Pith Number

pith:XQ3LJSJ3

pith:2025:XQ3LJSJ3UEX3IT7EGYVNPAWZAU

not attested not anchored not stored refs pending

Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$

Shen Lin, Xinxin Chen

arxiv:2512.24047 v2 · 2025-12-30 · 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{XQ3LJSJ3UEX3IT7EGYVNPAWZAU}

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	2026-07-27T01:19:53.978041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc36b4c93ba12fb44fe4362ad782d905176bf895a4d7bc2a6911af3927626d11

Aliases

arxiv: 2512.24047 · arxiv_version: 2512.24047v2 · doi: 10.48550/arxiv.2512.24047 · pith_short_12: XQ3LJSJ3UEX3 · pith_short_16: XQ3LJSJ3UEX3IT7E · pith_short_8: XQ3LJSJ3

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/XQ3LJSJ3UEX3IT7EGYVNPAWZAU \
  | 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: bc36b4c93ba12fb44fe4362ad782d905176bf895a4d7bc2a6911af3927626d11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b1b519db41b44031964921bb8da977ffd8178de79113860660d033d26e1167c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-12-30T07:44:41Z",
    "title_canon_sha256": "5a5642db996352bb7c53478063ae52d0b186a52c61f2673e27cbfb5710def21d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.24047",
    "kind": "arxiv",
    "version": 2
  }
}