Pith Number

pith:QLO4GZUB

pith:2009:QLO4GZUBSFLLUIHXJZ63B2FPPG

not attested not anchored not stored refs pending

On 2-adic orders of some binomial sums

Hao Pan, Zhi-Wei Sun

arxiv:0909.4945 v3 · 2009-09-27 · math.CO · 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{QLO4GZUBSFLLUIHXJZ63B2FPPG}

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	2026-05-18T04:41:36.791347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82ddc366819156ba20f74e7db0e8af79b710cc7f81860711a951bbadcae7d6cc

Aliases

arxiv: 0909.4945 · arxiv_version: 0909.4945v3 · doi: 10.48550/arxiv.0909.4945 · pith_short_12: QLO4GZUBSFLL · pith_short_16: QLO4GZUBSFLLUIHX · pith_short_8: QLO4GZUB

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/QLO4GZUBSFLLUIHXJZ63B2FPPG \
  | 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: 82ddc366819156ba20f74e7db0e8af79b710cc7f81860711a951bbadcae7d6cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d70cf9682d4f2ce10b770af9c69adc51a7b13330cca1bfcfe389a39dd99295c",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-09-27T16:53:44Z",
    "title_canon_sha256": "8f26ef61abf05a477407d0c18721d7df059337aa4bd19ee19da2b7f561312674"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4945",
    "kind": "arxiv",
    "version": 3
  }
}