{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XSUV3BQCRX5YU2A5AL2YN3CM7G","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":"2aa7bbd4546e63d382dac7153289d3a3b9c3b9e3f12472f70af812793f530d75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-12T16:07:44Z","title_canon_sha256":"7343d8d0ea95a9fa94afdc3fac004487aad865b851f82774b802113efe9baed4"},"schema_version":"1.0","source":{"id":"1803.04342","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04342","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04342v2","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04342","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"pith_short_12","alias_value":"XSUV3BQCRX5Y","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XSUV3BQCRX5YU2A5","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XSUV3BQC","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:530fae6af011993a89bd65395c9c81062089110c8ea3503301985f95af56a076","target":"graph","created_at":"2026-05-18T00:06:11Z","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 $n,k,r$ be positive integers with $n \\geq rk$ and $r \\geq 2$. Consider a circle $C$ with~$n$ points~$1,\\ldots,n$ in clockwise order. The $r$-stable \\emph{interlacing graph} $\\text{IG}_{n,k}^{(r)}$ is the graph with vertices corresponding to $k$-subsets $S$ of $\\{1,...,n\\}$ such that any two distinct points in~$S$ have distance at least~$r$ around the circle, and edges between~$k$-subsets $P$ and $Q$ if they \\emph{interlace}: after removing the points in~$P$ from $C$, the points in~$Q$ are in different connected components. In this paper we prove that the circular chromatic number of $\\text","authors_text":"Bart Litjens, Bart Sevenster, Llu\\'is Vena, Sven Polak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-12T16:07:44Z","title":"On the circular chromatic number of a subgraph of the Kneser graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04342","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":"sha256:7c63b2787de99e7c9c81a3fbe076dde45a98c26912b6982b2bd2475bee1dc028","target":"record","created_at":"2026-05-18T00:06:11Z","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":"2aa7bbd4546e63d382dac7153289d3a3b9c3b9e3f12472f70af812793f530d75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-12T16:07:44Z","title_canon_sha256":"7343d8d0ea95a9fa94afdc3fac004487aad865b851f82774b802113efe9baed4"},"schema_version":"1.0","source":{"id":"1803.04342","kind":"arxiv","version":2}},"canonical_sha256":"bca95d86028dfb8a681d02f586ec4cf98c2d1239d46aedeb78106ef5ca7f44ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bca95d86028dfb8a681d02f586ec4cf98c2d1239d46aedeb78106ef5ca7f44ca","first_computed_at":"2026-05-18T00:06:11.802197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:11.802197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CHYJVkhynHZ519rSuetPXZxDAUh5GrV4G1rRPGUJQmPE0qrXKmscvlne5gOsr3qMKB2pKQXdFK3kGV8St4I8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:11.802742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04342","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c63b2787de99e7c9c81a3fbe076dde45a98c26912b6982b2bd2475bee1dc028","sha256:530fae6af011993a89bd65395c9c81062089110c8ea3503301985f95af56a076"],"state_sha256":"c10f052113e6c402518e6c2201c3ba5582dee830b778795358e0ff7b4217dc89"}