{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XKUWB7NSNCJ7BLJESQRLB5HYTX","short_pith_number":"pith:XKUWB7NS","canonical_record":{"source":{"id":"1704.02891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-10T14:50:50Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"91af857c34cf239ae001b7c18dd86843afb470eaa56d3ad32d5d44d5194ab43f","abstract_canon_sha256":"f37ec8cc6c9b2bd5a4c46f02e36237430b12019717e6832d68c30b499b59653b"},"schema_version":"1.0"},"canonical_sha256":"baa960fdb26893f0ad249422b0f4f89dfef1f9588c55b8d7d082983d20eee404","source":{"kind":"arxiv","id":"1704.02891","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XKUWB7NSNCJ7BLJESQRLB5HYTX","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-10T14:50:50Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"91af857c34cf239ae001b7c18dd86843afb470eaa56d3ad32d5d44d5194ab43f","abstract_canon_sha256":"f37ec8cc6c9b2bd5a4c46f02e36237430b12019717e6832d68c30b499b59653b"},"schema_version":"1.0"},"canonical_sha256":"baa960fdb26893f0ad249422b0f4f89dfef1f9588c55b8d7d082983d20eee404","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:43.761486Z","signature_b64":"iUkvqTDmQzhQM2oWZo7szSEqyh4ayCXqV7DEND/g2012vnta25pev2a/tjtdDkwxRg3tej0T8BpAIbJRe+nlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baa960fdb26893f0ad249422b0f4f89dfef1f9588c55b8d7d082983d20eee404","last_reissued_at":"2026-05-18T00:46:43.760894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:43.760894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02891","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRMDB/TkRsXMN5scqqUN8/opo3zYMBGIAsoF5yvgDx2k1XiQdggbAulbpq1F7fzK5N10TN+kkCcLbHuKukIbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:43:52.999864Z"},"content_sha256":"62df7c6799291ab11835b64ba9ed8b44b74e968ec9246cc94f0d7bff9d296d0d","schema_version":"1.0","event_id":"sha256:62df7c6799291ab11835b64ba9ed8b44b74e968ec9246cc94f0d7bff9d296d0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XKUWB7NSNCJ7BLJESQRLB5HYTX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $\\epsilon$-entropy of some infinite dimensional compact ellipsoids and fractal dimension of attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.AP","authors_text":"Alain Haraux (LJLL), Mar\\'ia Anguiano","submitted_at":"2017-04-10T14:50:50Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02891","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1UcryDIjm9co3e7zqOjFJU2dUJWeZa6B9aAaypZl+vogwpQ8DhJqaUfmibBZ3EqM7Xn7d4b1oANFfB25xaP9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:43:53.000575Z"},"content_sha256":"c7c44df610c1b334191c4da7dc3f4a6b7ff57b6c923e9f43b6e696183233876c","schema_version":"1.0","event_id":"sha256:c7c44df610c1b334191c4da7dc3f4a6b7ff57b6c923e9f43b6e696183233876c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XKUWB7NSNCJ7BLJESQRLB5HYTX/bundle.json","state_url":"https://pith.science/pith/XKUWB7NSNCJ7BLJESQRLB5HYTX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XKUWB7NSNCJ7BLJESQRLB5HYTX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T03:43:53Z","links":{"resolver":"https://pith.science/pith/XKUWB7NSNCJ7BLJESQRLB5HYTX","bundle":"https://pith.science/pith/XKUWB7NSNCJ7BLJESQRLB5HYTX/bundle.json","state":"https://pith.science/pith/XKUWB7NSNCJ7BLJESQRLB5HYTX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XKUWB7NSNCJ7BLJESQRLB5HYTX/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79TsOZTkMJ8ci+en6uAO5Vth/E7zj/OrBQJz7elpvbZrAOSll6DdWqRfcxI6aWxH+HaDhPk6LNo8pEyR81WpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:43:53.004376Z","bundle_sha256":"4206bf2f91bfb8c3ad6e4b5ff0cda15d3d2660929d7e641a677b46f327304efd"}}