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Let $Adm(v)={(s,t): s+t\\leq b_v, s,t$ are non-negative integers$}$, where $b_v=\\lfloor v(v-1)/8\\rfloor$. It is established that $Fin(v)= Adm(v)\\setminus {(b_v-1,0),(b_v-1,1)}$ for any integer $v\\equiv 0,1 ({\\rm mod} 8)$ and $v\\geq 8$; $Fin(v)=Adm(v)$ for any integer $v\\equiv 2,3,4,5,6,7 ({\\rm mod} 8)$ and $v\\geq 4$."},"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":"1207.3931","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2012-07-17T10:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"fd844fc275d99a9b7c3622250d03199c094ca1b86b7454323d1af33db64119dd","abstract_canon_sha256":"085706965eab92de6f21cce667c55acd1ef698c4f3a3801f9b238c5b8b59e077"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:49.483975Z","signature_b64":"FeuM+hIuLr+uFftttY7L/isfqG9Qiu9FLdrwcFfhsEf4lBRbJx7T6nQPKN0JxojYMxW/wWxoii4+RowR1JOvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f91d4502d9bb75fda74cbc3516ca73c977a531d82cd8735fbb91b4edb800563","last_reissued_at":"2026-05-18T03:50:49.483209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:49.483209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The fine triangle intersections for maximum kite packings","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guizhi Zhang, Tao Feng, Yanxun Chang","submitted_at":"2012-07-17T10:03:34Z","abstract_excerpt":"In this paper the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let $Fin(v)={(s,t):$ $\\exists$ a pair of maximum kite packings of order $v$ intersecting in $s$ blocks and $s+t$ triangles$}$. Let $Adm(v)={(s,t): s+t\\leq b_v, s,t$ are non-negative integers$}$, where $b_v=\\lfloor v(v-1)/8\\rfloor$. It is established that $Fin(v)= Adm(v)\\setminus {(b_v-1,0),(b_v-1,1)}$ for any integer $v\\equiv 0,1 ({\\rm mod} 8)$ and $v\\geq 8$; $Fin(v)=Adm(v)$ for any integer $v\\equiv 2,3,4,5,6,7 ({\\rm mod} 8)$ and $v\\geq 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3931","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":"1207.3931","created_at":"2026-05-18T03:50:49.483338+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.3931v1","created_at":"2026-05-18T03:50:49.483338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3931","created_at":"2026-05-18T03:50:49.483338+00:00"},{"alias_kind":"pith_short_12","alias_value":"H6I5IUBNTO3V","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"H6I5IUBNTO3V7WTU","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"H6I5IUBN","created_at":"2026-05-18T12:27:06.952714+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/H6I5IUBNTO3V7WTUZPBVC3FHHS","json":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS.json","graph_json":"https://pith.science/api/pith-number/H6I5IUBNTO3V7WTUZPBVC3FHHS/graph.json","events_json":"https://pith.science/api/pith-number/H6I5IUBNTO3V7WTUZPBVC3FHHS/events.json","paper":"https://pith.science/paper/H6I5IUBN"},"agent_actions":{"view_html":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS","download_json":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS.json","view_paper":"https://pith.science/paper/H6I5IUBN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.3931&json=true","fetch_graph":"https://pith.science/api/pith-number/H6I5IUBNTO3V7WTUZPBVC3FHHS/graph.json","fetch_events":"https://pith.science/api/pith-number/H6I5IUBNTO3V7WTUZPBVC3FHHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS/action/storage_attestation","attest_author":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS/action/author_attestation","sign_citation":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS/action/citation_signature","submit_replication":"https://pith.science/pith/H6I5IUBNTO3V7WTUZPBVC3FHHS/action/replication_record"}},"created_at":"2026-05-18T03:50:49.483338+00:00","updated_at":"2026-05-18T03:50:49.483338+00:00"}