{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:P5WZN5FY2REWFOFHUYSTCOWGE6","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":"28699d709c76af5a0cc6fbd401dd05435c42e413bdf552c7078a8646a1576679","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-13T14:30:12Z","title_canon_sha256":"d181210e45a0e6e67945ee184b071ac938eaad5c75852660f652c497d368330d"},"schema_version":"1.0","source":{"id":"1008.2329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2329","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2329v1","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2329","created_at":"2026-05-18T04:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"P5WZN5FY2REW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P5WZN5FY2REWFOFH","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P5WZN5FY","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:61c8a858d7d0aff8b2eb8ef25d74bd51d48650a1452cee74d2b07b8298e83557","target":"graph","created_at":"2026-05-18T04:42:14Z","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":"Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then there is an ordinary differential equation in ${\\mathbb R}^{m+1}$, with $m >d$, that has unique solutions and reproduces the dynamics on $A$. Moreover, the dynamical system generated by this new ordinary differential equation has a global attractor $X$ arbitrarily close to $LA$, where $L$ is a homeomorphism from $A$ into ${\\mathbb R}^{m+1}$.","authors_text":"Eleonora Pinto de Moura, Jaime J. S\\'anchez-Gabites, James C. Robinson","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-13T14:30:12Z","title":"Embedding of global attractors and their dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2329","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":"sha256:981e4efd1b7b4268afba298f4ab70bf1952e2a3d36a6eb34454953334fbf0747","target":"record","created_at":"2026-05-18T04:42:14Z","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":"28699d709c76af5a0cc6fbd401dd05435c42e413bdf552c7078a8646a1576679","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-13T14:30:12Z","title_canon_sha256":"d181210e45a0e6e67945ee184b071ac938eaad5c75852660f652c497d368330d"},"schema_version":"1.0","source":{"id":"1008.2329","kind":"arxiv","version":1}},"canonical_sha256":"7f6d96f4b8d44962b8a7a625313ac627b510559bed193bc7a028670c36d999f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f6d96f4b8d44962b8a7a625313ac627b510559bed193bc7a028670c36d999f2","first_computed_at":"2026-05-18T04:42:14.190431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:14.190431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Y85yr+VceFMTUzkXwCsRmwvzW7Lzt/q0vpP+pHj9MkpOkXKEosIwewo6UqlM5J6lu5Hcct4aKBt09iqhAtyBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:14.190977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:981e4efd1b7b4268afba298f4ab70bf1952e2a3d36a6eb34454953334fbf0747","sha256:61c8a858d7d0aff8b2eb8ef25d74bd51d48650a1452cee74d2b07b8298e83557"],"state_sha256":"75f80967b0eb0d3fe2447ceefe3a900bde85ba56c9ba1f5564c75f5b37657fd3"}