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We prove the Haar--Siegel random-lattice version in a stronger, dimension-uniform form. Let \\(X_n=\\operatorname{SL}_n(\\R)/\\operatorname{SL}_n(\\Z)\\), let \\(\\mu_n\\) be its invariant probability measure, and let \\(\\gamma(L)=\\sup_{r\\ge1} N_L(r\\lambda_1(L))/r^n\\), where \\(N_L(R)\\) counts nonzero vectors of \\(L\\) of Eu"},"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":"2605.21966","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T03:55:47Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"540476f01a1752a218230e3044328702627ff6d420ceba8a10f5b49aac17bb63","abstract_canon_sha256":"3860b0c116167cd6935881a4c4f65928ecca766baff28f3b9be87376c9060a66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:17.536423Z","signature_b64":"DZnW3Plhzdkx5DMwoa+1ygkookJy8uR48zkBWsZQEHNrJReHzHtkckEvuTilF0GQrJqM2fVHA09K+F+N4ThAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c48f144b364d8dc87dcfc5ed03e9c6753faba5a779acd34f8039f166acdebb8e","last_reissued_at":"2026-05-22T01:04:17.535571Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:17.535571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Uniform Random-Lattice Tail Bound for the SVP Kissing-Profile Parameter","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Yaoran Yang, Yutong Zhang","submitted_at":"2026-05-21T03:55:47Z","abstract_excerpt":"A recent SICOMP paper on classical and quantum algorithms for the shortest vector problem introduced a lattice-dependent parameter \\(\\gamma(L)\\), bounded universally in the exponential sense by \\(2^{0.402n+o(n)}\\), and conjectured that this parameter is \\(2^{o(n)}\\) for most lattices. We prove the Haar--Siegel random-lattice version in a stronger, dimension-uniform form. Let \\(X_n=\\operatorname{SL}_n(\\R)/\\operatorname{SL}_n(\\Z)\\), let \\(\\mu_n\\) be its invariant probability measure, and let \\(\\gamma(L)=\\sup_{r\\ge1} N_L(r\\lambda_1(L))/r^n\\), where \\(N_L(R)\\) counts nonzero vectors of \\(L\\) of Eu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21966","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/2605.21966/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":"2605.21966","created_at":"2026-05-22T01:04:17.535723+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.21966v1","created_at":"2026-05-22T01:04:17.535723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21966","created_at":"2026-05-22T01:04:17.535723+00:00"},{"alias_kind":"pith_short_12","alias_value":"YSHRISZWJWG4","created_at":"2026-05-22T01:04:17.535723+00:00"},{"alias_kind":"pith_short_16","alias_value":"YSHRISZWJWG4Q7OP","created_at":"2026-05-22T01:04:17.535723+00:00"},{"alias_kind":"pith_short_8","alias_value":"YSHRISZW","created_at":"2026-05-22T01:04:17.535723+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/YSHRISZWJWG4Q7OPYXWQH2OGOU","json":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU.json","graph_json":"https://pith.science/api/pith-number/YSHRISZWJWG4Q7OPYXWQH2OGOU/graph.json","events_json":"https://pith.science/api/pith-number/YSHRISZWJWG4Q7OPYXWQH2OGOU/events.json","paper":"https://pith.science/paper/YSHRISZW"},"agent_actions":{"view_html":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU","download_json":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU.json","view_paper":"https://pith.science/paper/YSHRISZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.21966&json=true","fetch_graph":"https://pith.science/api/pith-number/YSHRISZWJWG4Q7OPYXWQH2OGOU/graph.json","fetch_events":"https://pith.science/api/pith-number/YSHRISZWJWG4Q7OPYXWQH2OGOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU/action/storage_attestation","attest_author":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU/action/author_attestation","sign_citation":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU/action/citation_signature","submit_replication":"https://pith.science/pith/YSHRISZWJWG4Q7OPYXWQH2OGOU/action/replication_record"}},"created_at":"2026-05-22T01:04:17.535723+00:00","updated_at":"2026-05-22T01:04:17.535723+00:00"}