Pith Number

pith:GCELXB4X

pith:2010:GCELXB4XJOVOWS64PHRGUADOIB

not attested not anchored not stored refs pending

Trajectory averaging for stochastic approximation MCMC algorithms

Faming Liang

arxiv:1011.2587 v1 · 2010-11-11 · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GCELXB4XJOVOWS64PHRGUADOIB}

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	2026-05-18T04:36:09.979875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3088bb87974baaeb4bdc79e26a006e4053b01f76044ad66d34d538db39cfb2cb

Aliases

arxiv: 1011.2587 · arxiv_version: 1011.2587v1 · doi: 10.48550/arxiv.1011.2587 · pith_short_12: GCELXB4XJOVO · pith_short_16: GCELXB4XJOVOWS64 · pith_short_8: GCELXB4X

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/GCELXB4XJOVOWS64PHRGUADOIB \
  | 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: 3088bb87974baaeb4bdc79e26a006e4053b01f76044ad66d34d538db39cfb2cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f10df2b0f311213c8fee53d54564fb1d805098ecf8b2d685101c2dbf285fb38d",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2010-11-11T07:40:28Z",
    "title_canon_sha256": "d08b8c1dd9fe821c2581dd2446467bd30357b69dd5f0011573b23955b12eba5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2587",
    "kind": "arxiv",
    "version": 1
  }
}