Pith Number

pith:KCDEB4LK

pith:2010:KCDEB4LKPJON6Z3XU5NGNBE77F

not attested not anchored not stored refs pending

The number of nonzero binomial coefficients modulo p^alpha

Eric Rowland

arxiv:1001.1783 v3 · 2010-01-12 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KCDEB4LKPJON6Z3XU5NGNBE77F}

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	2026-05-18T04:06:33.452033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

508640f16a7a5cdf6777a75a66849ff96cadb11254cf172afa3046930b0df631

Aliases

arxiv: 1001.1783 · arxiv_version: 1001.1783v3 · doi: 10.48550/arxiv.1001.1783 · pith_short_12: KCDEB4LKPJON · pith_short_16: KCDEB4LKPJON6Z3X · pith_short_8: KCDEB4LK

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/KCDEB4LKPJON6Z3XU5NGNBE77F \
  | 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: 508640f16a7a5cdf6777a75a66849ff96cadb11254cf172afa3046930b0df631

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33b37ce79319922c6269793a76195027b03ca8d203832815f93a352d77adc524",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-01-12T02:49:44Z",
    "title_canon_sha256": "567f41af039a7018919ac77ccef8a0d17b05326bb241bca1768a28de2b784f8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1783",
    "kind": "arxiv",
    "version": 3
  }
}