{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C2PJHI6VLUTVTEBGJU5BYIPKXV","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":"2968cc1c30038f773aa55b715a7d315de17d9fb8348ad0920d628d63f8b82dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T06:24:08Z","title_canon_sha256":"70ab25238b68e5d6f3e1bdcaa74f028b2d173331b3c1e1692609fbdf44724080"},"schema_version":"1.0","source":{"id":"1307.1218","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1218","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1218v4","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1218","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"C2PJHI6VLUTV","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C2PJHI6VLUTVTEBG","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C2PJHI6V","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:cdb16ff82fcbcd80606eccf5f757f9e2165d48c65a8d6044529b702cab40ce77","target":"graph","created_at":"2026-05-18T01:31:12Z","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":"We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fractional Laplace operator, $\\Delta^{\\alpha/2}$ for $\\alpha \\in (0,2)$. Our results are quantitative and we exhibit an example for which they are optimal. We cover the dependence on the nonlinearities, and for the first time, the Lipschitz dependence on $\\alpha$ in the $BV$-framework. The former estimate (dependence on nonlinearity) is robust in the sense that it is stable in the limits $\\alpha \\downarrow 0$ and $\\alpha \\up","authors_text":"Espen Jakobsen, Nathael Alibaud (LM-Besan\\c{c}on), Simone Cifani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T06:24:08Z","title":"Optimal continuous dependence estimates for fractional degenerate parabolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1218","kind":"arxiv","version":4},"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":"sha256:94101a3024dc26cfafa554540d01a5136d62efc8a4989137f65ff3ab2f5855f3","target":"record","created_at":"2026-05-18T01:31:12Z","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":"2968cc1c30038f773aa55b715a7d315de17d9fb8348ad0920d628d63f8b82dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T06:24:08Z","title_canon_sha256":"70ab25238b68e5d6f3e1bdcaa74f028b2d173331b3c1e1692609fbdf44724080"},"schema_version":"1.0","source":{"id":"1307.1218","kind":"arxiv","version":4}},"canonical_sha256":"169e93a3d55d275990264d3a1c21eabd69f0e7793906e54aa6e9c03d3cfacafd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"169e93a3d55d275990264d3a1c21eabd69f0e7793906e54aa6e9c03d3cfacafd","first_computed_at":"2026-05-18T01:31:12.033760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:12.033760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qXMwxS//zTD/aCyUOzZ5C6XZLHgVL2a1p51rJIMjj0vkAzmC21KCOXEgjepw4R+YjaBiv7cK83aQaCuPFQBqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:12.034249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1218","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94101a3024dc26cfafa554540d01a5136d62efc8a4989137f65ff3ab2f5855f3","sha256:cdb16ff82fcbcd80606eccf5f757f9e2165d48c65a8d6044529b702cab40ce77"],"state_sha256":"9da0f4ee5babdad348c82f1e7af33092a0db6e0a71a3f49266f0af5d879e3697"}