{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6DJBW2K3KJHPAVZQUB65Z7UNNR","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":"9e2255a27e99ab7162d690afd6fc7f196c7450d1e92ad0f9b4b2bf912c9286fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-28T12:53:23Z","title_canon_sha256":"2c4cc5afea0f227927b5f8d7d62c5659efbd635d337c9339f9526971996e1755"},"schema_version":"1.0","source":{"id":"1310.7403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7403","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7403v1","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7403","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"6DJBW2K3KJHP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6DJBW2K3KJHPAVZQ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6DJBW2K3","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:09e79f2a9dbef02b51936e319094a94cde3377b9be5e06dc494767362632b8de","target":"graph","created_at":"2026-05-18T03:08:45Z","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":"Let $K_v$ denote the complete graph of order $v$ and $K_v - I$ denote $K_v$ minus a 1-factor. In this article we investigate uniformly resolvable decompositions of $K_v$ and $K_v-I$ into $r$ classes containing only copies of $3$-stars and $s$ classes containing only copies of $3$-cycles. We completely determine the spectrum in the case where the number of resolution classes of 3-stars is maximum.","authors_text":"Salvatore Milici, Selda K\\\"u\\c{c}\\\"uk\\c{c}if\\c{c}i, Zsolt Tuza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-28T12:53:23Z","title":"Maximum uniformly resolvable decompositions of $K_v$ and $K_v - I$ into 3-stars and 3-cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7403","kind":"arxiv","version":1},"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:eb2b932ed262d6784d6b30878f654bfc92380f3f0f120088d430351892f37738","target":"record","created_at":"2026-05-18T03:08:45Z","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":"9e2255a27e99ab7162d690afd6fc7f196c7450d1e92ad0f9b4b2bf912c9286fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-28T12:53:23Z","title_canon_sha256":"2c4cc5afea0f227927b5f8d7d62c5659efbd635d337c9339f9526971996e1755"},"schema_version":"1.0","source":{"id":"1310.7403","kind":"arxiv","version":1}},"canonical_sha256":"f0d21b695b524ef05730a07ddcfe8d6c438cdaeece6b086aa30e1fae1ba5525a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0d21b695b524ef05730a07ddcfe8d6c438cdaeece6b086aa30e1fae1ba5525a","first_computed_at":"2026-05-18T03:08:45.446348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:45.446348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rdPMhD7xB48yUCTm5O1dBoaN3wBCmKXXh5YpuTJdrhatQWIf9ROPdgovPrBTKhNh0ltRi6JJEP3dxLoSy048AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:45.447013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb2b932ed262d6784d6b30878f654bfc92380f3f0f120088d430351892f37738","sha256:09e79f2a9dbef02b51936e319094a94cde3377b9be5e06dc494767362632b8de"],"state_sha256":"9837688e73f8927f2e5a44a433c6deb4348c0580046b846b3852c3213aa75fb3"}