{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TJTFWRY6G56KD5UWJ5FJ736IZV","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":"4a74d12018fe8e34f2bb663bc00fd5848188a70e4dc7f6d6f494fcf2f2b5da58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T10:02:05Z","title_canon_sha256":"95c5270aa17724d72e7f7c30c8552c6bb090ccd2682ca5ab072e7303bbf558c7"},"schema_version":"1.0","source":{"id":"1305.1133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1133","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1133v1","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1133","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"TJTFWRY6G56K","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TJTFWRY6G56KD5UW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TJTFWRY6","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:a466f1c950c3cf568fbe2d5a63721ba4ba7471ee4c1dd016b638b330bf8cb095","target":"graph","created_at":"2026-05-18T03:26:24Z","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":"In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.","authors_text":"Ferruccio Colombini, Francesco Fanelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T10:02:05Z","title":"A note on non-homogeneous hyperbolic operators with low-regularity coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1133","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":"sha256:185e60a23b407eb8e5f42a279872ec31f76bb8eb2c7d8b6af7c62d45b32d997e","target":"record","created_at":"2026-05-18T03:26:24Z","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":"4a74d12018fe8e34f2bb663bc00fd5848188a70e4dc7f6d6f494fcf2f2b5da58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T10:02:05Z","title_canon_sha256":"95c5270aa17724d72e7f7c30c8552c6bb090ccd2682ca5ab072e7303bbf558c7"},"schema_version":"1.0","source":{"id":"1305.1133","kind":"arxiv","version":1}},"canonical_sha256":"9a665b471e377ca1f6964f4a9fefc8cd5c1135fbd2b4c863c0625498b9fb38c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a665b471e377ca1f6964f4a9fefc8cd5c1135fbd2b4c863c0625498b9fb38c2","first_computed_at":"2026-05-18T03:26:24.050153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:24.050153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g2/wqHFfh1THUtPXDHgOr2W2YRzlpXT1mb0Xa/cUr1vK+AtXxyUaQlmKaXrcYp5T3DCPFLt0EUv+8K6QVmNZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:24.050928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:185e60a23b407eb8e5f42a279872ec31f76bb8eb2c7d8b6af7c62d45b32d997e","sha256:a466f1c950c3cf568fbe2d5a63721ba4ba7471ee4c1dd016b638b330bf8cb095"],"state_sha256":"6d78cb0c1f05f1cd123642e0985b958bafb3a86327fbec5055dc66b55ea81255"}