Pith Number

pith:MBPGJTHC

pith:2014:MBPGJTHCCBTJBTPNQMIMBJSY6Y

not attested not anchored not stored refs pending

Martingale inequalities of type Dzhaparidze and van Zanten

Ion Grama, Quansheng Liu, Xiequan Fan

arxiv:1404.4776 v2 · 2014-04-18 · 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{MBPGJTHCCBTJBTPNQMIMBJSY6Y}

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	2026-05-18T00:38:46.960858Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

605e64cce2106690cded8310c0a658f6008ce70478e318367aca5423b5a970f2

Aliases

arxiv: 1404.4776 · arxiv_version: 1404.4776v2 · doi: 10.48550/arxiv.1404.4776 · pith_short_12: MBPGJTHCCBTJ · pith_short_16: MBPGJTHCCBTJBTPN · pith_short_8: MBPGJTHC

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/MBPGJTHCCBTJBTPNQMIMBJSY6Y \
  | 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: 605e64cce2106690cded8310c0a658f6008ce70478e318367aca5423b5a970f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66dd7d0fb8d92bcd9f3e5c0692b3172762609ce9128a5e437505ce180f2065fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-04-18T12:55:25Z",
    "title_canon_sha256": "73b1f0a581374ea13193ec36ec70123f5d9571451ed1b9a1226e2ee6919ff88a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.4776",
    "kind": "arxiv",
    "version": 2
  }
}