Pith Number

pith:ZB57FUZR

pith:2016:ZB57FUZRF4QJZAZFZAKUD3KMMP

not attested not anchored not stored refs pending

An explicit generating function arising in counting binomial coefficients divisible by powers of primes

Lukas Spiegelhofer, Michael Wallner

arxiv:1604.07089 v5 · 2016-04-24 · 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{ZB57FUZRF4QJZAZFZAKUD3KMMP}

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	2026-05-18T00:31:05.520301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c87bf2d3312f209c8325c81541ed4c63edae78a02ca025cdc68cde51ea440d3b

Aliases

arxiv: 1604.07089 · arxiv_version: 1604.07089v5 · doi: 10.48550/arxiv.1604.07089 · pith_short_12: ZB57FUZRF4QJ · pith_short_16: ZB57FUZRF4QJZAZF · pith_short_8: ZB57FUZR

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/ZB57FUZRF4QJZAZFZAKUD3KMMP \
  | 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: c87bf2d3312f209c8325c81541ed4c63edae78a02ca025cdc68cde51ea440d3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e068e027583de911a8cd483f57720908905897b42cfa9a1e3a64b3946d20693e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-04-24T22:33:46Z",
    "title_canon_sha256": "8b79a345fbe6569898630b5349370eac42168aa0091f01450aa7b347b5adf31e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.07089",
    "kind": "arxiv",
    "version": 5
  }
}