Pith Number

pith:PW7IKLZA

pith:2012:PW7IKLZAPVKHYEY6KIH2ED3EL2

not attested not anchored not stored refs pending

Recursion Formulas for Spin Hurwitz Numbers

Junho Lee, Thomas H. Parker

arxiv:1212.1825 v2 · 2012-12-08 · math.SG · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PW7IKLZAPVKHYEY6KIH2ED3EL2}

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	2026-05-18T03:38:45.666500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dbe852f207d547c131e520fa20f645eb8ef1434b8bdca3f0e0e74eaf38c6c93

Aliases

arxiv: 1212.1825 · arxiv_version: 1212.1825v2 · doi: 10.48550/arxiv.1212.1825 · pith_short_12: PW7IKLZAPVKH · pith_short_16: PW7IKLZAPVKHYEY6 · pith_short_8: PW7IKLZA

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/PW7IKLZAPVKHYEY6KIH2ED3EL2 \
  | 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: 7dbe852f207d547c131e520fa20f645eb8ef1434b8bdca3f0e0e74eaf38c6c93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8333f62d236314699ff199a06e40876e6c985ec95855afe5b0bcc5215274381e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2012-12-08T18:39:59Z",
    "title_canon_sha256": "8da3ecdf78101101522be2945f42f19511d7f08929aee278f5023558c5e46e92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1825",
    "kind": "arxiv",
    "version": 2
  }
}