{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FE7JY2OBPVOV4NMEL4GWQMNF2H","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":"3d83873da30087659c3560376f990bd1d08edf1d91a9c61816a2d15bdb62a298","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2015-05-09T08:44:00Z","title_canon_sha256":"f2ac680f25fed835be1d4d5da924301bd62abad19816eb35d172b483571c6822"},"schema_version":"1.0","source":{"id":"1505.02245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02245","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02245v1","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02245","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"pith_short_12","alias_value":"FE7JY2OBPVOV","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FE7JY2OBPVOV4NME","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FE7JY2OB","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:b406e9f98117482182100e1a43a4d780b68166eddf2ea5b1d60eb2593d9914cf","target":"graph","created_at":"2026-05-18T01:15:46Z","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 study the contraction properties (up to shift) for admissible Rankine-Hugoniot discontinuities of $n\\times n$ systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in [47], using the spatially inhomogeneous pseudo-distance introduced in [50]. Our generalized criterion guarantees the contraction property for extremal shocks of a large class of systems, including the Euler system. Moreover, we introduce necessary conditions for contraction, specifically targeted for intermediate shocks. As an application, we show that intermediate shocks of th","authors_text":"Alexis F. Vasseur, Moon-Jin Kang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2015-05-09T08:44:00Z","title":"Criteria on contractions for entropic discontinuities of systems of conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02245","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":"sha256:68cae9b20220e3e6d5818882b0479b38dc17f9cbedd8e9e082f06e108a1dcf37","target":"record","created_at":"2026-05-18T01:15:46Z","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":"3d83873da30087659c3560376f990bd1d08edf1d91a9c61816a2d15bdb62a298","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2015-05-09T08:44:00Z","title_canon_sha256":"f2ac680f25fed835be1d4d5da924301bd62abad19816eb35d172b483571c6822"},"schema_version":"1.0","source":{"id":"1505.02245","kind":"arxiv","version":1}},"canonical_sha256":"293e9c69c17d5d5e35845f0d6831a5d1f3a1d557d0ca4c5e187c8619021d9524","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"293e9c69c17d5d5e35845f0d6831a5d1f3a1d557d0ca4c5e187c8619021d9524","first_computed_at":"2026-05-18T01:15:46.800040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:46.800040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IgeGXZzpMsqfBVffRRV2AT4FSmGiVlV9ItREuyUmCsGy3KlBVW2rqNKJC3VM6irTTxiqiWrIbtD6eeGzKlXsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:46.800493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68cae9b20220e3e6d5818882b0479b38dc17f9cbedd8e9e082f06e108a1dcf37","sha256:b406e9f98117482182100e1a43a4d780b68166eddf2ea5b1d60eb2593d9914cf"],"state_sha256":"8437633a20a14824060f34665c1cd3842b4ccbbb1c73ba2ea3fe1490950d1bf2"}