{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R4USJUEIM5TQ4ZE6WOXWXGCMPP","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":"68dc6a0298f20dbe855af0be1c538b6a459a77ecae5917c62ec63037ad210fd6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-13T13:26:23Z","title_canon_sha256":"09d00f05691e16698174408eab81c9c7843fa94ffd9f326c35652a9af7fefd29"},"schema_version":"1.0","source":{"id":"1305.2771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2771","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2771v1","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2771","created_at":"2026-05-18T02:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"R4USJUEIM5TQ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R4USJUEIM5TQ4ZE6","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R4USJUEI","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:e40bfb7c9d11ca6212af60aea74fbaff1bd8f4a816b5a37b2dc72f74227eef51","target":"graph","created_at":"2026-05-18T02:27:05Z","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 estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase spaces and we estimate the distance in terms of the distance of the resolvent operators of the corresponding elliptic operators and the distance of the nonlinearities of the equations.","authors_text":"Esperanza Santamar\\'ia, Jos\\'e M. Arrieta","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-13T13:26:23Z","title":"Estimates on the distance of inertial manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2771","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":"sha256:8089a74aa33aff02ad6b94f6d0f5bb8dc79b50971c2d226a06af34cc859f9394","target":"record","created_at":"2026-05-18T02:27:05Z","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":"68dc6a0298f20dbe855af0be1c538b6a459a77ecae5917c62ec63037ad210fd6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-13T13:26:23Z","title_canon_sha256":"09d00f05691e16698174408eab81c9c7843fa94ffd9f326c35652a9af7fefd29"},"schema_version":"1.0","source":{"id":"1305.2771","kind":"arxiv","version":1}},"canonical_sha256":"8f2924d08867670e649eb3af6b984c7be658c070587f440d9be156dc62c38479","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f2924d08867670e649eb3af6b984c7be658c070587f440d9be156dc62c38479","first_computed_at":"2026-05-18T02:27:05.915247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:05.915247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JJbi4fFnPaAcfbhE4o6Emb45nZMN/ffvgWk9El7XNegtQ9g5NS74JK80PESEZbX0gsY3Tr2HSf7UsHJeTyG2Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:05.916066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8089a74aa33aff02ad6b94f6d0f5bb8dc79b50971c2d226a06af34cc859f9394","sha256:e40bfb7c9d11ca6212af60aea74fbaff1bd8f4a816b5a37b2dc72f74227eef51"],"state_sha256":"caf1508b3f5859ed0eabb5018b69b4e9d028e07101991fa48e625546a868c6cd"}