Pith Number

pith:IF7373AD

pith:2007:IF7373AD5URJXYF7TWE7LXDLHA

not attested not anchored not stored refs pending

The birthday problem and Markov chain Monte Carlo

Ben Morris, Itai Benjamini

arxiv:math/0701390 v1 · 2007-01-14 · math.PR · math.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{IF7373AD5URJXYF7TWE7LXDLHA}

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

1 paper in Pith

Counting birthday collisions using partitions

Receipt and verification

First computed	2026-07-04T14:58:44.471951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

417fbfec03ed229be0bf9d89f5dc6b383b896d180066e4a9df5fd1a63d5cea77

Aliases

arxiv: math/0701390 · arxiv_version: math/0701390v1 · doi: 10.48550/arxiv.math/0701390 · pith_short_12: IF7373AD5URJ · pith_short_16: IF7373AD5URJXYF7 · pith_short_8: IF7373AD

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/IF7373AD5URJXYF7TWE7LXDLHA \
  | 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: 417fbfec03ed229be0bf9d89f5dc6b383b896d180066e4a9df5fd1a63d5cea77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e832f452909ad2589b99a10caf4cf50e2c02d75160f9ecd9a7470b5bd463bbc5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2007-01-14T19:14:02Z",
    "title_canon_sha256": "546fe5bddb3401db17d4048c8f8bd0954d42db6768817ad4754d7dc9f45f6485"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0701390",
    "kind": "arxiv",
    "version": 1
  }
}