{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QWWRS5JYYLDJO43GVPWQWBC2O4","short_pith_number":"pith:QWWRS5JY","schema_version":"1.0","canonical_sha256":"85ad197538c2c6977366abed0b045a7725267c82cc5c3b0a4216c5b20f1be483","source":{"kind":"arxiv","id":"2403.00519","version":1},"attestation_state":"computed","paper":{"title":"On two non-existence results for Cameron-Liebler $k$-sets in $\\mathrm{PG}(n,q)$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan De Beule, Jonathan Mannaert, Leo Storme","submitted_at":"2024-03-01T13:30:29Z","abstract_excerpt":"This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A Cameron-Liebler $k$-set is a collection of $k$-spaces in $\\mathrm{PG}(n,q)$ or $\\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the size of this collection. One of the main research questions remains the (non-)existence of Cameron-Liebler $k$-sets with parameter $x$. This paper improves two non-existence results. First we show that the parameter of a non-trivial Cameron-Liebler $k$-set in $\\mathrm{PG}(n,q)$ should be larger than $q^{n-\\frac{5k}{2}-1}$, which is an improvement of an earlier kn"},"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":"2403.00519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2024-03-01T13:30:29Z","cross_cats_sorted":[],"title_canon_sha256":"2b36fdb6b7ea8133acb9cb19e38b5975a66558914b3285d975c12d35860718ad","abstract_canon_sha256":"b75f5411faf61b663abdbac70b73c1eda5e4bbbdcaf608896b4e88ec8eb2e9ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:51:05.253569Z","signature_b64":"ySjfV2Or9XEMfaprVF5QalBEOi0QM+71nWWRcx02AKpYgx+0ZFGnyXScbxZhenhenB/hCyQhSBApr8H4IBn9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85ad197538c2c6977366abed0b045a7725267c82cc5c3b0a4216c5b20f1be483","last_reissued_at":"2026-07-05T07:51:05.253100Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:51:05.253100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On two non-existence results for Cameron-Liebler $k$-sets in $\\mathrm{PG}(n,q)$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan De Beule, Jonathan Mannaert, Leo Storme","submitted_at":"2024-03-01T13:30:29Z","abstract_excerpt":"This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A Cameron-Liebler $k$-set is a collection of $k$-spaces in $\\mathrm{PG}(n,q)$ or $\\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the size of this collection. One of the main research questions remains the (non-)existence of Cameron-Liebler $k$-sets with parameter $x$. This paper improves two non-existence results. First we show that the parameter of a non-trivial Cameron-Liebler $k$-set in $\\mathrm{PG}(n,q)$ should be larger than $q^{n-\\frac{5k}{2}-1}$, which is an improvement of an earlier kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.00519","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/2403.00519/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":"2403.00519","created_at":"2026-07-05T07:51:05.253156+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.00519v1","created_at":"2026-07-05T07:51:05.253156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.00519","created_at":"2026-07-05T07:51:05.253156+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWWRS5JYYLDJ","created_at":"2026-07-05T07:51:05.253156+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWWRS5JYYLDJO43G","created_at":"2026-07-05T07:51:05.253156+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWWRS5JY","created_at":"2026-07-05T07:51:05.253156+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.16288","citing_title":"A Survey of Cameron-Liebler Sets and Low Degree Boolean Functions in Grassmann Graphs","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4","json":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4.json","graph_json":"https://pith.science/api/pith-number/QWWRS5JYYLDJO43GVPWQWBC2O4/graph.json","events_json":"https://pith.science/api/pith-number/QWWRS5JYYLDJO43GVPWQWBC2O4/events.json","paper":"https://pith.science/paper/QWWRS5JY"},"agent_actions":{"view_html":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4","download_json":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4.json","view_paper":"https://pith.science/paper/QWWRS5JY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.00519&json=true","fetch_graph":"https://pith.science/api/pith-number/QWWRS5JYYLDJO43GVPWQWBC2O4/graph.json","fetch_events":"https://pith.science/api/pith-number/QWWRS5JYYLDJO43GVPWQWBC2O4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4/action/storage_attestation","attest_author":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4/action/author_attestation","sign_citation":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4/action/citation_signature","submit_replication":"https://pith.science/pith/QWWRS5JYYLDJO43GVPWQWBC2O4/action/replication_record"}},"created_at":"2026-07-05T07:51:05.253156+00:00","updated_at":"2026-07-05T07:51:05.253156+00:00"}