{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BOOZYFUINLFKMS4CEF6GUWWMNV","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":"9bbf986592942db691c0071c0187b0e68517c4ea9a75298bdc677662979ab26c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-30T21:56:34Z","title_canon_sha256":"e049fcdec730287d6007ffbf3cf9974ebe205000c132899263293f1c7de29129"},"schema_version":"1.0","source":{"id":"2607.28860","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28860","created_at":"2026-08-03T01:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28860v1","created_at":"2026-08-03T01:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28860","created_at":"2026-08-03T01:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"BOOZYFUINLFK","created_at":"2026-08-03T01:17:13Z"},{"alias_kind":"pith_short_16","alias_value":"BOOZYFUINLFKMS4C","created_at":"2026-08-03T01:17:13Z"},{"alias_kind":"pith_short_8","alias_value":"BOOZYFUI","created_at":"2026-08-03T01:17:13Z"}],"graph_snapshots":[{"event_id":"sha256:e3e6ae1d81d4ec3803735132eaa35c313aa4b63835d7a8908c19ee5f34164f9d","target":"graph","created_at":"2026-08-03T01:17:13Z","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/2607.28860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Several applications for systems of conservation laws of the form $U_t + (\\Phi (U) U)_x =0$, $U: R_t\\times R_x\\rightarrow R^n$ , $n\\geq 2$, with $\\Phi (U) = \\phi (r, \\Theta): R^n\\rightarrow R$, $r = |U|$, and $\\Theta = U/|U|\\in S^{n-1}$, are obtained by imposing structural conditions to provide a classification framework for solutions dependent on the form of $\\phi(U)$. By prescribing the evolution of a particular eigenvalue, we can categorize classes of such functions, $\\phi$, for which this evolution is met, into depending on either a scalar field $z=rK(\\Theta)$, where $K: S^{n-1}\\rightarrow","authors_text":"Katarzyna Saxton, Ralph Saxton","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-30T21:56:34Z","title":"Some remarks on structured Keyfitz-Kranzer systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28860","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":"sha256:0b84d651492e0635912ef569478a7af80feced1adad62e1256110e5eebfe0d8f","target":"record","created_at":"2026-08-03T01:17:13Z","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":"9bbf986592942db691c0071c0187b0e68517c4ea9a75298bdc677662979ab26c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-30T21:56:34Z","title_canon_sha256":"e049fcdec730287d6007ffbf3cf9974ebe205000c132899263293f1c7de29129"},"schema_version":"1.0","source":{"id":"2607.28860","kind":"arxiv","version":1}},"canonical_sha256":"0b9d9c16886acaa64b82217c6a5acc6d6c5097e5ede8c3d09ca45d7c06f551a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b9d9c16886acaa64b82217c6a5acc6d6c5097e5ede8c3d09ca45d7c06f551a6","first_computed_at":"2026-08-03T01:17:13.866822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:17:13.866822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSwaUaoJKef/Pwd4/S5ZYg/V51lOHKOFQDoUsr3jfN2KVERdFUeEJSEVmEKZozVkvQy5usaTok/54/geiyiDDg==","signature_status":"signed_v1","signed_at":"2026-08-03T01:17:13.868555Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28860","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b84d651492e0635912ef569478a7af80feced1adad62e1256110e5eebfe0d8f","sha256:e3e6ae1d81d4ec3803735132eaa35c313aa4b63835d7a8908c19ee5f34164f9d"],"state_sha256":"9f5594a3fdc374b3f50c645026caba519572ca746a9281b862bf0a723e4cf61e"}