Pith Number

pith:VY3DOXWC

pith:2016:VY3DOXWCJC7I4Q7CWPM46ZC75T

not attested not anchored not stored refs pending

New congruences involving products of two binomial coefficients

Guo-Shuai Mao, Zhi-Wei Sun

arxiv:1601.04782 v1 · 2016-01-19 · 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{VY3DOXWCJC7I4Q7CWPM46ZC75T}

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	2026-05-18T00:05:09.752552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae36375ec248be8e43e2b3d9cf645fecd44f1bc852a093731c2fcc8640ff9306

Aliases

arxiv: 1601.04782 · arxiv_version: 1601.04782v1 · doi: 10.48550/arxiv.1601.04782 · pith_short_12: VY3DOXWCJC7I · pith_short_16: VY3DOXWCJC7I4Q7C · pith_short_8: VY3DOXWC

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/VY3DOXWCJC7I4Q7CWPM46ZC75T \
  | 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: ae36375ec248be8e43e2b3d9cf645fecd44f1bc852a093731c2fcc8640ff9306

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33fab6f55b634cdb888b264d2a3de9cf3ac7af7af23a8b0195c2f53ec46b8f17",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-01-19T03:18:05Z",
    "title_canon_sha256": "034ec09b246ec7d16fed323e17ad25b1136b4ee1c98f6ebf54f7847c76f6d3b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.04782",
    "kind": "arxiv",
    "version": 1
  }
}