Pith Number

pith:ZTX6VEKU

pith:2013:ZTX6VEKUZTZUE3YNU5KDYSAGFU

not attested not anchored not stored refs pending

Central Limit Theorems for Supercritical Branching Markov Processes

R. Song, R. Zhang, Y.-X. Ren

arxiv:1305.0610 v1 · 2013-05-03 · 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{ZTX6VEKUZTZUE3YNU5KDYSAGFU}

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	2026-05-18T03:26:33.214311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccefea9154ccf3426f0da7543c48062d3936b5d1aebf6609406b5c6cf438847c

Aliases

arxiv: 1305.0610 · arxiv_version: 1305.0610v1 · doi: 10.48550/arxiv.1305.0610 · pith_short_12: ZTX6VEKUZTZU · pith_short_16: ZTX6VEKUZTZUE3YN · pith_short_8: ZTX6VEKU

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/ZTX6VEKUZTZUE3YNU5KDYSAGFU \
  | 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: ccefea9154ccf3426f0da7543c48062d3936b5d1aebf6609406b5c6cf438847c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a24e69ef3b6a0b9696ad22d550b66dd504101ca6e9da8d7a94338532686f4a65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-05-03T02:22:45Z",
    "title_canon_sha256": "9bbbc532db4377d56bf6444796f97d06db06d4a6eb148926f57312a4efa23753"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.0610",
    "kind": "arxiv",
    "version": 1
  }
}