{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XSFKBYLL3LHJF6H3KYT6YPBO7Y","short_pith_number":"pith:XSFKBYLL","schema_version":"1.0","canonical_sha256":"bc8aa0e16bdace92f8fb5627ec3c2efe3495cc9bef5dace94977abe6b20411a0","source":{"kind":"arxiv","id":"1301.4764","version":1},"attestation_state":"computed","paper":{"title":"The 3-way intersection problem for S(2, 4, v) designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nasrin Soltankhah, Saeedeh Rashidi","submitted_at":"2013-01-21T06:36:46Z","abstract_excerpt":"In this paper the 3-way intersection problem for $S(2,4,v)$ designs is investigated. Let $b_{v}=\\frac {v(v-1)}{12}$ and $I_{3}[v]=\\{0,1,...,b_{v}\\}\\setminus\\{b_{v}-7,b_{v}-6,b_{v}-5,b_{v}-4,b_{v}-3,b_{v}-2,b_{v}-1\\}$. Let $J_{3}[v]=\\{k|$ there exist three $S(2,4,v)$ designs with $k$ same common blocks$\\}$. We show that $J_{3}[v]\\subseteq I_{3}[v]$ for any positive integer $v\\equiv1, 4\\ (\\rm mod \\ 12)$ and $J_{3}[v]=I_{3}[v]$, for $ v\\geq49$ and $v=13 $. We find $J_{3}[16]$ completely. Also we determine some values of $J_{3}[v]$ for $\\ v=25,28,37$ and 40."},"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":"1301.4764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-21T06:36:46Z","cross_cats_sorted":[],"title_canon_sha256":"b9b1bd531bd925ab3935423e4e093155f2a5f3306ccdced1a3de13b2e7acf913","abstract_canon_sha256":"929a1868fc9c28489f031473aa2f8fe5161375a1700f6906cb4439c0ab3c9209"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:55.717710Z","signature_b64":"b7hYax1qpCCOAcc875jGkrslgYqGHrzKNqA2HOkoqZ7W87hueXI5dOsTHQhCifbEfoDI/0rbyI/jgUG9hWRcCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc8aa0e16bdace92f8fb5627ec3c2efe3495cc9bef5dace94977abe6b20411a0","last_reissued_at":"2026-05-18T03:35:55.716852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:55.716852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The 3-way intersection problem for S(2, 4, v) designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nasrin Soltankhah, Saeedeh Rashidi","submitted_at":"2013-01-21T06:36:46Z","abstract_excerpt":"In this paper the 3-way intersection problem for $S(2,4,v)$ designs is investigated. Let $b_{v}=\\frac {v(v-1)}{12}$ and $I_{3}[v]=\\{0,1,...,b_{v}\\}\\setminus\\{b_{v}-7,b_{v}-6,b_{v}-5,b_{v}-4,b_{v}-3,b_{v}-2,b_{v}-1\\}$. Let $J_{3}[v]=\\{k|$ there exist three $S(2,4,v)$ designs with $k$ same common blocks$\\}$. We show that $J_{3}[v]\\subseteq I_{3}[v]$ for any positive integer $v\\equiv1, 4\\ (\\rm mod \\ 12)$ and $J_{3}[v]=I_{3}[v]$, for $ v\\geq49$ and $v=13 $. We find $J_{3}[16]$ completely. Also we determine some values of $J_{3}[v]$ for $\\ v=25,28,37$ and 40."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4764","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":"1301.4764","created_at":"2026-05-18T03:35:55.716987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4764v1","created_at":"2026-05-18T03:35:55.716987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4764","created_at":"2026-05-18T03:35:55.716987+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSFKBYLL3LHJ","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSFKBYLL3LHJF6H3","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSFKBYLL","created_at":"2026-05-18T12:28:06.772260+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/XSFKBYLL3LHJF6H3KYT6YPBO7Y","json":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y.json","graph_json":"https://pith.science/api/pith-number/XSFKBYLL3LHJF6H3KYT6YPBO7Y/graph.json","events_json":"https://pith.science/api/pith-number/XSFKBYLL3LHJF6H3KYT6YPBO7Y/events.json","paper":"https://pith.science/paper/XSFKBYLL"},"agent_actions":{"view_html":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y","download_json":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y.json","view_paper":"https://pith.science/paper/XSFKBYLL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4764&json=true","fetch_graph":"https://pith.science/api/pith-number/XSFKBYLL3LHJF6H3KYT6YPBO7Y/graph.json","fetch_events":"https://pith.science/api/pith-number/XSFKBYLL3LHJF6H3KYT6YPBO7Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y/action/storage_attestation","attest_author":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y/action/author_attestation","sign_citation":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y/action/citation_signature","submit_replication":"https://pith.science/pith/XSFKBYLL3LHJF6H3KYT6YPBO7Y/action/replication_record"}},"created_at":"2026-05-18T03:35:55.716987+00:00","updated_at":"2026-05-18T03:35:55.716987+00:00"}