{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T5BVJUPN3C4JPDJIHC4CMPIO3F","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":"951bcf7bd733ec5a13deba85f6829bace61f8ec98019af96e9a8a9ce2ba77cb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-01T09:16:15Z","title_canon_sha256":"bd8ff466d2186b680b68d26e6811f3a2d62f2d5c59506abef68b6174ebe46dac"},"schema_version":"1.0","source":{"id":"1412.0386","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0386","created_at":"2026-05-18T01:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0386v3","created_at":"2026-05-18T01:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0386","created_at":"2026-05-18T01:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"T5BVJUPN3C4J","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T5BVJUPN3C4JPDJI","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T5BVJUPN","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:1090434045a95762426e33a3e40adb2ca604fb702ba6c69b17ec718c23cdb70b","target":"graph","created_at":"2026-05-18T01:29:54Z","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":"Following D.B. Karaguezian, V. Reiner, and M.L. Wachs (Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of $GL$-Complexes, Journal of Algebra 2001) we study the connectivity degree and shellability of multiple chessboard complexes. Our central new results (Theorems 3.2 and 4.4) provide sharp connectivity bounds relevant to applications in Tverberg type problems where multiple points of the same color are permitted. These results also provide a foundation for the new results of Tverberg-van Kampen-Flores type, as announced in arXiv:1502.05290 [math.CO].","authors_text":"Du\\v{s}ko Joji\\'c, Rade T. \\v{Z}ivaljevi\\'c, Sini\\v{s}a T. Vre\\'cica","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-01T09:16:15Z","title":"Multiple chessboard complexes and the colored Tverberg problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0386","kind":"arxiv","version":3},"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:c70f93ce47081f0ed52f24934ea46c93b9bcd6f0b3c796075fcacd8d373eff28","target":"record","created_at":"2026-05-18T01:29:54Z","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":"951bcf7bd733ec5a13deba85f6829bace61f8ec98019af96e9a8a9ce2ba77cb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-01T09:16:15Z","title_canon_sha256":"bd8ff466d2186b680b68d26e6811f3a2d62f2d5c59506abef68b6174ebe46dac"},"schema_version":"1.0","source":{"id":"1412.0386","kind":"arxiv","version":3}},"canonical_sha256":"9f4354d1edd8b8978d2838b8263d0ed94bb76c85fb33336f959560229233cc40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f4354d1edd8b8978d2838b8263d0ed94bb76c85fb33336f959560229233cc40","first_computed_at":"2026-05-18T01:29:54.685884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:54.685884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GPhPx9w4E9kCe77MCxpxShOUqATif0i5DLFKnVej+JvXB21M2StbgIVUWazIgwo1gXlhZUnHMKR9C4usWtQJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:54.686405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0386","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c70f93ce47081f0ed52f24934ea46c93b9bcd6f0b3c796075fcacd8d373eff28","sha256:1090434045a95762426e33a3e40adb2ca604fb702ba6c69b17ec718c23cdb70b"],"state_sha256":"15b86a88985eac1cc2971f7c0effe71396fd6f16f19ac14d32b6dbf3ab85ac59"}