Pith Number

pith:WDBJYSKG

pith:2013:WDBJYSKGNAHMKWXNALBJEEZNZF

not attested not anchored not stored refs pending

Cubic congruences and sums involving $\binom{3k}k$

Zhi-Hong Sun

arxiv:1310.6721 v7 · 2013-10-24 · 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{WDBJYSKGNAHMKWXNALBJEEZNZF}

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	2026-05-18T03:06:42.594958Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0c29c4946680ec55aed02c292132dc96d4d15983a73e1d67671174fa6fe8ba3

Aliases

arxiv: 1310.6721 · arxiv_version: 1310.6721v7 · doi: 10.48550/arxiv.1310.6721 · pith_short_12: WDBJYSKGNAHM · pith_short_16: WDBJYSKGNAHMKWXN · pith_short_8: WDBJYSKG

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/WDBJYSKGNAHMKWXNALBJEEZNZF \
  | 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: b0c29c4946680ec55aed02c292132dc96d4d15983a73e1d67671174fa6fe8ba3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dec4c2c55f06cec058dc7280235efaa5cf578ec1bb2b5ee0e91ff056b2dcc1d5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-10-24T19:36:53Z",
    "title_canon_sha256": "2b353820da0bdb3e5b6bf8ffcad4b345f0c2b1839b99abf27e1a748cc5c6387d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6721",
    "kind": "arxiv",
    "version": 7
  }
}