Pith Number

pith:3NOHSQZV

pith:2011:3NOHSQZV6TVUSZT7JV3FZKHEWE

not attested not anchored not stored refs pending

Congruences involving $\binom{4k}{2k}$ and $\binom{3k}k$

Zhi-Hong Sun

arxiv:1108.4840 v1 · 2011-08-24 · 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{3NOHSQZV6TVUSZT7JV3FZKHEWE}

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	2026-05-18T04:14:46.681823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db5c794335f4eb49667f4d765ca8e4b10cc9af1844b5ac29eab153b29dbcf915

Aliases

arxiv: 1108.4840 · arxiv_version: 1108.4840v1 · doi: 10.48550/arxiv.1108.4840 · pith_short_12: 3NOHSQZV6TVU · pith_short_16: 3NOHSQZV6TVUSZT7 · pith_short_8: 3NOHSQZV

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/3NOHSQZV6TVUSZT7JV3FZKHEWE \
  | 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: db5c794335f4eb49667f4d765ca8e4b10cc9af1844b5ac29eab153b29dbcf915

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87f815efdcf17a08d81ee20f7308a1485ffa3912919a7ea0bde793f4eed80632",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-24T13:47:04Z",
    "title_canon_sha256": "8d337bc93e67bb4d23a43411b0307bb6d2f99cc656c7f4076d9fe84c4123df2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4840",
    "kind": "arxiv",
    "version": 1
  }
}