Pith Number

pith:MGPO2AAU

pith:2013:MGPO2AAU6ZL7Z3U7JXVZ2GWOIY

not attested not anchored not stored refs pending

Central Limit Theorems for Stochastic Approximation with controlled Markov chain dynamics

Gersende Fort (LTCI)

arxiv:1309.3116 v1 · 2013-09-12 · 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{MGPO2AAU6ZL7Z3U7JXVZ2GWOIY}

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	2026-05-18T03:13:32.761321Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

619eed0014f657fcee9f4deb9d1ace460105622c0810dc10792e89d510ff88ff

Aliases

arxiv: 1309.3116 · arxiv_version: 1309.3116v1 · doi: 10.48550/arxiv.1309.3116 · pith_short_12: MGPO2AAU6ZL7 · pith_short_16: MGPO2AAU6ZL7Z3U7 · pith_short_8: MGPO2AAU

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/MGPO2AAU6ZL7Z3U7JXVZ2GWOIY \
  | 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: 619eed0014f657fcee9f4deb9d1ace460105622c0810dc10792e89d510ff88ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b649ece42acfe005a1fcf298b1ae9c08626efbcc06ea83f8f5825aec08158a97",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-09-12T11:27:24Z",
    "title_canon_sha256": "826adc875024f348bbd30f30da0bb824902897f16131193fedf53fae30b0a5e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3116",
    "kind": "arxiv",
    "version": 1
  }
}