Pith Number

pith:TTMDKAFZ

pith:2008:TTMDKAFZC5UMKNVQXRCI5Z3AP6

not attested not anchored not stored refs pending

On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications

Bernard Bercu (IMB, Guy Fayolle (INRIA Rocquencourt), INRIA Bordeaux - Sud-Ouest), Peggy C\'enac (IMB)

arxiv:0812.3528 v1 · 2008-12-18 · 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{TTMDKAFZC5UMKNVQXRCI5Z3AP6}

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	2026-05-17T23:59:18.431687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cd83500b91768c536b0bc448ee7607fb9280cd9d31342af628379dcacdb2bef

Aliases

arxiv: 0812.3528 · arxiv_version: 0812.3528v1 · doi: 10.48550/arxiv.0812.3528 · pith_short_12: TTMDKAFZC5UM · pith_short_16: TTMDKAFZC5UMKNVQ · pith_short_8: TTMDKAFZ

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/TTMDKAFZC5UMKNVQXRCI5Z3AP6 \
  | 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: 9cd83500b91768c536b0bc448ee7607fb9280cd9d31342af628379dcacdb2bef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dced43d45b4cc1c08dacc146a63760d669300b86408e5a2c03f4320d9c9249cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-18T13:13:36Z",
    "title_canon_sha256": "2ad04e72bd5de3997d2070744c14c8819fdd265b556cb8f19869f1dbc7aa6bd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.3528",
    "kind": "arxiv",
    "version": 1
  }
}