{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:3M2EYEWUNSEAEDB32O3MKX4RUD","short_pith_number":"pith:3M2EYEWU","schema_version":"1.0","canonical_sha256":"db344c12d46c88020c3bd3b6c55f91a0f21f10fc8048d7fdff2a8c041800914b","source":{"kind":"arxiv","id":"2312.06456","version":3},"attestation_state":"computed","paper":{"title":"New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Rich\\'ard Balka, Tam\\'as Keleti","submitted_at":"2023-12-11T15:45:15Z","abstract_excerpt":"We introduce a new family of fractal dimensions by restricting the set of diameters in the coverings in the usual definition of the Hausdorff dimension. Among others, we prove that this family contains continuum many distinct dimensions, and they share most of the properties of the Hausdorff dimension, which answers negatively a question of Fraser. On the other hand, we also prove that among these new dimensions only the Hausdorff dimension behaves nicely with respect to H\\\"older functions.\n  We also consider the supremum of these new dimensions, which turns out to be another interesting notio"},"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":"2312.06456","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2023-12-11T15:45:15Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"5692b34bccde053b697f4e06c56e3d9651e7872f3c381e0b72d00cdef23d9e25","abstract_canon_sha256":"55f30a12c23351c4e9003a6e927d7e4120c6323569992098ddeda9bf7c660080"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:03:45.236890Z","signature_b64":"aOKjCDoJ21K6jmSNQACi+ZWVZXueTFwbDHFjtH45OoHu8k0Ajsj9rtf9RYigfEz98HXlSuqKI2NPi4ZFRxKqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db344c12d46c88020c3bd3b6c55f91a0f21f10fc8048d7fdff2a8c041800914b","last_reissued_at":"2026-05-26T02:03:45.235888Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:03:45.235888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Rich\\'ard Balka, Tam\\'as Keleti","submitted_at":"2023-12-11T15:45:15Z","abstract_excerpt":"We introduce a new family of fractal dimensions by restricting the set of diameters in the coverings in the usual definition of the Hausdorff dimension. Among others, we prove that this family contains continuum many distinct dimensions, and they share most of the properties of the Hausdorff dimension, which answers negatively a question of Fraser. On the other hand, we also prove that among these new dimensions only the Hausdorff dimension behaves nicely with respect to H\\\"older functions.\n  We also consider the supremum of these new dimensions, which turns out to be another interesting notio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.06456","kind":"arxiv","version":3},"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/2312.06456/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":"2312.06456","created_at":"2026-05-26T02:03:45.236019+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.06456v3","created_at":"2026-05-26T02:03:45.236019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.06456","created_at":"2026-05-26T02:03:45.236019+00:00"},{"alias_kind":"pith_short_12","alias_value":"3M2EYEWUNSEA","created_at":"2026-05-26T02:03:45.236019+00:00"},{"alias_kind":"pith_short_16","alias_value":"3M2EYEWUNSEAEDB3","created_at":"2026-05-26T02:03:45.236019+00:00"},{"alias_kind":"pith_short_8","alias_value":"3M2EYEWU","created_at":"2026-05-26T02:03:45.236019+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/3M2EYEWUNSEAEDB32O3MKX4RUD","json":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD.json","graph_json":"https://pith.science/api/pith-number/3M2EYEWUNSEAEDB32O3MKX4RUD/graph.json","events_json":"https://pith.science/api/pith-number/3M2EYEWUNSEAEDB32O3MKX4RUD/events.json","paper":"https://pith.science/paper/3M2EYEWU"},"agent_actions":{"view_html":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD","download_json":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD.json","view_paper":"https://pith.science/paper/3M2EYEWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.06456&json=true","fetch_graph":"https://pith.science/api/pith-number/3M2EYEWUNSEAEDB32O3MKX4RUD/graph.json","fetch_events":"https://pith.science/api/pith-number/3M2EYEWUNSEAEDB32O3MKX4RUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD/action/storage_attestation","attest_author":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD/action/author_attestation","sign_citation":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD/action/citation_signature","submit_replication":"https://pith.science/pith/3M2EYEWUNSEAEDB32O3MKX4RUD/action/replication_record"}},"created_at":"2026-05-26T02:03:45.236019+00:00","updated_at":"2026-05-26T02:03:45.236019+00:00"}