Pith Number

pith:LQAGRCN5

pith:2011:LQAGRCN5OSK5ZHTXO7WGPNST2D

not attested not anchored not stored refs pending

Almost Sure Invariance Principles via Martingale Approximation

Costel Peligrad, Florence Merlev\`ede, Magda Peligrad

arxiv:1103.6266 v2 · 2011-03-31 · 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{LQAGRCN5OSK5ZHTXO7WGPNST2D}

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	2026-05-18T04:23:02.175282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c006889bd7495dc9e7777ec67b653d0d947f00ed7abea6d2b9a8b63fb023bae

Aliases

arxiv: 1103.6266 · arxiv_version: 1103.6266v2 · doi: 10.48550/arxiv.1103.6266 · pith_short_12: LQAGRCN5OSK5 · pith_short_16: LQAGRCN5OSK5ZHTX · pith_short_8: LQAGRCN5

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/LQAGRCN5OSK5ZHTXO7WGPNST2D \
  | 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: 5c006889bd7495dc9e7777ec67b653d0d947f00ed7abea6d2b9a8b63fb023bae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7b2fe56387d02c3db0176c1094e33103c22dfa65ea615804904ebe810b8b0ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-31T18:45:03Z",
    "title_canon_sha256": "2d59bcf24bef7c3ca051e40b2398021f64f853925148476a6c59d319a6ab38c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.6266",
    "kind": "arxiv",
    "version": 2
  }
}