Pith Number

pith:XZ4EEJCO

pith:2010:XZ4EEJCOT3ECPTLXDNI7FU3VWO

not attested not anchored not stored refs pending

Bounding Standard Gaussian Tail Probabilities

Lutz Duembgen

arxiv:1012.2063 v3 · 2010-12-09 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZ4EEJCOT3ECPTLXDNI7FU3VWO}

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.

Cited by

1 paper in Pith

Strengthened inequalities for the mean width and the $\ell$-norm

Receipt and verification

First computed	2026-05-18T04:32:55.534969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be7842244e9ec827cd771b51f2d375b3a41968a117765f954320b8b92be73ece

Aliases

arxiv: 1012.2063 · arxiv_version: 1012.2063v3 · doi: 10.48550/arxiv.1012.2063 · pith_short_12: XZ4EEJCOT3EC · pith_short_16: XZ4EEJCOT3ECPTLX · pith_short_8: XZ4EEJCO

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/XZ4EEJCOT3ECPTLXDNI7FU3VWO \
  | 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: be7842244e9ec827cd771b51f2d375b3a41968a117765f954320b8b92be73ece

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe8dceef8a26ee12ac3e5a7c2bdb27496ee30d31689ea998ca4bb581f2489041",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2010-12-09T18:02:46Z",
    "title_canon_sha256": "982d5e96c6a9dbe0dd231247b782bdfd1862f937f31dba711700836bb64f3f95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2063",
    "kind": "arxiv",
    "version": 3
  }
}