{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KXDK4DJ4GEILUFCGKHZWJIDN55","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":"82011f1db26342e1ac2f1af7484343c530a27bdcf0c3c74766b1a5e75f64df07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-06T09:21:20Z","title_canon_sha256":"be816a51a33a86b3b28f2f43125062a10112bb2891689dea466d9c3848bd6d42"},"schema_version":"1.0","source":{"id":"2208.03477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.03477","created_at":"2026-07-05T04:46:40Z"},{"alias_kind":"arxiv_version","alias_value":"2208.03477v1","created_at":"2026-07-05T04:46:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.03477","created_at":"2026-07-05T04:46:40Z"},{"alias_kind":"pith_short_12","alias_value":"KXDK4DJ4GEIL","created_at":"2026-07-05T04:46:40Z"},{"alias_kind":"pith_short_16","alias_value":"KXDK4DJ4GEILUFCG","created_at":"2026-07-05T04:46:40Z"},{"alias_kind":"pith_short_8","alias_value":"KXDK4DJ4","created_at":"2026-07-05T04:46:40Z"}],"graph_snapshots":[{"event_id":"sha256:dbfa4c5802504cb27fb722bda26b4f54a2c6d5d194ace9399a7e64c5e1320742","target":"graph","created_at":"2026-07-05T04:46:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.03477/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper complements the study of the wave equation with discontinuous coefficients initiated in \\cite{DGL:22} in the case of time-dependent coefficients. Here we assume that the equation coefficients are depending on space only and we formulate Levi conditions on the lower order terms to guarantee the existence of a very weak solution as defined in \\cite{GR:14}. As a toy model we study the wave equation in conservative form with discontinuous velocity and we provide a qualitative analysis of the corresponding very weak solution via numerical methods.","authors_text":"Claudia Garetto, Costas Loizou, Marco Discacciati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-06T09:21:20Z","title":"On the wave equation with space dependent coefficients: singularities and lower order terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.03477","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:ab58cc6ac935cc037c94876bb5d10e121dea3f61dc78c2b551ba0856cb5b792b","target":"record","created_at":"2026-07-05T04:46:40Z","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":"82011f1db26342e1ac2f1af7484343c530a27bdcf0c3c74766b1a5e75f64df07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-06T09:21:20Z","title_canon_sha256":"be816a51a33a86b3b28f2f43125062a10112bb2891689dea466d9c3848bd6d42"},"schema_version":"1.0","source":{"id":"2208.03477","kind":"arxiv","version":1}},"canonical_sha256":"55c6ae0d3c3110ba144651f364a06def6931ec8270209b9c848efbf14328319c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55c6ae0d3c3110ba144651f364a06def6931ec8270209b9c848efbf14328319c","first_computed_at":"2026-07-05T04:46:40.998401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:46:40.998401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wGe3010u0zeCG73TwZf8XkZffpQ96rXh81zBVz3IiULyWrwos4jrI//KhSsd2EmeX7NKwiy9xpYxoSPeBTBrDg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:46:40.998811Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.03477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab58cc6ac935cc037c94876bb5d10e121dea3f61dc78c2b551ba0856cb5b792b","sha256:dbfa4c5802504cb27fb722bda26b4f54a2c6d5d194ace9399a7e64c5e1320742"],"state_sha256":"eeffa016d4bee34d1b4ca276d59bedbd92a790315d5cc230dc8dae9b75f4e45c"}