Pith Number

pith:R4XT7FJN

pith:2026:R4XT7FJNY7XO66O2QB45SADZZI

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Explicit cutoff profiles for colored top-$m$-to-random shuffles

Ivan Z. Feng

The p-colored top-m-to-random shuffle on the wreath product has its mixing cutoff at k = floor(n/m (log n + c)), where the number of never-chosen labels converges in law to Poisson(e^{-c}).

arxiv:2604.09933 v2 · 2026-04-10 · math.PR · math.CO

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\pithnumber{R4XT7FJNY7XO66O2QB45SADZZI}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

At k=⌊n/m (log n + c)⌋, the number of never-chosen labels converges in law to Poisson(e^{-c}), giving the total-variation profile f_p(c), the separation profile, and the corresponding L^q(U), L^∞(U), χ², and relative-entropy profiles.

C2weakest assumption

That the Nakano-Sadahiro-Sakurai basis elements B_m yield exact nested-set occupancy mixtures on the wreath product G_{n,p}, allowing the likelihood ratio to reduce to the single statistic L_p.

C3one line summary

Explicit cutoff profiles for total variation, separation, and other distances are obtained for colored top-m-to-random shuffles, with unused labels converging to Poisson(e^{-c}) at the cutoff time.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-28T02:04:47.539704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f2f3f952dc7eeef79da8079d90079ca202d9c7b676ed0e0f0f87380ff6ab68b

Aliases

arxiv: 2604.09933 · arxiv_version: 2604.09933v2 · doi: 10.48550/arxiv.2604.09933 · pith_short_12: R4XT7FJNY7XO · pith_short_16: R4XT7FJNY7XO66O2 · pith_short_8: R4XT7FJN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/R4XT7FJNY7XO66O2QB45SADZZI \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8f2f3f952dc7eeef79da8079d90079ca202d9c7b676ed0e0f0f87380ff6ab68b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d61c349c88eb1c250f485d01e45079e7331ac20dc230fc41b7968527ce52893",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-10T22:22:55Z",
    "title_canon_sha256": "454f4d3e4acb92ae91e954aaf7db176251be1070b56aa94d87452440f4d79655"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.09933",
    "kind": "arxiv",
    "version": 2
  }
}