Pith Number

pith:4V74OHNZ

pith:2011:4V74OHNZ7ORXNAAZ3UVPHWQFQB

not attested not anchored not stored refs pending

On Refined Versions of the Azuma-Hoeffding Inequality with Applications in Information Theory

Igal Sason

arxiv:1111.1977 v9 · 2011-11-08 · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4V74OHNZ7ORXNAAZ3UVPHWQFQB}

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	2026-05-18T03:31:07.001529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e57fc71db9fba3768019dd2af3da05804e08d8304edb2743746803de9741f1a0

Aliases

arxiv: 1111.1977 · arxiv_version: 1111.1977v9 · doi: 10.48550/arxiv.1111.1977 · pith_short_12: 4V74OHNZ7ORX · pith_short_16: 4V74OHNZ7ORXNAAZ · pith_short_8: 4V74OHNZ

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/4V74OHNZ7ORXNAAZ3UVPHWQFQB \
  | 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: e57fc71db9fba3768019dd2af3da05804e08d8304edb2743746803de9741f1a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02e1b0d0dece461b597793d606656bb2283fa595bcda7630c571f959444bef01",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2011-11-08T17:13:55Z",
    "title_canon_sha256": "f731dc49a91f6de4d4587a1fb186540efce3c7b2e74c842aa21eb61b61566557"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1977",
    "kind": "arxiv",
    "version": 9
  }
}