Pith Number

pith:ZP3D3Q5E

pith:2018:ZP3D3Q5EF3N3Z745YJOXTLI7IK

not attested not anchored not stored refs pending

Limit theorems for the minimal position of a branching random walk in random environment

Wanting Hou, Wenming Hong, Xiaoyue Zhang

arxiv:1809.04245 v2 · 2018-09-12 · 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{ZP3D3Q5EF3N3Z745YJOXTLI7IK}

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	2026-05-18T00:05:40.750775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbf63dc3a42edbbcff9dc25d79ad1f42add5b13488df51e18e1b575f6b32fca1

Aliases

arxiv: 1809.04245 · arxiv_version: 1809.04245v2 · doi: 10.48550/arxiv.1809.04245 · pith_short_12: ZP3D3Q5EF3N3 · pith_short_16: ZP3D3Q5EF3N3Z745 · pith_short_8: ZP3D3Q5E

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/ZP3D3Q5EF3N3Z745YJOXTLI7IK \
  | 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: cbf63dc3a42edbbcff9dc25d79ad1f42add5b13488df51e18e1b575f6b32fca1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87d91f3c90a5ffd20ad7132f075a9ad99f0c9bd7ab21da10d97572b4b87030b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-09-12T03:21:10Z",
    "title_canon_sha256": "78a0f80ac104af416ffe1d7082e955a67282260a53d977eb61643d2c87866abc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.04245",
    "kind": "arxiv",
    "version": 2
  }
}