Pith Number

pith:AQDSA5E7

pith:2017:AQDSA5E7SQV65ME7PWOFW6LQJR

not attested not anchored not stored refs pending

The index of coincidence for the binomial distribution is log-convex

Ioan Rasa

arxiv:1706.05178 v1 · 2017-06-16 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AQDSA5E7SQV65ME7PWOFW6LQJR}

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	2026-05-18T00:42:14.530900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

040720749f942beeb09f7d9c5b79704c6e951806262cd87408a429bb5d7308f0

Aliases

arxiv: 1706.05178 · arxiv_version: 1706.05178v1 · doi: 10.48550/arxiv.1706.05178 · pith_short_12: AQDSA5E7SQV6 · pith_short_16: AQDSA5E7SQV65ME7 · pith_short_8: AQDSA5E7

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/AQDSA5E7SQV65ME7PWOFW6LQJR \
  | 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: 040720749f942beeb09f7d9c5b79704c6e951806262cd87408a429bb5d7308f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39d9de4c0024f809853d8bcff76bdaf8de812781dcd5b2bc8c15494febfe0004",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-06-16T08:28:34Z",
    "title_canon_sha256": "7219de6098108cd13e288aafaee19cec70493488ca7765cd1b7733088ea43d89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.05178",
    "kind": "arxiv",
    "version": 1
  }
}