Pith Number

pith:6FGCRDLQ

pith:2020:6FGCRDLQREYYMEFEXE76M5ZK53

not attested not anchored not stored refs pending

On the probability that a binomial variable is at most its expectation

Svante Janson

arxiv:2009.13781 v2 · 2020-09-29 · 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{6FGCRDLQREYYMEFEXE76M5ZK53}

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	2026-07-05T01:43:59.355635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f14c288d7089318610a4b93fe6772aeee30f8ac64bcd04c4494ee8b65068b153

Aliases

arxiv: 2009.13781 · arxiv_version: 2009.13781v2 · doi: 10.48550/arxiv.2009.13781 · pith_short_12: 6FGCRDLQREYY · pith_short_16: 6FGCRDLQREYYMEFE · pith_short_8: 6FGCRDLQ

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/6FGCRDLQREYYMEFEXE76M5ZK53 \
  | 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: f14c288d7089318610a4b93fe6772aeee30f8ac64bcd04c4494ee8b65068b153

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93b4db25bafda93a27d6ce84d6421a6734d380ffc9150e78acd4c1f0bb470155",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-09-29T05:07:50Z",
    "title_canon_sha256": "4d1af5448f65381ed01634a570996e41c8dce32054a4a5fe82dd0f7f918a7870"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.13781",
    "kind": "arxiv",
    "version": 2
  }
}