Pith Number

pith:BCNVI26R

pith:2013:BCNVI26RX3TY5B7XHXOEB3OQYG

not attested not anchored not stored refs pending

Proof of two divisibility properties of binomial coefficients conjectured by Z.-W. Sun

Victor J. W. Guo

arxiv:1312.7548 v2 · 2013-12-29 · 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{BCNVI26RX3TY5B7XHXOEB3OQYG}

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	2026-05-18T03:03:31.352475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

089b546bd1bee78e87f73ddc40edd0c19b471561fa0c6903b770c549454a10a6

Aliases

arxiv: 1312.7548 · arxiv_version: 1312.7548v2 · doi: 10.48550/arxiv.1312.7548 · pith_short_12: BCNVI26RX3TY · pith_short_16: BCNVI26RX3TY5B7X · pith_short_8: BCNVI26R

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/BCNVI26RX3TY5B7XHXOEB3OQYG \
  | 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: 089b546bd1bee78e87f73ddc40edd0c19b471561fa0c6903b770c549454a10a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b33f5127fbdd871bf32db5138a63ee502f2d1209598d0a544a3e997ee305fd0e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-29T15:18:41Z",
    "title_canon_sha256": "f1748b41a7ec45f0d1d05ad0a402a9d84381a5ecb17fef0c46ff370f20e49f9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7548",
    "kind": "arxiv",
    "version": 2
  }
}