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We prove here that $|J(\\mathfrak{L}_1, \\mathfrak{L}_2,\\mathfrak{L}_3)|\\lesssim (L_1L_2L_3)^{1/2}$, and we extend our results to multijoints formed by real algebra"},"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":"1401.6392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-24T16:23:41Z","cross_cats_sorted":["math.AG","math.CA"],"title_canon_sha256":"c531a41ce234db3947be7ca41ea2b96a4dd3b3d64ed42cb9832b0064784356bf","abstract_canon_sha256":"c748ecdc8347e2b1cb607ece3901d5d0ebd2539d211022a38e1e9c9d2a7a9a30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:12.179006Z","signature_b64":"/Gs2GXWNUBY2sem4O6zW68MIM/pghNOVFFpaTwA2/vzgiyzN7pHI05UctBOR2Kg12ZYOEq/LmC8GpKiw9lFQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e95738ee729147022fdf7d657b0200deb8572d1f26026bcf3fa48cabbb33f23","last_reissued_at":"2026-05-18T03:01:12.178206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:12.178206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting multijoints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CA"],"primary_cat":"math.CO","authors_text":"Marina Iliopoulou","submitted_at":"2014-01-24T16:23:41Z","abstract_excerpt":"Let $\\mathfrak{L}_1$, $\\mathfrak{L}_2$, $\\mathfrak{L}_3$ be finite collections of $L_1$, $L_2$, $L_3$, respectively, lines in $\\mathbb{R}^3$, and $J(\\mathfrak{L}_1, \\mathfrak{L}_2,\\mathfrak{L}_3)$ the set of multijoints formed by them, i.e. the set of points $x \\in \\mathbb{R}^3$, each of which lies in at least one line $l_i \\in \\mathfrak{L}_i$, for all $i=1,2,3$, such that the directions of $l_1$, $l_2$ and $l_3$ span $\\mathbb{R}^3$. We prove here that $|J(\\mathfrak{L}_1, \\mathfrak{L}_2,\\mathfrak{L}_3)|\\lesssim (L_1L_2L_3)^{1/2}$, and we extend our results to multijoints formed by real algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6392","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":"1401.6392","created_at":"2026-05-18T03:01:12.178339+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6392v1","created_at":"2026-05-18T03:01:12.178339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6392","created_at":"2026-05-18T03:01:12.178339+00:00"},{"alias_kind":"pith_short_12","alias_value":"J2KXHDXHFEKH","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"J2KXHDXHFEKHAIX5","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"J2KXHDXH","created_at":"2026-05-18T12:28:33.132498+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/J2KXHDXHFEKHAIX567LFPMBABX","json":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX.json","graph_json":"https://pith.science/api/pith-number/J2KXHDXHFEKHAIX567LFPMBABX/graph.json","events_json":"https://pith.science/api/pith-number/J2KXHDXHFEKHAIX567LFPMBABX/events.json","paper":"https://pith.science/paper/J2KXHDXH"},"agent_actions":{"view_html":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX","download_json":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX.json","view_paper":"https://pith.science/paper/J2KXHDXH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6392&json=true","fetch_graph":"https://pith.science/api/pith-number/J2KXHDXHFEKHAIX567LFPMBABX/graph.json","fetch_events":"https://pith.science/api/pith-number/J2KXHDXHFEKHAIX567LFPMBABX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX/action/storage_attestation","attest_author":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX/action/author_attestation","sign_citation":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX/action/citation_signature","submit_replication":"https://pith.science/pith/J2KXHDXHFEKHAIX567LFPMBABX/action/replication_record"}},"created_at":"2026-05-18T03:01:12.178339+00:00","updated_at":"2026-05-18T03:01:12.178339+00:00"}