Pith Number

pith:4GBGWBFB

pith:2009:4GBGWBFBHHC65NNFQDLKJ6JX7B

not attested not anchored not stored refs pending

An involution for symmetry of hook length and part length of partitions

Heesung Shin, Jiang Zeng

arxiv:0907.4880 v2 · 2009-07-28 · 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{4GBGWBFBHHC65NNFQDLKJ6JX7B}

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	2026-07-05T04:06:38.567985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1826b04a139c5eeb5a580d6a4f937f8513ae2a64d6a09a1b80fdf6407c05b15

Aliases

arxiv: 0907.4880 · arxiv_version: 0907.4880v2 · doi: 10.48550/arxiv.0907.4880 · pith_short_12: 4GBGWBFBHHC6 · pith_short_16: 4GBGWBFBHHC65NNF · pith_short_8: 4GBGWBFB

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/4GBGWBFBHHC65NNFQDLKJ6JX7B \
  | 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: e1826b04a139c5eeb5a580d6a4f937f8513ae2a64d6a09a1b80fdf6407c05b15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5b46b2950d29a9c367c46a498c348ed3882303f7a1dee37be707de8b69590da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-07-28T10:20:52Z",
    "title_canon_sha256": "ab857f5a2fb1ecdca74f676e8f4c0d3635db66fd3cdaf892933837f0e2d434d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.4880",
    "kind": "arxiv",
    "version": 2
  }
}