Pith Number

pith:BYNRXJZ7

pith:2024:BYNRXJZ7SHQJKA4K4VYA7COC72

not attested not anchored not stored refs pending

An Extension of P\'{o}lya's Enumeration Theorem

Xiongfeng Zhan, Xueyi Huang

arxiv:2412.12508 v2 · 2024-12-17 · 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{BYNRXJZ7SHQJKA4K4VYA7COC72}

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	2026-07-05T10:13:45.651881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e1b1ba73f91e095038ae5700f89c2fe85ec183ff1d8b3e91683063f2aa7388d

Aliases

arxiv: 2412.12508 · arxiv_version: 2412.12508v2 · doi: 10.48550/arxiv.2412.12508 · pith_short_12: BYNRXJZ7SHQJ · pith_short_16: BYNRXJZ7SHQJKA4K · pith_short_8: BYNRXJZ7

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/BYNRXJZ7SHQJKA4K4VYA7COC72 \
  | 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: 0e1b1ba73f91e095038ae5700f89c2fe85ec183ff1d8b3e91683063f2aa7388d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b43b2749045eec0bed87e6c92487b91388ab9e7a6673b24f5654ae42a250d213",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-17T03:32:49Z",
    "title_canon_sha256": "1618cdf08d38966b0485b7a940b5d140c7102af0af8e248e8f1920a5eef50a6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.12508",
    "kind": "arxiv",
    "version": 2
  }
}