Pith Number

pith:P5KXUXAD

pith:2007:P5KXUXAD4Y5ANAMTELA4QXZSTD

not attested not anchored not stored refs pending

Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas

Jiang Zeng, Victor J. W. Guo

arxiv:0707.4328 v1 · 2007-07-30 · 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{P5KXUXAD4Y5ANAMTELA4QXZSTD}

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	2026-05-18T04:26:01.633857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f557a5c03e63a06819322c1c85f3298d7a4304aed2a5bfcd3107e3fadf17a37

Aliases

arxiv: 0707.4328 · arxiv_version: 0707.4328v1 · doi: 10.48550/arxiv.0707.4328 · pith_short_12: P5KXUXAD4Y5A · pith_short_16: P5KXUXAD4Y5ANAMT · pith_short_8: P5KXUXAD

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/P5KXUXAD4Y5ANAMTELA4QXZSTD \
  | 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: 7f557a5c03e63a06819322c1c85f3298d7a4304aed2a5bfcd3107e3fadf17a37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ade2afab2e1245d1aa5f0953cb28c17ad2e57338d2b7a1c461fb3ea93829f01d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-07-30T02:12:25Z",
    "title_canon_sha256": "796a46ed430beccacf3d95d6cd94c529b360b4bc9e7fd90e0a9278a9d17bbc8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.4328",
    "kind": "arxiv",
    "version": 1
  }
}