Pith Number

pith:AYL3ITCH

pith:2022:AYL3ITCHOIOHIRVY7HQQPMEE57

not attested not anchored not stored refs pending

Cutoff in the Bernoulli-Laplace model with $O(n)$ swaps

Caroline Bang, David P. Herzog, Elizabeth Sprangel, Joseph S. Alameda, J\"urgen Kritschgau, Zachary Brennan

arxiv:2203.08647 v2 · 2022-03-16 · math.PR · math.CO · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AYL3ITCHOIOHIRVY7HQQPMEE57}

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.

Receipt and verification

First computed	2026-07-05T04:06:03.773935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0617b44c47721c7446b8f9e107b084efea5578ea8d8ae82d5ba6074e32c0e010

Aliases

arxiv: 2203.08647 · arxiv_version: 2203.08647v2 · doi: 10.48550/arxiv.2203.08647 · pith_short_12: AYL3ITCHOIOH · pith_short_16: AYL3ITCHOIOHIRVY · pith_short_8: AYL3ITCH

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/AYL3ITCHOIOHIRVY7HQQPMEE57 \
  | 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: 0617b44c47721c7446b8f9e107b084efea5578ea8d8ae82d5ba6074e32c0e010

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "329ae3b3b9bb662fd0a4afe66a1c4594fce6b2c61f9df527cbd7cd0953d467e6",
    "cross_cats_sorted": [
      "math.CO",
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-03-16T14:33:33Z",
    "title_canon_sha256": "07bce0b2d997cfe6156e047a978a7ec8d00dc9df53a93b8e6f2bcd5b098284fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.08647",
    "kind": "arxiv",
    "version": 2
  }
}