Pith Number

pith:UBDXTOL5

pith:2008:UBDXTOL5HFRGZ4HM6HH47HISPT

not attested not anchored not stored refs pending

Binomial coefficients and the ring of p-adic integers

Wei Zhang, Zhi-Wei Sun

arxiv:0812.3089 v5 · 2008-12-16 · 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{UBDXTOL5HFRGZ4HM6HH47HISPT}

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	2026-05-18T04:30:59.954514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a04779b97d39626cf0ecf1cfcf9d127cf725ea37d69c7ad64f285266e7f36359

Aliases

arxiv: 0812.3089 · arxiv_version: 0812.3089v5 · doi: 10.48550/arxiv.0812.3089 · pith_short_12: UBDXTOL5HFRG · pith_short_16: UBDXTOL5HFRGZ4HM · pith_short_8: UBDXTOL5

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/UBDXTOL5HFRGZ4HM6HH47HISPT \
  | 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: a04779b97d39626cf0ecf1cfcf9d127cf725ea37d69c7ad64f285266e7f36359

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aef61f4bb25b7a0749982c13b349b486cb7d23f9a827fcb54f5d78b88cc71cfc",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-12-16T16:02:40Z",
    "title_canon_sha256": "6c5a6487c7628519d10c51865d969ae18024ad3fe381248a373244a56ea68bf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.3089",
    "kind": "arxiv",
    "version": 5
  }
}