Pith Number

pith:VNKXCUC3

pith:2017:VNKXCUC3XMUZKGGHAFNSYY6J24

not attested not anchored not stored refs pending

Nearly Equal Distributions of the Rank and the Crank of Partitions

Kathy Q. Ji, Wenston J.T. Zang, William Y.C. Chen

arxiv:1704.00882 v1 · 2017-04-04 · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VNKXCUC3XMUZKGGHAFNSYY6J24}

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	2026-05-18T00:47:18.955308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab5571505bbb299518c7015b2c63c9d71d4cfd5aead48b403c8717744dd8ee29

Aliases

arxiv: 1704.00882 · arxiv_version: 1704.00882v1 · doi: 10.48550/arxiv.1704.00882 · pith_short_12: VNKXCUC3XMUZ · pith_short_16: VNKXCUC3XMUZKGGH · pith_short_8: VNKXCUC3

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/VNKXCUC3XMUZKGGHAFNSYY6J24 \
  | 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: ab5571505bbb299518c7015b2c63c9d71d4cfd5aead48b403c8717744dd8ee29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb74a75ffa5539092a38e9ba96d1ca8e18cd5707f6857536d4dab565d5731173",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-04-04T06:02:58Z",
    "title_canon_sha256": "bc9f2beeb4c9d66422eda02b66be32fd28de6e4611dadc0b7ec7502979f1bd19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.00882",
    "kind": "arxiv",
    "version": 1
  }
}