Pith Number

pith:ZVLG4C5P

pith:2010:ZVLG4C5P372TJ5YWG2SVFWP4XE

not attested not anchored not stored refs pending

Convergence rates for a branching process in a random environment

Chunmao Huang, Quansheng Liu

arxiv:1010.6111 v2 · 2010-10-28 · 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{ZVLG4C5P372TJ5YWG2SVFWP4XE}

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	2026-05-18T03:33:26.864877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd566e0bafdff534f71636a552d9fcb9349fcb42cb5fc6adb6fe1057f0b9f55d

Aliases

arxiv: 1010.6111 · arxiv_version: 1010.6111v2 · doi: 10.48550/arxiv.1010.6111 · pith_short_12: ZVLG4C5P372T · pith_short_16: ZVLG4C5P372TJ5YW · pith_short_8: ZVLG4C5P

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/ZVLG4C5P372TJ5YWG2SVFWP4XE \
  | 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: cd566e0bafdff534f71636a552d9fcb9349fcb42cb5fc6adb6fe1057f0b9f55d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79c0ac0c60e4fe45fda58d133a59976e226f19294da99fc20a97125c14722f53",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-10-28T23:37:45Z",
    "title_canon_sha256": "9146c0f6dacfe7a3f1ef8e8806d279beb586b8d2143594de5a79ee381481077f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.6111",
    "kind": "arxiv",
    "version": 2
  }
}