Pith Number

pith:APQYWZ2A

pith:2012:APQYWZ2AIF2DIXD5BRUM45TEK6

not attested not anchored not stored refs pending

Biased random walk on critical Galton-Watson trees conditioned to survive

Alexander Fribergh, David A. Croydon, Takashi Kumagai

arxiv:1203.4078 v1 · 2012-03-19 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APQYWZ2AIF2DIXD5BRUM45TEK6}

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	2026-05-18T03:59:48.336819Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03e18b67404174345c7d0c68ce766457b418daceca67c98721f8b73948d8f4b6

Aliases

arxiv: 1203.4078 · arxiv_version: 1203.4078v1 · doi: 10.48550/arxiv.1203.4078 · pith_short_12: APQYWZ2AIF2D · pith_short_16: APQYWZ2AIF2DIXD5 · pith_short_8: APQYWZ2A

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/APQYWZ2AIF2DIXD5BRUM45TEK6 \
  | 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: 03e18b67404174345c7d0c68ce766457b418daceca67c98721f8b73948d8f4b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64ded187ffbb0c2503f0a54b4c9785373bb8fb80ed45cce672aab6b91321a35e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-19T11:08:07Z",
    "title_canon_sha256": "9ead6c4d85d20c1c796e671586e00fcb40975829ef0510a20c1a12aad5ccaee6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4078",
    "kind": "arxiv",
    "version": 1
  }
}