{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PDDSWM2PUSV3MM65EIZWB75MIB","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":"3d7df28d760c0d9e0273a5a915562f582bb92b424966f20d4980ec57b7df2e40","cross_cats_sorted":["math.GR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-31T20:54:40Z","title_canon_sha256":"c7bc1fb8aef2313cbe23a2403d8f6bd085299c906d9a456b8099d4f69b0b5431"},"schema_version":"1.0","source":{"id":"1811.00113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00113","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00113v1","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00113","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"pith_short_12","alias_value":"PDDSWM2PUSV3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDDSWM2PUSV3MM65","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDDSWM2P","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:798091fc5771bdf34237bf300fced2ffad20b2337fe7faf6b303ccb166e20d42","target":"graph","created_at":"2026-05-18T00:01:48Z","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":"For each prime $p$, we study the eigenvalues of a 3-regular graph on roughly $p^2$ vertices constructed from the Markoff surface. We show they asymptotically follow the Kesten-McKay law, which also describes the eigenvalues of a random regular graph. The proof is based on the method of moments and takes advantage of a natural group action on the Markoff surface.","authors_text":"Matthew de Courcy-Ireland, Michael Magee","cross_cats":["math.GR","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-31T20:54:40Z","title":"Kesten-McKay law for the Markoff surface mod p"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00113","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":"sha256:6b6a0cf30f885c9980cffcc17cfd4ea160e3ef0ba77676116879d5e5305c4a6e","target":"record","created_at":"2026-05-18T00:01:48Z","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":"3d7df28d760c0d9e0273a5a915562f582bb92b424966f20d4980ec57b7df2e40","cross_cats_sorted":["math.GR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-31T20:54:40Z","title_canon_sha256":"c7bc1fb8aef2313cbe23a2403d8f6bd085299c906d9a456b8099d4f69b0b5431"},"schema_version":"1.0","source":{"id":"1811.00113","kind":"arxiv","version":1}},"canonical_sha256":"78c72b334fa4abb633dd223360ffac4070d4a2529d0d463fedb2d82f89d0a3d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78c72b334fa4abb633dd223360ffac4070d4a2529d0d463fedb2d82f89d0a3d0","first_computed_at":"2026-05-18T00:01:48.230846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:48.230846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kjJW8FbPKDDlkRiL6oLAiW27KfaQOfpp2MuG/vdBVRlb5o6nRRd7FhrO0UJfgQlN2WQwOb1UXWGHhGfX3GbEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:48.231377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.00113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b6a0cf30f885c9980cffcc17cfd4ea160e3ef0ba77676116879d5e5305c4a6e","sha256:798091fc5771bdf34237bf300fced2ffad20b2337fe7faf6b303ccb166e20d42"],"state_sha256":"7caee5da57f777d315fd611fc7c722cbcfd8fb74699542427d4439652b6a78b2"}