Pith Number

pith:MNCUMMO2

pith:1999:MNCUMMO2IBGJ2QPDVDGQHVTL7V

not attested not anchored not stored refs pending

Hilbert schemes, wreath products, and the McKay correspondence

Weiqiang Wang

arxiv:math/9912104 v1 · 1999-12-13 · math.AG · hep-th · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MNCUMMO2IBGJ2QPDVDGQHVTL7V}

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	2026-07-04T14:41:31.686448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63454631da404c9d41e3a8cd03d66bfd776afedb6370547a78aa50433c5fb946

Aliases

arxiv: math/9912104 · arxiv_version: math/9912104v1 · doi: 10.48550/arxiv.math/9912104 · pith_short_12: MNCUMMO2IBGJ · pith_short_16: MNCUMMO2IBGJ2QPD · pith_short_8: MNCUMMO2

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/MNCUMMO2IBGJ2QPDVDGQHVTL7V \
  | 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: 63454631da404c9d41e3a8cd03d66bfd776afedb6370547a78aa50433c5fb946

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f6652901c900e1d96651fa9dff345568329fd88c88efba2b32f9a1669aa2f35",
    "cross_cats_sorted": [
      "hep-th",
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "1999-12-13T16:58:38Z",
    "title_canon_sha256": "2a9eab102e5b0da35e24183efdaa1cece9c0ca245c620dcd166f3972d6303184"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9912104",
    "kind": "arxiv",
    "version": 1
  }
}