{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SQHMKS2373QL7GAHIFOLXOF7RK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"74328825b43631aa29df42ba7de92c2833491790a69be269b14aa7b2eaeaebbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T19:09:34Z","title_canon_sha256":"1d47b702266a19adf5df42baf383fc5cd98e0403735c717bc1e2808a5ca42870"},"schema_version":"1.0","source":{"id":"1408.5867","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5867","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5867v2","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5867","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"SQHMKS2373QL","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SQHMKS2373QL7GAH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SQHMKS23","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:6a5d7579c1f830285340cd2a27076425edcd875c0686f8122e717cdc6bf3d056","target":"graph","created_at":"2026-05-18T01:37:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 (|\\","authors_text":"Marina Iliopoulou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T19:09:34Z","title":"Incidence bounds on multijoints and generic joints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5867","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:835acd1ca7e9192084fbd619f6f23b2994b102a6b548f275ea8422781f493601","target":"record","created_at":"2026-05-18T01:37:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"74328825b43631aa29df42ba7de92c2833491790a69be269b14aa7b2eaeaebbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-25T19:09:34Z","title_canon_sha256":"1d47b702266a19adf5df42baf383fc5cd98e0403735c717bc1e2808a5ca42870"},"schema_version":"1.0","source":{"id":"1408.5867","kind":"arxiv","version":2}},"canonical_sha256":"940ec54b5bfee0bf9807415cbbb8bf8aa1088ca00f7cf582d42e9ac44298ea76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"940ec54b5bfee0bf9807415cbbb8bf8aa1088ca00f7cf582d42e9ac44298ea76","first_computed_at":"2026-05-18T01:37:16.055918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:16.055918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"phIMspx7m/+hhJv6K7SBqatWu9oQtHefEAfK5eGaNiaVWwnH11WPAPK6IEIZ2dDA+K7DC2rrkjZt3jOClBeaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:16.056638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5867","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:835acd1ca7e9192084fbd619f6f23b2994b102a6b548f275ea8422781f493601","sha256:6a5d7579c1f830285340cd2a27076425edcd875c0686f8122e717cdc6bf3d056"],"state_sha256":"5e48b842df34ac2582ccb7f03e51e94cd48839a98b6867ab9079cf9ecd8ea86f"}