors' formulation of entropy inequalities are weak-in-space but strong-in-time. In the absence of a-priori path continuity for the solutions, we take a critical outlook towards this formulation and offer an entropy formulation which is weak-in-time and weak-in-space","authors_text":"Ananta K. Majee, Imran H. Biswas","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-30T12:50:21Z","title":"Stochastic conservation laws: weak-in-time formulation and strong entropy condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7087","kind":"arxiv","version":2},"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":"sha256:9e96066d1bb7e991ad86c4570e2c17e9546359453060f2dfeda4ac4efb32eb83","target":"record","created_at":"2026-05-18T02:44:08Z","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":"30581d6c4d066df13ed793ab6efc3c5fe2baf14f5d0e6d2d6951c5951d3a40ef","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-30T12:50:21Z","title_canon_sha256":"1a3afd261e15a10e5f1350b366b9d8e76a8b77f3f76def6bef3df9f1f58e3515"},"schema_version":"1.0","source":{"id":"1305.7087","kind":"arxiv","version":2}},"canonical_sha256":"0cb8e77727ec36a20e0b7ec6617f873cf936b8263b1172dab89c80276b7eff6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cb8e77727ec36a20e0b7ec6617f873cf936b8263b1172dab89c80276b7eff6b","first_computed_at":"2026-05-18T02:44:08.542521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:08.542521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8uARWfw8JLfufHBhVMj7gmnAOqcPrRP57zGnEvCtnGaGlCr7ckTWjo/toyiAsV/ITjTUeODEDgtC/K6b346Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:08.542980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e96066d1bb7e991ad86c4570e2c17e9546359453060f2dfeda4ac4efb32eb83","sha256:9bf2568c228296af514eefe41a54a53d6bd70119bf5974edf6c6791b62747c15"],"state_sha256":"6536cd93c57d36390b7cf42b638ababfccd19fe58fd0f0264077c25d668c1628"}