Pith Number

pith:4TNCITGU

pith:2025:4TNCITGUQFV4MWDZPKBMR2O7ZI

not attested not anchored not stored refs pending

Counting the number of group orbits by marrying the Burnside process with importance sampling

Chenyang Zhong, Persi Diaconis

arxiv:2501.11731 v2 · 2025-01-20 · math.PR · math.CO · math.GR · stat.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4TNCITGUQFV4MWDZPKBMR2O7ZI}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

2 papers in Pith

The dual Burnside process

Estimating the size of a set using cascading exclusion

Receipt and verification

First computed	2026-07-05T10:35:44.707010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4da244cd4816bc658797a82c8e9dfca10deec5455ed8a4b0dc35c3e1d9d6390

Aliases

arxiv: 2501.11731 · arxiv_version: 2501.11731v2 · doi: 10.48550/arxiv.2501.11731 · pith_short_12: 4TNCITGUQFV4 · pith_short_16: 4TNCITGUQFV4MWDZ · pith_short_8: 4TNCITGU

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/4TNCITGUQFV4MWDZPKBMR2O7ZI \
  | 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: e4da244cd4816bc658797a82c8e9dfca10deec5455ed8a4b0dc35c3e1d9d6390

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "696382bf01aa074645135934d2163e3b54c1d2371b2c17061dd2a0551514e8fb",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR",
      "stat.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-01-20T20:31:36Z",
    "title_canon_sha256": "a018d28205dbeaf1665f243a97b0af7d4c7aa12f6ac7c67b397e5bdf5d1a3e2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.11731",
    "kind": "arxiv",
    "version": 2
  }
}