Pith Number

pith:BSILOIOS

pith:2011:BSILOIOSH2YOVFQRQC5DNXMUP3

not attested not anchored not stored refs pending

Congruences involving $\binom{2k}k^2\binom{4k}{2k}m^{-k}$

Zhi-Hong Sun

arxiv:1104.3047 v2 · 2011-04-15 · 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{BSILOIOSH2YOVFQRQC5DNXMUP3}

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	2026-05-18T04:24:05.694988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c90b721d23eb0ea961180ba36dd947efd93adf412bd88de38b30b9bbbc600a4

Aliases

arxiv: 1104.3047 · arxiv_version: 1104.3047v2 · doi: 10.48550/arxiv.1104.3047 · pith_short_12: BSILOIOSH2YO · pith_short_16: BSILOIOSH2YOVFQR · pith_short_8: BSILOIOS

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/BSILOIOSH2YOVFQRQC5DNXMUP3 \
  | 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: 0c90b721d23eb0ea961180ba36dd947efd93adf412bd88de38b30b9bbbc600a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc7794e567818f425f83d1beda4aeefbbbac0561f7b40e21c5a36ad821d0b9ec",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-15T13:16:27Z",
    "title_canon_sha256": "412b0f6a2e97cc358b5853ad5747e908025d424fbf57d86360720e226095b967"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3047",
    "kind": "arxiv",
    "version": 2
  }
}