{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ILI5H4UYCIWYPX2ITZC3MDUR7L","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":"00cd4ec3e5fb1ddeaadddb3d7af49c154e3c60e675448af920e3bca3e2e85796","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-29T12:12:24Z","title_canon_sha256":"e9e4d279c1b014e49fd195c5a7a56461c94f4b6d286852832d22e792d6ac12a9"},"schema_version":"1.0","source":{"id":"1409.8093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8093","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8093v2","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8093","created_at":"2026-05-18T02:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"ILI5H4UYCIWY","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ILI5H4UYCIWYPX2I","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ILI5H4UY","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:c79ad112fc5d332493cae7e7f6b63e238ef7205022f7b2bfc430312e7cededa9","target":"graph","created_at":"2026-05-18T02:40:55Z","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":"We define a new statistic $\\mathsf{sor}$ on the set of colored permutations $\\mathsf{G}_{r,n}$ and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the arrangements of $n$ non-attacking rooks on a fixed Ferrers shape we show that the following two sequences of set-valued statistics are joint equidistributed: $(\\ell,\\mathsf{Rmil}^0,\\mathsf{Rmil}^1,...,\\mathsf{Rmil}^{r-1}$, $\\mathsf{Lmil}^0,\\mathsf{Lmil}^1,...,\\mathsf{Lmil}^{r-1}$, $\\mathsf{Lmal}^0,\\mathsf{Lmal}^1,...,\\mathsf{Lmal}^{r-1}$, $\\mathsf{Lmap}^0,\\mathsf{Lma","authors_text":"Sen-Peng Eu, Tsai-Lien Wong, Yuan-Hsun Lo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-29T12:12:24Z","title":"The sorting index on colored permutations and even-signed permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8093","kind":"arxiv","version":2},"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":"sha256:142500af92485ec0a6a99b54cf28477e5b4fa606f9f68ed464ebfa6333b6c179","target":"record","created_at":"2026-05-18T02:40:55Z","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":"00cd4ec3e5fb1ddeaadddb3d7af49c154e3c60e675448af920e3bca3e2e85796","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-29T12:12:24Z","title_canon_sha256":"e9e4d279c1b014e49fd195c5a7a56461c94f4b6d286852832d22e792d6ac12a9"},"schema_version":"1.0","source":{"id":"1409.8093","kind":"arxiv","version":2}},"canonical_sha256":"42d1d3f298122d87df489e45b60e91faf956489b247cf7d34281c5c0cc38caa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42d1d3f298122d87df489e45b60e91faf956489b247cf7d34281c5c0cc38caa2","first_computed_at":"2026-05-18T02:40:55.312715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:55.312715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4+pfD4EImcZ8oC6Ce8iKiQ4VTJ+Wk9UtM1Trt0cHha/v5XXGKyZEf1yHibNMGs7ISPXYmvZiw0yFLJJCXGqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:55.313170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:142500af92485ec0a6a99b54cf28477e5b4fa606f9f68ed464ebfa6333b6c179","sha256:c79ad112fc5d332493cae7e7f6b63e238ef7205022f7b2bfc430312e7cededa9"],"state_sha256":"f980969f654ce4b973fb7d44a8b28db2ff8c93f0a462c9f3401f8a344312dfe5"}