{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:26GM7VGUCCXQD45ZK23K2FUOAC","short_pith_number":"pith:26GM7VGU","schema_version":"1.0","canonical_sha256":"d78ccfd4d410af01f3b956b6ad168e00933c91dc050fabd50cffa8110ff83dad","source":{"kind":"arxiv","id":"2308.12975","version":2},"attestation_state":"computed","paper":{"title":"Interpolating with generalized Assouad dimensions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS","math.MG","math.PR"],"primary_cat":"math.CA","authors_text":"Alex Rutar, Amlan Banaji, Sascha Troscheit","submitted_at":"2023-08-18T14:30:01Z","abstract_excerpt":"The $\\phi$-Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectrum with a more general form of scale sensitivity that is often closely related to \"phase-transition\" phenomena in sets.\n  In this article we establish a number of key properties of the $\\phi$-Assouad dimensions which help to clarify their behaviour. We prove for any bounded doubling metric space $F$ and $\\alpha\\in\\mathbb{R}$ satisfying $\\overline{\\operatorname{dim}}_{\\mathrm{B}}F<\\alpha\\leq\\operatorname{dim}_{\\mathr"},"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":"2308.12975","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CA","submitted_at":"2023-08-18T14:30:01Z","cross_cats_sorted":["math.DS","math.MG","math.PR"],"title_canon_sha256":"653eb360081e953bf3093277e5dbd436d0dee8999fb2231de2672c04f470f688","abstract_canon_sha256":"086932746a627691a10ad1a48c9a50f68e5672eff2d88695d9b52ecf17649f84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:03:40.616266Z","signature_b64":"+L9hfmMsNHQ8TuIRLntLZws3Mmnvxrv3R8otgAxhEUvknE05iS7ZYcIv916dDts06lV3u14bGA3ntuICnSf/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d78ccfd4d410af01f3b956b6ad168e00933c91dc050fabd50cffa8110ff83dad","last_reissued_at":"2026-06-08T01:03:40.615214Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:03:40.615214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpolating with generalized Assouad dimensions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS","math.MG","math.PR"],"primary_cat":"math.CA","authors_text":"Alex Rutar, Amlan Banaji, Sascha Troscheit","submitted_at":"2023-08-18T14:30:01Z","abstract_excerpt":"The $\\phi$-Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectrum with a more general form of scale sensitivity that is often closely related to \"phase-transition\" phenomena in sets.\n  In this article we establish a number of key properties of the $\\phi$-Assouad dimensions which help to clarify their behaviour. We prove for any bounded doubling metric space $F$ and $\\alpha\\in\\mathbb{R}$ satisfying $\\overline{\\operatorname{dim}}_{\\mathrm{B}}F<\\alpha\\leq\\operatorname{dim}_{\\mathr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.12975","kind":"arxiv","version":2},"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/2308.12975/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":"2308.12975","created_at":"2026-06-08T01:03:40.615378+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.12975v2","created_at":"2026-06-08T01:03:40.615378+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.12975","created_at":"2026-06-08T01:03:40.615378+00:00"},{"alias_kind":"pith_short_12","alias_value":"26GM7VGUCCXQ","created_at":"2026-06-08T01:03:40.615378+00:00"},{"alias_kind":"pith_short_16","alias_value":"26GM7VGUCCXQD45Z","created_at":"2026-06-08T01:03:40.615378+00:00"},{"alias_kind":"pith_short_8","alias_value":"26GM7VGU","created_at":"2026-06-08T01:03:40.615378+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.09899","citing_title":"The attainable almost sure large dimensions","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC","json":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC.json","graph_json":"https://pith.science/api/pith-number/26GM7VGUCCXQD45ZK23K2FUOAC/graph.json","events_json":"https://pith.science/api/pith-number/26GM7VGUCCXQD45ZK23K2FUOAC/events.json","paper":"https://pith.science/paper/26GM7VGU"},"agent_actions":{"view_html":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC","download_json":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC.json","view_paper":"https://pith.science/paper/26GM7VGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.12975&json=true","fetch_graph":"https://pith.science/api/pith-number/26GM7VGUCCXQD45ZK23K2FUOAC/graph.json","fetch_events":"https://pith.science/api/pith-number/26GM7VGUCCXQD45ZK23K2FUOAC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC/action/storage_attestation","attest_author":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC/action/author_attestation","sign_citation":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC/action/citation_signature","submit_replication":"https://pith.science/pith/26GM7VGUCCXQD45ZK23K2FUOAC/action/replication_record"}},"created_at":"2026-06-08T01:03:40.615378+00:00","updated_at":"2026-06-08T01:03:40.615378+00:00"}