Pith Number

pith:ABDA6QSZ

pith:2011:ABDA6QSZ344ENPXR3QNBK6K2EP

not attested not anchored not stored refs pending

Markovian stochastic approximation with expanding projections

Christophe Andrieu, Matti Vihola

arxiv:1111.5421 v2 · 2011-11-23 · math.PR · stat.CO · stat.ME

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ABDA6QSZ344ENPXR3QNBK6K2EP}

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	2026-05-18T02:56:58.626009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00460f4259df3846bef1dc1a15795a23f622a83a3c4e895f957e3568214594fc

Aliases

arxiv: 1111.5421 · arxiv_version: 1111.5421v2 · doi: 10.48550/arxiv.1111.5421 · pith_short_12: ABDA6QSZ344E · pith_short_16: ABDA6QSZ344ENPXR · pith_short_8: ABDA6QSZ

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/ABDA6QSZ344ENPXR3QNBK6K2EP \
  | 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: 00460f4259df3846bef1dc1a15795a23f622a83a3c4e895f957e3568214594fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "483b27aaf64b3a40ae2f5ccb87d9aca783b0594cd99ac1350c12482856ec0574",
    "cross_cats_sorted": [
      "stat.CO",
      "stat.ME"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-23T07:31:58Z",
    "title_canon_sha256": "ebf693a8727e9cb29718eb8a0f1ae6f580c63d9dcd113a4ed219d4a1bb587d21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.5421",
    "kind": "arxiv",
    "version": 2
  }
}