{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5JA2LOA7ABUNKMQCJQEEN7YYND","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":"49365ff08c11ecdd2f4835d152d90c43af50e84ae1b2c277a0e4f055857de24c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-29T14:38:00Z","title_canon_sha256":"f89d862eb4e537f228ac21b243ca2cea4418faf3896ff20d676bcd3bfbf5377e"},"schema_version":"1.0","source":{"id":"1001.5415","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.5415","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1001.5415v2","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.5415","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"5JA2LOA7ABUN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5JA2LOA7ABUNKMQC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5JA2LOA7","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:7463b6797b057ae1e625ac9fc994a81080d6ace0189b53949b51a2b5d22ebb0a","target":"graph","created_at":"2026-05-18T02:58:22Z","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 show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation of the problem, which is the limit of the solution of the stochastic parabolic approximation.","authors_text":"Arnaud Debussche (INRIA - IRMAR, IRMAR), Julien Vovelle (ICJ)","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-29T14:38:00Z","title":"Scalar conservation laws with stochastic forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5415","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":"sha256:7c1df6716f83410cefb73d7e9550d10367c3b548b96beb10f57c7b46d2f63304","target":"record","created_at":"2026-05-18T02:58:22Z","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":"49365ff08c11ecdd2f4835d152d90c43af50e84ae1b2c277a0e4f055857de24c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-29T14:38:00Z","title_canon_sha256":"f89d862eb4e537f228ac21b243ca2cea4418faf3896ff20d676bcd3bfbf5377e"},"schema_version":"1.0","source":{"id":"1001.5415","kind":"arxiv","version":2}},"canonical_sha256":"ea41a5b81f0068d532024c0846ff1868d0fcce6e77fc8517fecd8be20401caba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea41a5b81f0068d532024c0846ff1868d0fcce6e77fc8517fecd8be20401caba","first_computed_at":"2026-05-18T02:58:22.330246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:22.330246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oS9L/QyvtiKuS5z1AUbYXJ4HSVAF1wsk9a4Na3mdBKLdgUOjV5gRFmnd9uQ93tNTnix7zRjvLUxvYXEMaMZXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:22.330718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.5415","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c1df6716f83410cefb73d7e9550d10367c3b548b96beb10f57c7b46d2f63304","sha256:7463b6797b057ae1e625ac9fc994a81080d6ace0189b53949b51a2b5d22ebb0a"],"state_sha256":"10ad4bd506cb445afd6145f2944b09e93cb27f3633126fe53c8c170df3154844"}