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We prove that the set $\\mathcal{H}$ of higgledy-piggledy $k$-subspaces has to contain more than $\\min{|\\mathbb{F}|,\\sum_{i=0}^k\\lfloor\\frac{d-k+i}{i+1}\\rfloor}$ elements. We also prove that $\\mathcal{H}$ has to contain more than $(k+1)\\cdot(d-k)$ elements if the field $\\mathbb{F}$ is algebraically closed.\n  An $r$-u"},"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":"1409.6227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-22T16:09:46Z","cross_cats_sorted":[],"title_canon_sha256":"d26c539e8c43caffa9e8e168d33eb5933db2572850ce356161ac8296c0644792","abstract_canon_sha256":"c1bf6833726f9e57f17e8ff2c69d27b27ae6e93e60cd97ad5db4637f7a4f3586"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:13.579275Z","signature_b64":"S6bpJIqQTJgYgctS3QODfoF5RjKtaiH1sqZ/9RRou2O+gcAn0b3Lc5nvS162KKM7yFaiAPWTNlcM3uz4BkW1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"318bbb112f8f348270430b0969d4b85088e97f28ac6e5d7b852fc17a5962604f","last_reissued_at":"2026-05-18T02:42:13.578859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:13.578859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higgledy-piggledy subspaces and uniform subspace designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"P\\'eter Sziklai, Szabolcs L. Fancsali","submitted_at":"2014-09-22T16:09:46Z","abstract_excerpt":"In this article, we investigate collections of `well-spread-out' projective (and linear) subspaces. Projective $k$-subspaces in $\\mathsf{PG}(d,\\mathbb{F})$ are in `higgledy-piggledy arrangement' if they meet each projective subspace of co-dimension $k$ in a generator set of points. We prove that the set $\\mathcal{H}$ of higgledy-piggledy $k$-subspaces has to contain more than $\\min{|\\mathbb{F}|,\\sum_{i=0}^k\\lfloor\\frac{d-k+i}{i+1}\\rfloor}$ elements. We also prove that $\\mathcal{H}$ has to contain more than $(k+1)\\cdot(d-k)$ elements if the field $\\mathbb{F}$ is algebraically closed.\n  An $r$-u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6227","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":""},"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":"1409.6227","created_at":"2026-05-18T02:42:13.578924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.6227v1","created_at":"2026-05-18T02:42:13.578924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6227","created_at":"2026-05-18T02:42:13.578924+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGF3WEJPR42I","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGF3WEJPR42IE4CD","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGF3WEJP","created_at":"2026-05-18T12:28:30.664211+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/GGF3WEJPR42IE4CDBMEWTVFYKC","json":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC.json","graph_json":"https://pith.science/api/pith-number/GGF3WEJPR42IE4CDBMEWTVFYKC/graph.json","events_json":"https://pith.science/api/pith-number/GGF3WEJPR42IE4CDBMEWTVFYKC/events.json","paper":"https://pith.science/paper/GGF3WEJP"},"agent_actions":{"view_html":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC","download_json":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC.json","view_paper":"https://pith.science/paper/GGF3WEJP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.6227&json=true","fetch_graph":"https://pith.science/api/pith-number/GGF3WEJPR42IE4CDBMEWTVFYKC/graph.json","fetch_events":"https://pith.science/api/pith-number/GGF3WEJPR42IE4CDBMEWTVFYKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC/action/storage_attestation","attest_author":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC/action/author_attestation","sign_citation":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC/action/citation_signature","submit_replication":"https://pith.science/pith/GGF3WEJPR42IE4CDBMEWTVFYKC/action/replication_record"}},"created_at":"2026-05-18T02:42:13.578924+00:00","updated_at":"2026-05-18T02:42:13.578924+00:00"}