Pith Number

pith:ZO5U3SR7

pith:2026:ZO5U3SR7V5NBPVLE2AFO4HBSV7

not attested not anchored not stored refs pending

Binomial coefficients with divisors avoiding an interval

Alexandru Zaharescu, Hung M. Bui, Kyle Pratt

arxiv:2605.21221 v1 · 2026-05-20 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZO5U3SR7V5NBPVLE2AFO4HBSV7}

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	2026-05-21T01:05:44.170795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbbb4dca3faf5a17d564d00aee1c32afdd7798e05c422ba8cc3caac056401ece

Aliases

arxiv: 2605.21221 · arxiv_version: 2605.21221v1 · doi: 10.48550/arxiv.2605.21221 · pith_short_12: ZO5U3SR7V5NB · pith_short_16: ZO5U3SR7V5NBPVLE · pith_short_8: ZO5U3SR7

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/ZO5U3SR7V5NBPVLE2AFO4HBSV7 \
  | 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: cbbb4dca3faf5a17d564d00aee1c32afdd7798e05c422ba8cc3caac056401ece

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1282bdf7eece5e7d2616681cdf0da86e7b52f927079aecb20638ba31871698d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-20T14:14:12Z",
    "title_canon_sha256": "0ff70d86b5803f29c537aa723ab282e330482f2f4d19a009a8b50252eecc3d5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21221",
    "kind": "arxiv",
    "version": 1
  }
}