{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VVLDQF2ADNCDHSTKS3DYPK3BZI","short_pith_number":"pith:VVLDQF2A","schema_version":"1.0","canonical_sha256":"ad563817401b4433ca6a96c787ab61ca28925c7c728ba7072e99b02f66265be6","source":{"kind":"arxiv","id":"2505.18348","version":2},"attestation_state":"computed","paper":{"title":"Rates of convergence in the Free Multiplicative Central Limit Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Marwa Banna, Nicolas Gilliers, Pei-Lun Tseng","submitted_at":"2025-05-23T20:09:51Z","abstract_excerpt":"We provide the first quantitative estimates for the rate of convergence in the free multiplicative central limit theorem (CLT), in terms of the Kolmogorov and $r$-Wasserstein distances for $r \\geq 1$. While the free additive CLT has been thoroughly studied, including convergence rates, the multiplicative setting remained open in this regard. We consider products of the form $$ \\pi_n^{g,n^{-1/2}x} := g\\left(\\frac{x_1}{\\sqrt{n}}\\right) \\cdots g\\left(\\frac{x_n}{\\sqrt{n}}\\right),$$ where $x_1, \\dots, x_n$ are freely independent self-adjoint operators with common variance $\\sigma^2$ and $g \\colon \\"},"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":"2505.18348","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2025-05-23T20:09:51Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a0673f56d527b54adc585dc067adea7f2daa9bdb183402a0cab7c702039d21c4","abstract_canon_sha256":"c3724f309e544f5f90c83ef499136476ee500f2b81a329e7c475bd83f8c0592a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:30:44.103440Z","signature_b64":"fIlf4ZmaDZmFmSglS8RGYlOWlKNMn8uio+j63B2DK2feV4x3IgNzOYBQ7AjMhPKrYYSY2fne0UWlYC/HZCrACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad563817401b4433ca6a96c787ab61ca28925c7c728ba7072e99b02f66265be6","last_reissued_at":"2026-07-05T11:30:44.102932Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:30:44.102932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rates of convergence in the Free Multiplicative Central Limit Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Marwa Banna, Nicolas Gilliers, Pei-Lun Tseng","submitted_at":"2025-05-23T20:09:51Z","abstract_excerpt":"We provide the first quantitative estimates for the rate of convergence in the free multiplicative central limit theorem (CLT), in terms of the Kolmogorov and $r$-Wasserstein distances for $r \\geq 1$. While the free additive CLT has been thoroughly studied, including convergence rates, the multiplicative setting remained open in this regard. We consider products of the form $$ \\pi_n^{g,n^{-1/2}x} := g\\left(\\frac{x_1}{\\sqrt{n}}\\right) \\cdots g\\left(\\frac{x_n}{\\sqrt{n}}\\right),$$ where $x_1, \\dots, x_n$ are freely independent self-adjoint operators with common variance $\\sigma^2$ and $g \\colon \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.18348","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/2505.18348/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":"2505.18348","created_at":"2026-07-05T11:30:44.102991+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.18348v2","created_at":"2026-07-05T11:30:44.102991+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.18348","created_at":"2026-07-05T11:30:44.102991+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVLDQF2ADNCD","created_at":"2026-07-05T11:30:44.102991+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVLDQF2ADNCDHSTK","created_at":"2026-07-05T11:30:44.102991+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVLDQF2A","created_at":"2026-07-05T11:30:44.102991+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/VVLDQF2ADNCDHSTKS3DYPK3BZI","json":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI.json","graph_json":"https://pith.science/api/pith-number/VVLDQF2ADNCDHSTKS3DYPK3BZI/graph.json","events_json":"https://pith.science/api/pith-number/VVLDQF2ADNCDHSTKS3DYPK3BZI/events.json","paper":"https://pith.science/paper/VVLDQF2A"},"agent_actions":{"view_html":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI","download_json":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI.json","view_paper":"https://pith.science/paper/VVLDQF2A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.18348&json=true","fetch_graph":"https://pith.science/api/pith-number/VVLDQF2ADNCDHSTKS3DYPK3BZI/graph.json","fetch_events":"https://pith.science/api/pith-number/VVLDQF2ADNCDHSTKS3DYPK3BZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI/action/storage_attestation","attest_author":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI/action/author_attestation","sign_citation":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI/action/citation_signature","submit_replication":"https://pith.science/pith/VVLDQF2ADNCDHSTKS3DYPK3BZI/action/replication_record"}},"created_at":"2026-07-05T11:30:44.102991+00:00","updated_at":"2026-07-05T11:30:44.102991+00:00"}