{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:VR7Z7JUNZRWMXFL4NRMTW5KSMY","short_pith_number":"pith:VR7Z7JUN","schema_version":"1.0","canonical_sha256":"ac7f9fa68dcc6ccb957c6c593b75526609e8b6580256800e80f4bbb01abede93","source":{"kind":"arxiv","id":"2606.12380","version":1},"attestation_state":"computed","paper":{"title":"Forbidden Intersection Theorems for Matrix Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Esty Kelman, Nathan Lindzey, Ohad Sheinfeld","submitted_at":"2026-06-10T17:43:13Z","abstract_excerpt":"A family of $m \\times n$ matrices $\\mathcal{F} \\subseteq \\mathbb{F}_q^{m \\times n}$ is {$(t-1)$-intersection-free} if $\\dim \\ker(A-B) \\neq t-1$ for all $A,B \\in \\mathcal{F}$. A \\emph{forbidden $(t-1)$-intersection problem} for a collection of matrices asks for the size and structure of extremal $(t-1)$-intersection-free families within that collection.\n  We solve this problem in $\\mathrm{GL}(n,q)$ for all pairs $(n,t)$ such that $t<c\\cdot n$ where $c$ is a universal constant. We show that the $t$-umvirates and their duals, are the only maximal $(t-1)$-intersection-free families $\\mathcal{F} \\s"},"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":"2606.12380","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-10T17:43:13Z","cross_cats_sorted":[],"title_canon_sha256":"150f32981190a16ca54f2a7a4a6e89cce0e2bff02d122295452910cbd85fbfb5","abstract_canon_sha256":"9ad908eba97dbbe65bb1cbda081a781846ff0270412d082e34f477a518b5338d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T02:09:49.181038Z","signature_b64":"nUaMnZkBjKfBN+MhWKAwTP06LtUJIN9x+t3aqUQOxIikqSIr7gibki9XMnTiTuhX9cScKQm5mnPYt0nlmVSgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac7f9fa68dcc6ccb957c6c593b75526609e8b6580256800e80f4bbb01abede93","last_reissued_at":"2026-06-11T02:09:49.180488Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T02:09:49.180488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forbidden Intersection Theorems for Matrix Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Esty Kelman, Nathan Lindzey, Ohad Sheinfeld","submitted_at":"2026-06-10T17:43:13Z","abstract_excerpt":"A family of $m \\times n$ matrices $\\mathcal{F} \\subseteq \\mathbb{F}_q^{m \\times n}$ is {$(t-1)$-intersection-free} if $\\dim \\ker(A-B) \\neq t-1$ for all $A,B \\in \\mathcal{F}$. A \\emph{forbidden $(t-1)$-intersection problem} for a collection of matrices asks for the size and structure of extremal $(t-1)$-intersection-free families within that collection.\n  We solve this problem in $\\mathrm{GL}(n,q)$ for all pairs $(n,t)$ such that $t<c\\cdot n$ where $c$ is a universal constant. We show that the $t$-umvirates and their duals, are the only maximal $(t-1)$-intersection-free families $\\mathcal{F} \\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12380","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/2606.12380/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":"2606.12380","created_at":"2026-06-11T02:09:49.180574+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.12380v1","created_at":"2026-06-11T02:09:49.180574+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12380","created_at":"2026-06-11T02:09:49.180574+00:00"},{"alias_kind":"pith_short_12","alias_value":"VR7Z7JUNZRWM","created_at":"2026-06-11T02:09:49.180574+00:00"},{"alias_kind":"pith_short_16","alias_value":"VR7Z7JUNZRWMXFL4","created_at":"2026-06-11T02:09:49.180574+00:00"},{"alias_kind":"pith_short_8","alias_value":"VR7Z7JUN","created_at":"2026-06-11T02:09:49.180574+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/VR7Z7JUNZRWMXFL4NRMTW5KSMY","json":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY.json","graph_json":"https://pith.science/api/pith-number/VR7Z7JUNZRWMXFL4NRMTW5KSMY/graph.json","events_json":"https://pith.science/api/pith-number/VR7Z7JUNZRWMXFL4NRMTW5KSMY/events.json","paper":"https://pith.science/paper/VR7Z7JUN"},"agent_actions":{"view_html":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY","download_json":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY.json","view_paper":"https://pith.science/paper/VR7Z7JUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.12380&json=true","fetch_graph":"https://pith.science/api/pith-number/VR7Z7JUNZRWMXFL4NRMTW5KSMY/graph.json","fetch_events":"https://pith.science/api/pith-number/VR7Z7JUNZRWMXFL4NRMTW5KSMY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY/action/storage_attestation","attest_author":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY/action/author_attestation","sign_citation":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY/action/citation_signature","submit_replication":"https://pith.science/pith/VR7Z7JUNZRWMXFL4NRMTW5KSMY/action/replication_record"}},"created_at":"2026-06-11T02:09:49.180574+00:00","updated_at":"2026-06-11T02:09:49.180574+00:00"}