{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3KMT47BFQ5RBCMRT6RLBUZURMY","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":"fe39e797241df501f2b6f082aaaf887178cfd92c9f9554787572aa4b75a6d505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-28T15:48:55Z","title_canon_sha256":"850578645659fa2bc9e262061b03a056421bd7c34f5808edbd2b0e417253c0f9"},"schema_version":"1.0","source":{"id":"1401.7231","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7231","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7231v3","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7231","created_at":"2026-05-18T02:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"3KMT47BFQ5RB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3KMT47BFQ5RBCMRT","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3KMT47BF","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:49e8192cf4a8755b542a1083e0ff126fc917d5eb683eb7ba98fe3376e7c16c05","target":"graph","created_at":"2026-05-18T02:32:00Z","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":"This paper explores two generalizations of the classical Aubin-Lions Lemma. First we give a sufficient condition to commute weak limit and multiplication of two functions. We deduce from this criteria a compactness Theorem for degenerate parabolic equations. Secondly, we state and prove a compactness Theorem for non-cylindrical domains, including the case of dual estimates involving only divergence-free test functions.","authors_text":"Ayman Moussa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-28T15:48:55Z","title":"Some variants of the classical Aubin-Lions Lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7231","kind":"arxiv","version":3},"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:d9762c2f1b979f055a47b1d4368df9fb587792ed3754623cb36f70f4fca46bf3","target":"record","created_at":"2026-05-18T02:32:00Z","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":"fe39e797241df501f2b6f082aaaf887178cfd92c9f9554787572aa4b75a6d505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-28T15:48:55Z","title_canon_sha256":"850578645659fa2bc9e262061b03a056421bd7c34f5808edbd2b0e417253c0f9"},"schema_version":"1.0","source":{"id":"1401.7231","kind":"arxiv","version":3}},"canonical_sha256":"da993e7c258762113233f4561a66916606e49d9e3c1d8e609d4dead68e9ce301","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da993e7c258762113233f4561a66916606e49d9e3c1d8e609d4dead68e9ce301","first_computed_at":"2026-05-18T02:32:00.164049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:00.164049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DFeDJCq9l47xIHNPlI32xDNhItOAfmlNay9qEQfyG044ws28CdAhOabB7onbtfnstYS+Ul0YmjDmt6ZUHRBxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:00.164477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7231","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9762c2f1b979f055a47b1d4368df9fb587792ed3754623cb36f70f4fca46bf3","sha256:49e8192cf4a8755b542a1083e0ff126fc917d5eb683eb7ba98fe3376e7c16c05"],"state_sha256":"3966e7947c26c3b5e26deda517ecbe7bb8465050b05cedc763d0eba5de020f62"}