{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ICRUKJR2Z76TNAVYTKXJRZZLZS","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":"6691168f6dc2d5fe61bb951fb1e67ab692aa91c307a8767fbc6b5c9a68c70a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-06-12T03:25:52Z","title_canon_sha256":"4716dd3ead80529c1548dc95ed71c932a14d57050597096e71ebfb984ccfffde"},"schema_version":"1.0","source":{"id":"0806.1993","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1993","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1993v3","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1993","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"pith_short_12","alias_value":"ICRUKJR2Z76T","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"ICRUKJR2Z76TNAVY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"ICRUKJR2","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:4d1476a86dba189a0d08a55f91e10e7d8c6c00106856ed6996a34acaebfe9689","target":"graph","created_at":"2026-05-18T04:23:54Z","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":"We begin with a new analysis of formal words. Let w be a formal word in letters g_1,...,g_k. The word map associated with w maps the permutations s_1,...,s_k in S_n to the permutation obtained by replacing for each i, every occurrence of g_i in w by s_i. We investigate the random variable X_w^n that counts the fixed points in this permutation when the s_i are selected uniformly at random. A major ingredient of our work is a new categorization of words which considerably extends the dichotomy of primitive vs. imprimitive words. We establish some results and make a few conjectures about the rela","authors_text":"Doron Puder, Nati Linial","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-06-12T03:25:52Z","title":"Words Maps and Spectra of Random Graph Lifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1993","kind":"arxiv","version":3},"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":"sha256:03dafcda98303f62d2f7970727e797e21dd14ba103a36414f51f59168b9b8e9e","target":"record","created_at":"2026-05-18T04:23:54Z","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":"6691168f6dc2d5fe61bb951fb1e67ab692aa91c307a8767fbc6b5c9a68c70a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-06-12T03:25:52Z","title_canon_sha256":"4716dd3ead80529c1548dc95ed71c932a14d57050597096e71ebfb984ccfffde"},"schema_version":"1.0","source":{"id":"0806.1993","kind":"arxiv","version":3}},"canonical_sha256":"40a345263acffd3682b89aae98e72bcc9354a3921074c1dcbe94952950c82637","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40a345263acffd3682b89aae98e72bcc9354a3921074c1dcbe94952950c82637","first_computed_at":"2026-05-18T04:23:54.618535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:54.618535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QbDLu0/lJBfNaQYDInxeuPyClcGHk8JCl36pY8NYLsOTM7VRMY8EckFlEUCBA0/hlATvBI/6dLNbf3RlmNblBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:54.618949Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.1993","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03dafcda98303f62d2f7970727e797e21dd14ba103a36414f51f59168b9b8e9e","sha256:4d1476a86dba189a0d08a55f91e10e7d8c6c00106856ed6996a34acaebfe9689"],"state_sha256":"fc39957ae7a808110bc3f74df354ea456aae18a1b33704df469147a3f4c8e2f9"}