{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4TUPWHSLKA6D6LPJK6EUZZT6UD","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":"fdc4a825cc42b26d60740cde22ce0db3f3f03994d9ccd493ebd0b4404e365f30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-16T13:23:42Z","title_canon_sha256":"3bd2c5c2850a43bf1096ef05ed71faebadc13cbe9ac7df67fc598b825dbe0200"},"schema_version":"1.0","source":{"id":"1603.05087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05087","created_at":"2026-05-18T01:18:58Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05087v1","created_at":"2026-05-18T01:18:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05087","created_at":"2026-05-18T01:18:58Z"},{"alias_kind":"pith_short_12","alias_value":"4TUPWHSLKA6D","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4TUPWHSLKA6D6LPJ","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4TUPWHSL","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:3b4c7417287c533454884ed6712ef84c52648aa51c40daeae3a469c66af4b5d4","target":"graph","created_at":"2026-05-18T01:18:58Z","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 goal of this paper is to prove the existence and stability of shocks for viscous scalar conservation laws with space periodic flux, in the multi-dimensional case. Such a result had been proved by the first author in one space dimension, but the extension to a multi-dimensional setting makes the existence proof non-trivial. We construct approximate solutions by restricting the size of the domain and then passing to the limit as the size of the domain goes to infinity. One of the key steps is a \" normalization \" procedure, which ensures that the limit objects obtained by the approximation sc","authors_text":"Anne-Laure Dalibard (LJLL), Moon-Jin Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-16T13:23:42Z","title":"Existence and stability of planar shocks of viscous scalar conservation laws with space-periodic flux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05087","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":"sha256:30a5bb599b48a701d5fa01a06bc69040e862ac1b7c05b950f600c01bc9aa6125","target":"record","created_at":"2026-05-18T01:18:58Z","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":"fdc4a825cc42b26d60740cde22ce0db3f3f03994d9ccd493ebd0b4404e365f30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-16T13:23:42Z","title_canon_sha256":"3bd2c5c2850a43bf1096ef05ed71faebadc13cbe9ac7df67fc598b825dbe0200"},"schema_version":"1.0","source":{"id":"1603.05087","kind":"arxiv","version":1}},"canonical_sha256":"e4e8fb1e4b503c3f2de957894ce67ea0f2fd976564f0f59c50098437d4a92f7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4e8fb1e4b503c3f2de957894ce67ea0f2fd976564f0f59c50098437d4a92f7e","first_computed_at":"2026-05-18T01:18:58.051571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:58.051571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d6Z9Tei2xSF1eWiPB4b5DVj0d1puV4MvmmACRJf2JqDAQYBP7ViOMYJFLBj77+s98HuAAmT/071TcAY+Qug1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:58.052002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30a5bb599b48a701d5fa01a06bc69040e862ac1b7c05b950f600c01bc9aa6125","sha256:3b4c7417287c533454884ed6712ef84c52648aa51c40daeae3a469c66af4b5d4"],"state_sha256":"30311f54c5ad9f8418b03021914ab58adb599837dacdd7e65a4e5010514582d6"}