Pith Number

pith:AQNMX3HE

pith:2011:AQNMX3HEAIYQ573HEZHJTF5VM2

not attested not anchored not stored refs pending

Hoeffding's inequality for supermartingales

Ion Grama, Quansheng Liu, Xiequan Fan

arxiv:1109.4359 v5 · 2011-09-20 · 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{AQNMX3HEAIYQ573HEZHJTF5VM2}

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	2026-05-18T03:06:52.103131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

041acbece402310eff67264e9997b566a38dc64e1bd3395da156cf4e7253aa38

Aliases

arxiv: 1109.4359 · arxiv_version: 1109.4359v5 · doi: 10.48550/arxiv.1109.4359 · pith_short_12: AQNMX3HEAIYQ · pith_short_16: AQNMX3HEAIYQ573H · pith_short_8: AQNMX3HE

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/AQNMX3HEAIYQ573HEZHJTF5VM2 \
  | 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: 041acbece402310eff67264e9997b566a38dc64e1bd3395da156cf4e7253aa38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58187864c31bf5e6f6a44f3a257acff8b3bff31476c942f1515a0b169a1ae90c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-20T17:03:45Z",
    "title_canon_sha256": "4bed6660dcab96ab01ca131535bafbec21e48b84c1b64218a5b9058d34002d2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4359",
    "kind": "arxiv",
    "version": 5
  }
}