{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XKUWB7NSNCJ7BLJESQRLB5HYTX","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":"f37ec8cc6c9b2bd5a4c46f02e36237430b12019717e6832d68c30b499b59653b","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-10T14:50:50Z","title_canon_sha256":"91af857c34cf239ae001b7c18dd86843afb470eaa56d3ad32d5d44d5194ab43f"},"schema_version":"1.0","source":{"id":"1704.02891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02891","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02891v1","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02891","created_at":"2026-05-18T00:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"XKUWB7NSNCJ7","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XKUWB7NSNCJ7BLJE","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XKUWB7NS","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:c7c44df610c1b334191c4da7dc3f4a6b7ff57b6c923e9f43b6e696183233876c","target":"graph","created_at":"2026-05-18T00:46:43Z","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 prove an estimation of the Kolmogorov $\\epsilon$-entropy in H of the unitary ball in the space V, where H is a Hilbert space and V is a Sobolev-like subspace of H. Then, by means of Zelik's result [5], an estimate of the fractal dimension of the attractors of some nonlinear parabolic equations is established.","authors_text":"Alain Haraux (LJLL), Mar\\'ia Anguiano","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-10T14:50:50Z","title":"The $\\epsilon$-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02891","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":"sha256:62df7c6799291ab11835b64ba9ed8b44b74e968ec9246cc94f0d7bff9d296d0d","target":"record","created_at":"2026-05-18T00:46:43Z","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":"f37ec8cc6c9b2bd5a4c46f02e36237430b12019717e6832d68c30b499b59653b","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-10T14:50:50Z","title_canon_sha256":"91af857c34cf239ae001b7c18dd86843afb470eaa56d3ad32d5d44d5194ab43f"},"schema_version":"1.0","source":{"id":"1704.02891","kind":"arxiv","version":1}},"canonical_sha256":"baa960fdb26893f0ad249422b0f4f89dfef1f9588c55b8d7d082983d20eee404","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baa960fdb26893f0ad249422b0f4f89dfef1f9588c55b8d7d082983d20eee404","first_computed_at":"2026-05-18T00:46:43.760894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:43.760894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iUkvqTDmQzhQM2oWZo7szSEqyh4ayCXqV7DEND/g2012vnta25pev2a/tjtdDkwxRg3tej0T8BpAIbJRe+nlAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:43.761486Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62df7c6799291ab11835b64ba9ed8b44b74e968ec9246cc94f0d7bff9d296d0d","sha256:c7c44df610c1b334191c4da7dc3f4a6b7ff57b6c923e9f43b6e696183233876c"],"state_sha256":"ef65b4292e7cc7e38a6af8a4686c74d6f6e2d19b38f22c7ce5d53fa211532bc0"}