Pith Number

pith:IWAYH7KK

pith:2012:IWAYH7KKV4D3LPV6AZC6UVOAST

not attested not anchored not stored refs pending

First order transition for the branching random walk at the critical parameter

Thomas Madaule

arxiv:1206.3835 v5 · 2012-06-18 · 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{IWAYH7KKV4D3LPV6AZC6UVOAST}

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	2026-05-18T03:16:40.540528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

458183fd4aaf07b5bebe0645ea55c094e19acdc632e5cd03b279cd9a6a95b245

Aliases

arxiv: 1206.3835 · arxiv_version: 1206.3835v5 · doi: 10.48550/arxiv.1206.3835 · pith_short_12: IWAYH7KKV4D3 · pith_short_16: IWAYH7KKV4D3LPV6 · pith_short_8: IWAYH7KK

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/IWAYH7KKV4D3LPV6AZC6UVOAST \
  | 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: 458183fd4aaf07b5bebe0645ea55c094e19acdc632e5cd03b279cd9a6a95b245

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21c5edf56d4460fb6e169610fb25851e014583c7f88339e1ab07c1fa132fdf28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-18T06:06:40Z",
    "title_canon_sha256": "c1bb35b8b4406ef5619eecd3b7c702d6690b2e12b619010a7cdd1e99311acd83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3835",
    "kind": "arxiv",
    "version": 5
  }
}