Pith Number

pith:IPUMJYBZ

pith:2012:IPUMJYBZTDHJNPRANQQOCWEKG2

not attested not anchored not stored refs pending

On the Maximal Displacement of a Critical Branching Random Walk

Steven P. Lalley, Yuan Shao

arxiv:1212.2933 v2 · 2012-12-12 · 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{IPUMJYBZTDHJNPRANQQOCWEKG2}

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	2026-05-18T02:55:20.664942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43e8c4e03998ce96be206c20e1588a36b14f8925f4442ab16e60457aeffb3b28

Aliases

arxiv: 1212.2933 · arxiv_version: 1212.2933v2 · doi: 10.48550/arxiv.1212.2933 · pith_short_12: IPUMJYBZTDHJ · pith_short_16: IPUMJYBZTDHJNPRA · pith_short_8: IPUMJYBZ

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/IPUMJYBZTDHJNPRANQQOCWEKG2 \
  | 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: 43e8c4e03998ce96be206c20e1588a36b14f8925f4442ab16e60457aeffb3b28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c46745047536b6d29f3bc84e02c9fbd94f5a6b6c6aa751658b352eb7d26b5dc3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-12T19:08:44Z",
    "title_canon_sha256": "8373b984725dbc9212f55d067d8f09377d3ea562885859400533f9495c310f4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2933",
    "kind": "arxiv",
    "version": 2
  }
}