{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WTJZL65FKTEMMEEITZNSHBRIOB","short_pith_number":"pith:WTJZL65F","schema_version":"1.0","canonical_sha256":"b4d395fba554c8c610889e5b2386287071e61a4acc9652b78e30fbd1f274fc1d","source":{"kind":"arxiv","id":"2602.09029","version":5},"attestation_state":"computed","paper":{"title":"Fixed-Composition Shuffle Asymptotics in the Full-Support Gaussian Regime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alex Shvets","submitted_at":"2026-01-17T00:09:44Z","abstract_excerpt":"We study privacy amplification by shuffling for binary-input local randomizers with a fixed finite output alphabet and full support. For a dataset containing exactly k ones among n users, let T_{n,k} denote the shuffled histogram law. In the interior fixed-composition regime, we identify the covariance and Fisher constant governing the neighboring pair (T_{n,k},T_{n,k+1}). The correct covariance is Sigma_pi=(1-pi)Sigma_0+pi Sigma_1 rather than the multinomial covariance of the mixture. With v=W_1-W_0, the resulting constant is I_pi=v^T Sigma_pi^+ v. We prove exact likelihood-ratio identities a"},"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":"2602.09029","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-01-17T00:09:44Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"675b696c15be950f10a24b348e7d2f6dc805b82ad9e194b1f0b2f56bb69cccc0","abstract_canon_sha256":"3976420481561137a0d4253ac23ae8efc0dd9f3c3adf02cf503c0ac0fd55c229"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:20.849767Z","signature_b64":"Lotvmonyy0PDq2RRiqnz2k3ofq0nqFXldIQr094A0cSt4cepkql9Wp3vOZecr69V/xIvm4sU6C0s+S67OWU9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4d395fba554c8c610889e5b2386287071e61a4acc9652b78e30fbd1f274fc1d","last_reissued_at":"2026-06-23T02:13:20.849433Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:20.849433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed-Composition Shuffle Asymptotics in the Full-Support Gaussian Regime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alex Shvets","submitted_at":"2026-01-17T00:09:44Z","abstract_excerpt":"We study privacy amplification by shuffling for binary-input local randomizers with a fixed finite output alphabet and full support. For a dataset containing exactly k ones among n users, let T_{n,k} denote the shuffled histogram law. In the interior fixed-composition regime, we identify the covariance and Fisher constant governing the neighboring pair (T_{n,k},T_{n,k+1}). The correct covariance is Sigma_pi=(1-pi)Sigma_0+pi Sigma_1 rather than the multinomial covariance of the mixture. With v=W_1-W_0, the resulting constant is I_pi=v^T Sigma_pi^+ v. We prove exact likelihood-ratio identities a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.09029","kind":"arxiv","version":5},"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/2602.09029/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":"2602.09029","created_at":"2026-06-23T02:13:20.849488+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.09029v5","created_at":"2026-06-23T02:13:20.849488+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.09029","created_at":"2026-06-23T02:13:20.849488+00:00"},{"alias_kind":"pith_short_12","alias_value":"WTJZL65FKTEM","created_at":"2026-06-23T02:13:20.849488+00:00"},{"alias_kind":"pith_short_16","alias_value":"WTJZL65FKTEMMEEI","created_at":"2026-06-23T02:13:20.849488+00:00"},{"alias_kind":"pith_short_8","alias_value":"WTJZL65F","created_at":"2026-06-23T02:13:20.849488+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.18080","citing_title":"Growing Alphabets in Canonical Shuffle Experiments: Likelihood-Ratio Laws, Estimation Bounds, and Low-Budget Equivariant Design","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB","json":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB.json","graph_json":"https://pith.science/api/pith-number/WTJZL65FKTEMMEEITZNSHBRIOB/graph.json","events_json":"https://pith.science/api/pith-number/WTJZL65FKTEMMEEITZNSHBRIOB/events.json","paper":"https://pith.science/paper/WTJZL65F"},"agent_actions":{"view_html":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB","download_json":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB.json","view_paper":"https://pith.science/paper/WTJZL65F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.09029&json=true","fetch_graph":"https://pith.science/api/pith-number/WTJZL65FKTEMMEEITZNSHBRIOB/graph.json","fetch_events":"https://pith.science/api/pith-number/WTJZL65FKTEMMEEITZNSHBRIOB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB/action/storage_attestation","attest_author":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB/action/author_attestation","sign_citation":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB/action/citation_signature","submit_replication":"https://pith.science/pith/WTJZL65FKTEMMEEITZNSHBRIOB/action/replication_record"}},"created_at":"2026-06-23T02:13:20.849488+00:00","updated_at":"2026-06-23T02:13:20.849488+00:00"}