Pith Number

pith:2P3TKILQ

pith:2014:2P3TKILQKDD5PY25P6FJSQER4Z

not attested not anchored not stored refs pending

Some binomial sums involving absolute values

Helmut Prodinger, Hideyuki Ohtsuka, Judy-anne H. Osborn, Richard P. Brent

arxiv:1411.1477 v2 · 2014-11-06 · math.CO · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2P3TKILQKDD5PY25P6FJSQER4Z}

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	2026-05-18T01:13:45.020987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3f735217050c7d7e35d7f8a994091e66e2dc75d2462d075e7256b2aefd97cb8

Aliases

arxiv: 1411.1477 · arxiv_version: 1411.1477v2 · doi: 10.48550/arxiv.1411.1477 · pith_short_12: 2P3TKILQKDD5 · pith_short_16: 2P3TKILQKDD5PY25 · pith_short_8: 2P3TKILQ

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/2P3TKILQKDD5PY25P6FJSQER4Z \
  | 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: d3f735217050c7d7e35d7f8a994091e66e2dc75d2462d075e7256b2aefd97cb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85a989a3a12d0a16ab1ac493769fa47c7a39042e72a4ea2d4c6e79ad8c0714e7",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-11-06T02:41:45Z",
    "title_canon_sha256": "98c7ced5be051d1a3adc55207894944282c30875eb71e3d5711773c9e0bddc73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.1477",
    "kind": "arxiv",
    "version": 2
  }
}