{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:VB4ITHAQ3VBSM7LRZ44DPJYRUZ","short_pith_number":"pith:VB4ITHAQ","schema_version":"1.0","canonical_sha256":"a878899c10dd43267d71cf3837a711a64b4371aa5dbc0f483552f304c0b1f484","source":{"kind":"arxiv","id":"2412.12999","version":3},"attestation_state":"computed","paper":{"title":"Intermediate dimensions of complementary sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Nicolas Angelini, Ursula Molter","submitted_at":"2024-12-17T15:23:54Z","abstract_excerpt":"Given a positive, non-increasing sequence $a$ with finite sum equal to $1$, we consider the family of all closed subsets of $[0,1]$ whose complementary open intervals have lengths given by a rearrangement of the sequence $a$. We study the full range of possible $\\theta$-intermediate dimensions of these sets and, under suitable assumptions on the sequence, we show that this range forms a closed interval, whose endpoints we compute explicitly. This paper fills a gap in the literature concerning the dimensional properties of complementary sets."},"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":"2412.12999","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-12-17T15:23:54Z","cross_cats_sorted":[],"title_canon_sha256":"086d25ed32a95aa80bdf1b82a9e1827d5e8d5de606005d66c0d7283de94adfca","abstract_canon_sha256":"db2213bd8066f89b9e9dcdd97838d1630461407e309c9e7dd4b9dc8c75386131"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T14:05:16.211284Z","signature_b64":"UFTq+31SluNNVeOYFORm8ED5dujv18LIAq1Rs5nu6KJSMvRd+Fx+nNVy+xQBwRZxdk17EAFCgQjVc5D/nMSsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a878899c10dd43267d71cf3837a711a64b4371aa5dbc0f483552f304c0b1f484","last_reissued_at":"2026-06-03T14:05:16.210681Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T14:05:16.210681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intermediate dimensions of complementary sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Nicolas Angelini, Ursula Molter","submitted_at":"2024-12-17T15:23:54Z","abstract_excerpt":"Given a positive, non-increasing sequence $a$ with finite sum equal to $1$, we consider the family of all closed subsets of $[0,1]$ whose complementary open intervals have lengths given by a rearrangement of the sequence $a$. We study the full range of possible $\\theta$-intermediate dimensions of these sets and, under suitable assumptions on the sequence, we show that this range forms a closed interval, whose endpoints we compute explicitly. This paper fills a gap in the literature concerning the dimensional properties of complementary sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.12999","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/2412.12999/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":"2412.12999","created_at":"2026-06-03T14:05:16.210744+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.12999v3","created_at":"2026-06-03T14:05:16.210744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.12999","created_at":"2026-06-03T14:05:16.210744+00:00"},{"alias_kind":"pith_short_12","alias_value":"VB4ITHAQ3VBS","created_at":"2026-06-03T14:05:16.210744+00:00"},{"alias_kind":"pith_short_16","alias_value":"VB4ITHAQ3VBSM7LR","created_at":"2026-06-03T14:05:16.210744+00:00"},{"alias_kind":"pith_short_8","alias_value":"VB4ITHAQ","created_at":"2026-06-03T14:05:16.210744+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/VB4ITHAQ3VBSM7LRZ44DPJYRUZ","json":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ.json","graph_json":"https://pith.science/api/pith-number/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/graph.json","events_json":"https://pith.science/api/pith-number/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/events.json","paper":"https://pith.science/paper/VB4ITHAQ"},"agent_actions":{"view_html":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ","download_json":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ.json","view_paper":"https://pith.science/paper/VB4ITHAQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.12999&json=true","fetch_graph":"https://pith.science/api/pith-number/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/action/storage_attestation","attest_author":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/action/author_attestation","sign_citation":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/action/citation_signature","submit_replication":"https://pith.science/pith/VB4ITHAQ3VBSM7LRZ44DPJYRUZ/action/replication_record"}},"created_at":"2026-06-03T14:05:16.210744+00:00","updated_at":"2026-06-03T14:05:16.210744+00:00"}