Pith Number

pith:ADWVSFYP

pith:2010:ADWVSFYPHAO52G5UG2FSSVWXIO

not attested not anchored not stored refs pending

$L\log L$ condition for supercritical branching Hunt processes

Renming Song, Rong-Li Liu, Yan-Xia Ren

arxiv:1009.4481 v1 · 2010-09-22 · 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{ADWVSFYPHAO52G5UG2FSSVWXIO}

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	2026-05-18T04:40:30.378562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00ed59170f381ddd1bb4368b2956d743b7fb9f986de8f42fad3e4e3e7bdd5ce8

Aliases

arxiv: 1009.4481 · arxiv_version: 1009.4481v1 · doi: 10.48550/arxiv.1009.4481 · pith_short_12: ADWVSFYPHAO5 · pith_short_16: ADWVSFYPHAO52G5U · pith_short_8: ADWVSFYP

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/ADWVSFYPHAO52G5UG2FSSVWXIO \
  | 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: 00ed59170f381ddd1bb4368b2956d743b7fb9f986de8f42fad3e4e3e7bdd5ce8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1547c63f271e9a8a1ad5a5e59b533f96db36dc47959784a90043fa2bfc24a0e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-09-22T21:21:59Z",
    "title_canon_sha256": "e80ef1fd86dddf0da21073b57d2dd222d9be8a3023dba7025d6016ba00ba6162"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4481",
    "kind": "arxiv",
    "version": 1
  }
}