{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SUAJLOBCARDJ75HGDOOKBIOVCZ","short_pith_number":"pith:SUAJLOBC","schema_version":"1.0","canonical_sha256":"950095b82204469ff4e61b9ca0a1d5166e8c7bd89400d2b9ef502f07363c71ed","source":{"kind":"arxiv","id":"2504.08988","version":2},"attestation_state":"computed","paper":{"title":"Strong convergence of uniformly random permutation representations of surface groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GR","math.OA","math.PR","math.SP"],"primary_cat":"math.GT","authors_text":"Doron Puder, Michael Magee, Ramon van Handel","submitted_at":"2025-04-11T21:41:56Z","abstract_excerpt":"Let $\\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\\mathrm{Hom}(\\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of $S_n$. We prove the strong convergence in probability as $n\\to\\infty$ of this sequence of random representations to the regular representation of $\\Gamma$.\n  As a consequence, for any closed hyperbolic surface $X$, with probability tending to one as $n\\to\\infty$, a uniformly random degree-$n$ covering space of $X$ has near optimal relative spectral gap -- ignori"},"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":"2504.08988","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GT","submitted_at":"2025-04-11T21:41:56Z","cross_cats_sorted":["math.GR","math.OA","math.PR","math.SP"],"title_canon_sha256":"c30fa8bf70b77df49e4877d959ff463d920d8c8b1835ddab359b1a8ad12f3a71","abstract_canon_sha256":"a676296201548c9a7bff6bf868fda992b125b46b661ccb35f42a8a7d003ceed8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:55:34.046726Z","signature_b64":"QSMNg4uDHw40VdQ791ugiZh/+kJhqAVttLdKdN8eIQSc+oCx+Zo/7t9KByQYEwpiKso3sO86fxZUT6l5cnrhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"950095b82204469ff4e61b9ca0a1d5166e8c7bd89400d2b9ef502f07363c71ed","last_reissued_at":"2026-07-05T10:55:34.046234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:55:34.046234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong convergence of uniformly random permutation representations of surface groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GR","math.OA","math.PR","math.SP"],"primary_cat":"math.GT","authors_text":"Doron Puder, Michael Magee, Ramon van Handel","submitted_at":"2025-04-11T21:41:56Z","abstract_excerpt":"Let $\\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\\mathrm{Hom}(\\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of $S_n$. We prove the strong convergence in probability as $n\\to\\infty$ of this sequence of random representations to the regular representation of $\\Gamma$.\n  As a consequence, for any closed hyperbolic surface $X$, with probability tending to one as $n\\to\\infty$, a uniformly random degree-$n$ covering space of $X$ has near optimal relative spectral gap -- ignori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.08988","kind":"arxiv","version":2},"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/2504.08988/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":"2504.08988","created_at":"2026-07-05T10:55:34.046284+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.08988v2","created_at":"2026-07-05T10:55:34.046284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.08988","created_at":"2026-07-05T10:55:34.046284+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUAJLOBCARDJ","created_at":"2026-07-05T10:55:34.046284+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUAJLOBCARDJ75HG","created_at":"2026-07-05T10:55:34.046284+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUAJLOBC","created_at":"2026-07-05T10:55:34.046284+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06331","citing_title":"Bass notes of random hyperbolic surfaces of large genus","ref_index":38,"is_internal_anchor":true},{"citing_arxiv_id":"2311.17733","citing_title":"Stable Invariants of Words from Random Matrices","ref_index":53,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21582","citing_title":"Quantum Mixing for Schr\\\"odinger eigenfunctions in Benjamini-Schramm limit","ref_index":73,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ","json":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ.json","graph_json":"https://pith.science/api/pith-number/SUAJLOBCARDJ75HGDOOKBIOVCZ/graph.json","events_json":"https://pith.science/api/pith-number/SUAJLOBCARDJ75HGDOOKBIOVCZ/events.json","paper":"https://pith.science/paper/SUAJLOBC"},"agent_actions":{"view_html":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ","download_json":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ.json","view_paper":"https://pith.science/paper/SUAJLOBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.08988&json=true","fetch_graph":"https://pith.science/api/pith-number/SUAJLOBCARDJ75HGDOOKBIOVCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/SUAJLOBCARDJ75HGDOOKBIOVCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ/action/storage_attestation","attest_author":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ/action/author_attestation","sign_citation":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ/action/citation_signature","submit_replication":"https://pith.science/pith/SUAJLOBCARDJ75HGDOOKBIOVCZ/action/replication_record"}},"created_at":"2026-07-05T10:55:34.046284+00:00","updated_at":"2026-07-05T10:55:34.046284+00:00"}