Pith Number

pith:YFF4ZJS3

pith:2010:YFF4ZJS3B6O6BIJRYJBZKO76WX

not attested not anchored not stored refs pending

Some congruences involving binomial coefficients

Hui-Qin Cao, Zhi-Wei Sun

arxiv:1006.3069 v4 · 2010-06-15 · 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{YFF4ZJS3B6O6BIJRYJBZKO76WX}

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	2026-05-18T02:17:52.676449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c14bcca65b0f9de0a131c243953bfeb5fc5c28f99f56ecbbe8a60edf9130b308

Aliases

arxiv: 1006.3069 · arxiv_version: 1006.3069v4 · doi: 10.48550/arxiv.1006.3069 · pith_short_12: YFF4ZJS3B6O6 · pith_short_16: YFF4ZJS3B6O6BIJR · pith_short_8: YFF4ZJS3

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/YFF4ZJS3B6O6BIJRYJBZKO76WX \
  | 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: c14bcca65b0f9de0a131c243953bfeb5fc5c28f99f56ecbbe8a60edf9130b308

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d11b3e4206f389940898f4f4689e4774d5590c0c66d3bd3d51ccae03c51d7edc",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-06-15T19:59:20Z",
    "title_canon_sha256": "598ab06044b1a8f861c9aa9629111336d10864cdf6f3cac80f973c39d4b8dc0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3069",
    "kind": "arxiv",
    "version": 4
  }
}