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It is known that there are $\\lesssim_n |\\mathfrak{L}|^{\\frac{n}{n-1}}$ joints formed by $\\mathfrak{L}$.\n  We say that a point $x \\in \\mathbb{F}^n$ is a multijoint formed by the finite collections $\\mathfrak{L}_1,\\ldots,\\mathfrak{L}_n$ of lines in $\\mathbb{F}^n$ if there exist at least $n$ lines through $x$, one from each collection, spanning $\\mathbb{F}^n$. We show that there are $\\lesssim_n (|\\"},"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":"1408.5867","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T19:09:34Z","cross_cats_sorted":[],"title_canon_sha256":"1d47b702266a19adf5df42baf383fc5cd98e0403735c717bc1e2808a5ca42870","abstract_canon_sha256":"74328825b43631aa29df42ba7de92c2833491790a69be269b14aa7b2eaeaebbb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:16.056638Z","signature_b64":"phIMspx7m/+hhJv6K7SBqatWu9oQtHefEAfK5eGaNiaVWwnH11WPAPK6IEIZ2dDA+K7DC2rrkjZt3jOClBeaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"940ec54b5bfee0bf9807415cbbb8bf8aa1088ca00f7cf582d42e9ac44298ea76","last_reissued_at":"2026-05-18T01:37:16.055918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:16.055918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incidence bounds on multijoints and generic joints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marina Iliopoulou","submitted_at":"2014-08-25T19:09:34Z","abstract_excerpt":"A point $x \\in \\mathbb{F}^n$ is a joint formed by a finite collection $\\mathfrak{L}$ of lines in $\\mathbb{F}^n$ if there exist at least $n$ lines in $\\mathfrak{L}$ through $x$ that span $\\mathbb{F}^n$. It is known that there are $\\lesssim_n |\\mathfrak{L}|^{\\frac{n}{n-1}}$ joints formed by $\\mathfrak{L}$.\n  We say that a point $x \\in \\mathbb{F}^n$ is a multijoint formed by the finite collections $\\mathfrak{L}_1,\\ldots,\\mathfrak{L}_n$ of lines in $\\mathbb{F}^n$ if there exist at least $n$ lines through $x$, one from each collection, spanning $\\mathbb{F}^n$. We show that there are $\\lesssim_n (|\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5867","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":""},"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":"1408.5867","created_at":"2026-05-18T01:37:16.056029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5867v2","created_at":"2026-05-18T01:37:16.056029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5867","created_at":"2026-05-18T01:37:16.056029+00:00"},{"alias_kind":"pith_short_12","alias_value":"SQHMKS2373QL","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SQHMKS2373QL7GAH","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SQHMKS23","created_at":"2026-05-18T12:28:49.207871+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/SQHMKS2373QL7GAHIFOLXOF7RK","json":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK.json","graph_json":"https://pith.science/api/pith-number/SQHMKS2373QL7GAHIFOLXOF7RK/graph.json","events_json":"https://pith.science/api/pith-number/SQHMKS2373QL7GAHIFOLXOF7RK/events.json","paper":"https://pith.science/paper/SQHMKS23"},"agent_actions":{"view_html":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK","download_json":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK.json","view_paper":"https://pith.science/paper/SQHMKS23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5867&json=true","fetch_graph":"https://pith.science/api/pith-number/SQHMKS2373QL7GAHIFOLXOF7RK/graph.json","fetch_events":"https://pith.science/api/pith-number/SQHMKS2373QL7GAHIFOLXOF7RK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK/action/storage_attestation","attest_author":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK/action/author_attestation","sign_citation":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK/action/citation_signature","submit_replication":"https://pith.science/pith/SQHMKS2373QL7GAHIFOLXOF7RK/action/replication_record"}},"created_at":"2026-05-18T01:37:16.056029+00:00","updated_at":"2026-05-18T01:37:16.056029+00:00"}