{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YISF46I3A4MKKDY5M2O6TKIW6H","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":"c268de37a4a4ff4ad57bff9296f621ae1554802744505205c2b102f3ff5aacb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-09-04T22:51:36Z","title_canon_sha256":"cb3f75b626095c5a3b6cbdb32aadfb8de79088fb09615ae8233a4c72f4664a90"},"schema_version":"1.0","source":{"id":"2209.01704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.01704","created_at":"2026-07-05T04:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"2209.01704v1","created_at":"2026-07-05T04:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.01704","created_at":"2026-07-05T04:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"YISF46I3A4MK","created_at":"2026-07-05T04:54:32Z"},{"alias_kind":"pith_short_16","alias_value":"YISF46I3A4MKKDY5","created_at":"2026-07-05T04:54:32Z"},{"alias_kind":"pith_short_8","alias_value":"YISF46I3","created_at":"2026-07-05T04:54:32Z"}],"graph_snapshots":[{"event_id":"sha256:946d8105eb4a3366d3d52ee6af85fe136150c33c1a5883a22d88be4aee1d01eb","target":"graph","created_at":"2026-07-05T04:54:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.01704/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If $X=(V(X),E(X))$ and $Y=(V(Y),E(Y))$ are $n$-vertex graphs, then their friends-and-strangers graph $\\mathsf{FS}(X,Y)$ is the graph whose vertices are the bijections from $V(X)$ to $V(Y)$ in which two bijections $\\sigma$ and $\\sigma'$ are adjacent if and only if there is an edge $\\{a,b\\}\\in E(X)$ such that $\\{\\sigma(a),\\sigma(b)\\}\\in E(Y)$ and $\\sigma'=\\sigma\\circ (a\\,\\,b)$, where $(a\\,\\,b)$ is the permutation of $V(X)$ that swaps $a$ and $b$. We prove general theorems that provide necessary and/or sufficient conditions for $\\mathsf{FS}(X,Y)$ to be connected. As a corollary, we obtain a compl","authors_text":"Alan Lee, Colin Defant, David Dong, Michelle Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-09-04T22:51:36Z","title":"Connectedness and Cycle Spaces of Friends-and-Strangers Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.01704","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":"sha256:37163297073554fbc4caecb406112869d77f7d19d2fde9786fc6273db3769baf","target":"record","created_at":"2026-07-05T04:54:32Z","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":"c268de37a4a4ff4ad57bff9296f621ae1554802744505205c2b102f3ff5aacb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-09-04T22:51:36Z","title_canon_sha256":"cb3f75b626095c5a3b6cbdb32aadfb8de79088fb09615ae8233a4c72f4664a90"},"schema_version":"1.0","source":{"id":"2209.01704","kind":"arxiv","version":1}},"canonical_sha256":"c2245e791b0718a50f1d669de9a916f1febee41a629284a93776a1cfec7589d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2245e791b0718a50f1d669de9a916f1febee41a629284a93776a1cfec7589d5","first_computed_at":"2026-07-05T04:54:32.853964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:54:32.853964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LV5ANSDP46kKIeS1C/R/RjhUlTEjeE3oUGVHQbp+M8Gm6Y1wYInmygF6D3lOtdSZ5OqiCKjwgPZiRmke72rgDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:54:32.854430Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.01704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37163297073554fbc4caecb406112869d77f7d19d2fde9786fc6273db3769baf","sha256:946d8105eb4a3366d3d52ee6af85fe136150c33c1a5883a22d88be4aee1d01eb"],"state_sha256":"dcd4ff7fa0ea4c48cdca8f0d13305f9c33309c6b59dd50760fd86b8ce5fb3174"}