{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4SCLVZNY5ZWAK35WAPQCNC7F6P","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":"dc10972a07da1610e6cd0b75d6e33bbdaa41a639b12edd1e1f9d8f287a2e2007","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-11-29T18:36:54Z","title_canon_sha256":"dcc1ac7c18161d69e9215e4e603d69a32085547209ca98f5062b56cf5cdc30fd"},"schema_version":"1.0","source":{"id":"1911.13284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.13284","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1911.13284v1","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.13284","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"4SCLVZNY5ZWA","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"pith_short_16","alias_value":"4SCLVZNY5ZWAK35W","created_at":"2026-07-05T00:22:53Z"},{"alias_kind":"pith_short_8","alias_value":"4SCLVZNY","created_at":"2026-07-05T00:22:53Z"}],"graph_snapshots":[{"event_id":"sha256:6f6b7b96eb25626788a4bfa3f9acc2abc555547ecfaa65a9f51c1de788d518c9","target":"graph","created_at":"2026-07-05T00:22:53Z","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/1911.13284/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a finite group, and $\\alpha$ a nontrivial character of $G$. The McKay graph ${\\mathcal M}(G,\\alpha)$ has the irreducible characters of $G$ as vertices, with an edge from $\\chi_1$ to $\\chi_2$ if $\\chi_2$ is a constituent of $\\alpha\\chi_1$. We study the diameters of McKay graphs for simple groups $G$. For $G$ a group of Lie type, we show that for any $\\alpha$, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for $G={\\rm PSL}_n(q)$ or ${\\rm PSU}_n(q)$. We also bound the diameter for symmetric and alternating groups.","authors_text":"Aner Shalev, Martin W. Liebeck, Pham Huu Tiep","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-11-29T18:36:54Z","title":"On the diameters of McKay graphs for finite simple groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.13284","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":"sha256:88f128bd0d9097d18b0a74de097401711dfc77bf54e2eef5295b13980344bfb5","target":"record","created_at":"2026-07-05T00:22:53Z","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":"dc10972a07da1610e6cd0b75d6e33bbdaa41a639b12edd1e1f9d8f287a2e2007","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-11-29T18:36:54Z","title_canon_sha256":"dcc1ac7c18161d69e9215e4e603d69a32085547209ca98f5062b56cf5cdc30fd"},"schema_version":"1.0","source":{"id":"1911.13284","kind":"arxiv","version":1}},"canonical_sha256":"e484bae5b8ee6c056fb603e0268be5f3cc82e8fa100a1281b9989cb10edc9ddd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e484bae5b8ee6c056fb603e0268be5f3cc82e8fa100a1281b9989cb10edc9ddd","first_computed_at":"2026-07-05T00:22:53.640825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:53.640825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S+xu1j98++1Yhg/qe96dfBpdz91dJNg7LzndiWiHwfuaGVNW5qge13iodzl3iaqO3+R7npYtU6qCO+puAJweCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:53.641176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.13284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88f128bd0d9097d18b0a74de097401711dfc77bf54e2eef5295b13980344bfb5","sha256:6f6b7b96eb25626788a4bfa3f9acc2abc555547ecfaa65a9f51c1de788d518c9"],"state_sha256":"6f27481f20185b25f6449565101c4902283fba8b47e7a11557296cdf672c6a99"}