{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OQYEXDRYW2ZSOUCM473AXGFW4E","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":"2073660edf28a1b1a9746155f4a83e9c5e01fa00fc252e1af388497eb030c96b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-28T09:32:21Z","title_canon_sha256":"e110c2364b2498627e9ac0f38da286d866294920c00a504e0c3c386a11490785"},"schema_version":"1.0","source":{"id":"1507.07695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07695","created_at":"2026-05-18T01:36:12Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07695v1","created_at":"2026-05-18T01:36:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07695","created_at":"2026-05-18T01:36:12Z"},{"alias_kind":"pith_short_12","alias_value":"OQYEXDRYW2ZS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OQYEXDRYW2ZSOUCM","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OQYEXDRY","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:33b96991bd8591a0c4196bc35ee69b50d4f5cdf6081d9de46aaa20265aae534b","target":"graph","created_at":"2026-05-18T01:36:12Z","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 provide two-sided estimates for the source solution of $d$-dimensional critical fractal Burgers equation $u_t-\\Delta^{\\alpha/2}+b\\cdot \\nabla\\left(u|u|^q\\right)=0$, $q=(\\alpha-1)/d$, $\\alpha\\in(1,2)$, $b\\in\\mathbb{R}^d$, by the density function of the isotropic $\\alpha$-stable process.","authors_text":"Grzegorz Serafin, Tomasz Jakubowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-28T09:32:21Z","title":"Stable estimates for source solution of critical fractal Burgers equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07695","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":"sha256:22471529b1d375a710df24f2277657f7b64d02af5625cd8c58c73a201ead93a4","target":"record","created_at":"2026-05-18T01:36:12Z","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":"2073660edf28a1b1a9746155f4a83e9c5e01fa00fc252e1af388497eb030c96b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-28T09:32:21Z","title_canon_sha256":"e110c2364b2498627e9ac0f38da286d866294920c00a504e0c3c386a11490785"},"schema_version":"1.0","source":{"id":"1507.07695","kind":"arxiv","version":1}},"canonical_sha256":"74304b8e38b6b327504ce7f60b98b6e1392cf00a8e8812542236271c4b6a4618","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74304b8e38b6b327504ce7f60b98b6e1392cf00a8e8812542236271c4b6a4618","first_computed_at":"2026-05-18T01:36:12.109274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:12.109274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZQaNC/f0lTyHfgRrbNLpizgJe5IhY33D2mQ6gBFDNdu00bOugS05ykUnjFmgl0EKeRIZraSxdHVXt21H39Y5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:12.109970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22471529b1d375a710df24f2277657f7b64d02af5625cd8c58c73a201ead93a4","sha256:33b96991bd8591a0c4196bc35ee69b50d4f5cdf6081d9de46aaa20265aae534b"],"state_sha256":"134ce7e8fd036ddac2c416ba4aa59f3673a8c1bb88b6c5f4894a1bc2b2b66fb0"}