{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:QFXHTTFL2LMLFT6SEYZ6XAUCWD","short_pith_number":"pith:QFXHTTFL","schema_version":"1.0","canonical_sha256":"816e79ccabd2d8b2cfd22633eb8282b0ee23bcabde255df0746bad6ea657f829","source":{"kind":"arxiv","id":"math/0703067","version":1},"attestation_state":"computed","paper":{"title":"Low regularity classes and entropy numbers","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Walter Trebels","submitted_at":"2007-03-02T19:21:10Z","abstract_excerpt":"We note a sharp embedding of the Besov space $B^\\infty_{0,q}(\\bbT)$ into exponential classes and prove entropy estimates for the compact embedding of subclasses with logarithmic smoothness, considered by Kashin and Temlyakov."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0703067","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2007-03-02T19:21:10Z","cross_cats_sorted":[],"title_canon_sha256":"55395b077f4f608039df2201da4dc01ba34b2a1ad323b520b83f27282bb583a7","abstract_canon_sha256":"619755486e2f9ae4bd2492fb2bd885a5a0f6390388fa23207ff091f5adb7ca88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:23:15.577059Z","signature_b64":"Sfkn6SGYWC+Td/d6izU8WGjdVG/jG2VVnCjUcu5hbxckVOAfih00TGRLYWQ0U/EQbC1sZvf3W1h07Z/oV/sBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"816e79ccabd2d8b2cfd22633eb8282b0ee23bcabde255df0746bad6ea657f829","last_reissued_at":"2026-07-04T17:23:15.576633Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:23:15.576633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low regularity classes and entropy numbers","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Walter Trebels","submitted_at":"2007-03-02T19:21:10Z","abstract_excerpt":"We note a sharp embedding of the Besov space $B^\\infty_{0,q}(\\bbT)$ into exponential classes and prove entropy estimates for the compact embedding of subclasses with logarithmic smoothness, considered by Kashin and Temlyakov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703067","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0703067/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0703067","created_at":"2026-07-04T17:23:15.576699+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0703067v1","created_at":"2026-07-04T17:23:15.576699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703067","created_at":"2026-07-04T17:23:15.576699+00:00"},{"alias_kind":"pith_short_12","alias_value":"QFXHTTFL2LML","created_at":"2026-07-04T17:23:15.576699+00:00"},{"alias_kind":"pith_short_16","alias_value":"QFXHTTFL2LMLFT6S","created_at":"2026-07-04T17:23:15.576699+00:00"},{"alias_kind":"pith_short_8","alias_value":"QFXHTTFL","created_at":"2026-07-04T17:23:15.576699+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD","json":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD.json","graph_json":"https://pith.science/api/pith-number/QFXHTTFL2LMLFT6SEYZ6XAUCWD/graph.json","events_json":"https://pith.science/api/pith-number/QFXHTTFL2LMLFT6SEYZ6XAUCWD/events.json","paper":"https://pith.science/paper/QFXHTTFL"},"agent_actions":{"view_html":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD","download_json":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD.json","view_paper":"https://pith.science/paper/QFXHTTFL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0703067&json=true","fetch_graph":"https://pith.science/api/pith-number/QFXHTTFL2LMLFT6SEYZ6XAUCWD/graph.json","fetch_events":"https://pith.science/api/pith-number/QFXHTTFL2LMLFT6SEYZ6XAUCWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD/action/storage_attestation","attest_author":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD/action/author_attestation","sign_citation":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD/action/citation_signature","submit_replication":"https://pith.science/pith/QFXHTTFL2LMLFT6SEYZ6XAUCWD/action/replication_record"}},"created_at":"2026-07-04T17:23:15.576699+00:00","updated_at":"2026-07-04T17:23:15.576699+00:00"}