{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:YISF46I3A4MKKDY5M2O6TKIW6H","short_pith_number":"pith:YISF46I3","schema_version":"1.0","canonical_sha256":"c2245e791b0718a50f1d669de9a916f1febee41a629284a93776a1cfec7589d5","source":{"kind":"arxiv","id":"2209.01704","version":1},"attestation_state":"computed","paper":{"title":"Connectedness and Cycle Spaces of Friends-and-Strangers Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Lee, Colin Defant, David Dong, Michelle Wei","submitted_at":"2022-09-04T22:51:36Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2209.01704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-09-04T22:51:36Z","cross_cats_sorted":[],"title_canon_sha256":"cb3f75b626095c5a3b6cbdb32aadfb8de79088fb09615ae8233a4c72f4664a90","abstract_canon_sha256":"c268de37a4a4ff4ad57bff9296f621ae1554802744505205c2b102f3ff5aacb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:54:32.854430Z","signature_b64":"LV5ANSDP46kKIeS1C/R/RjhUlTEjeE3oUGVHQbp+M8Gm6Y1wYInmygF6D3lOtdSZ5OqiCKjwgPZiRmke72rgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2245e791b0718a50f1d669de9a916f1febee41a629284a93776a1cfec7589d5","last_reissued_at":"2026-07-05T04:54:32.853964Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:54:32.853964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectedness and Cycle Spaces of Friends-and-Strangers Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Lee, Colin Defant, David Dong, Michelle Wei","submitted_at":"2022-09-04T22:51:36Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.01704","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.01704/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2209.01704","created_at":"2026-07-05T04:54:32.854020+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.01704v1","created_at":"2026-07-05T04:54:32.854020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.01704","created_at":"2026-07-05T04:54:32.854020+00:00"},{"alias_kind":"pith_short_12","alias_value":"YISF46I3A4MK","created_at":"2026-07-05T04:54:32.854020+00:00"},{"alias_kind":"pith_short_16","alias_value":"YISF46I3A4MKKDY5","created_at":"2026-07-05T04:54:32.854020+00:00"},{"alias_kind":"pith_short_8","alias_value":"YISF46I3","created_at":"2026-07-05T04:54:32.854020+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H","json":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H.json","graph_json":"https://pith.science/api/pith-number/YISF46I3A4MKKDY5M2O6TKIW6H/graph.json","events_json":"https://pith.science/api/pith-number/YISF46I3A4MKKDY5M2O6TKIW6H/events.json","paper":"https://pith.science/paper/YISF46I3"},"agent_actions":{"view_html":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H","download_json":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H.json","view_paper":"https://pith.science/paper/YISF46I3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.01704&json=true","fetch_graph":"https://pith.science/api/pith-number/YISF46I3A4MKKDY5M2O6TKIW6H/graph.json","fetch_events":"https://pith.science/api/pith-number/YISF46I3A4MKKDY5M2O6TKIW6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H/action/storage_attestation","attest_author":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H/action/author_attestation","sign_citation":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H/action/citation_signature","submit_replication":"https://pith.science/pith/YISF46I3A4MKKDY5M2O6TKIW6H/action/replication_record"}},"created_at":"2026-07-05T04:54:32.854020+00:00","updated_at":"2026-07-05T04:54:32.854020+00:00"}