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We prove that if $\\lambda_n\\to\\lambda\\in(0,\\infty)$ and $b_n\\to\\infty$, then $E_{k_n}^{(m_n)}\\Rightarrow\\mathrm{Poisson}(\\lambda)$. Combining this with the exact nested-set reduction for colored top-$m$-to-random shuffles, we obtain growing-block total variation, separation, and integrated likelihood-ratio profile"},"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":"2606.29530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-28T17:53:07Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f1b1d854359e8061f4f6fa8e2ce1dc9c1aaff034f594c6ddda45f366075af578","abstract_canon_sha256":"dc1bc55f552fdd79b8daaf8e38d902ea813ba9547d5923456047f73d3d0b8030"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:18:10.495829Z","signature_b64":"YlXrU/glXZGyVByfY45lvIxbjDjNI9Z2G8DuMDM9Q1/hAxIjcSFZoMdWk5Kxuw7OHo+5pWDCdQQR339aMmiUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8751cd90a35d18ce38ddfc417dae07f69d7b18df2b3cce68c23608118392ef4f","last_reissued_at":"2026-06-30T01:18:10.495161Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:18:10.495161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cutoff profiles for colored top-m-to-random shuffles with growing block size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Ivan Z. Feng","submitted_at":"2026-06-28T17:53:07Z","abstract_excerpt":"We study the $p$-colored top-$m$-to-random shuffle on $C_p\\wr S_n$ when the block size $m=m_n$ grows with $n$. Let $E_{k_n}^{(m_n)}$ be the number of labels never touched after $k_n$ independent uniform $m_n$-subset draws, and set $b_n=n-m_n$, $q_n=b_n/n$, and $\\lambda_n=nq_n^{k_n}$. We prove that if $\\lambda_n\\to\\lambda\\in(0,\\infty)$ and $b_n\\to\\infty$, then $E_{k_n}^{(m_n)}\\Rightarrow\\mathrm{Poisson}(\\lambda)$. Combining this with the exact nested-set reduction for colored top-$m$-to-random shuffles, we obtain growing-block total variation, separation, and integrated likelihood-ratio profile"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29530","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/2606.29530/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":"2606.29530","created_at":"2026-06-30T01:18:10.495256+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29530v1","created_at":"2026-06-30T01:18:10.495256+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29530","created_at":"2026-06-30T01:18:10.495256+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5I43EFDLUMM","created_at":"2026-06-30T01:18:10.495256+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5I43EFDLUMM4OG5","created_at":"2026-06-30T01:18:10.495256+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5I43EFD","created_at":"2026-06-30T01:18:10.495256+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/Q5I43EFDLUMM4OG57RAX3LQH62","json":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62.json","graph_json":"https://pith.science/api/pith-number/Q5I43EFDLUMM4OG57RAX3LQH62/graph.json","events_json":"https://pith.science/api/pith-number/Q5I43EFDLUMM4OG57RAX3LQH62/events.json","paper":"https://pith.science/paper/Q5I43EFD"},"agent_actions":{"view_html":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62","download_json":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62.json","view_paper":"https://pith.science/paper/Q5I43EFD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29530&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5I43EFDLUMM4OG57RAX3LQH62/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5I43EFDLUMM4OG57RAX3LQH62/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62/action/storage_attestation","attest_author":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62/action/author_attestation","sign_citation":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62/action/citation_signature","submit_replication":"https://pith.science/pith/Q5I43EFDLUMM4OG57RAX3LQH62/action/replication_record"}},"created_at":"2026-06-30T01:18:10.495256+00:00","updated_at":"2026-06-30T01:18:10.495256+00:00"}