Pith Number

pith:54BJ2I4N

pith:2013:54BJ2I4NPZH2S42MANZDY6RL3L

not attested not anchored not stored refs pending

Inequalities for binomial coefficients

Zhi-Hong Sun

arxiv:1310.0353 v2 · 2013-10-01 · 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{54BJ2I4NPZH2S42MANZDY6RL3L}

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	2026-05-18T03:11:12.289088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef029d238d7e4fa9734c03723c7a2bdad25b25bee7c133cfa07f63c7f7ce4ccc

Aliases

arxiv: 1310.0353 · arxiv_version: 1310.0353v2 · doi: 10.48550/arxiv.1310.0353 · pith_short_12: 54BJ2I4NPZH2 · pith_short_16: 54BJ2I4NPZH2S42M · pith_short_8: 54BJ2I4N

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/54BJ2I4NPZH2S42MANZDY6RL3L \
  | 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: ef029d238d7e4fa9734c03723c7a2bdad25b25bee7c133cfa07f63c7f7ce4ccc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cc5d30d02b12cde52587fb77fd5e1c1afcb174a619504aba3860860c5495579",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-10-01T15:42:45Z",
    "title_canon_sha256": "fc0167ddb8975915db602aaa1055017a873da28eec74ae91602122a300f848dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.0353",
    "kind": "arxiv",
    "version": 2
  }
}