Pith Number

pith:7PWN77R4

pith:2000:7PWN77R4BIYGRCINIBLUF7JW3H

not attested not anchored not stored refs pending

Toda equations for Hurwitz numbers

Andrei Okounkov

arxiv:math/0004128 v1 · 2000-04-19 · math.AG · math-ph · math.CO · math.MP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7PWN77R4BIYGRCINIBLUF7JW3H}

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.

Cited by

1 paper in Pith

The String Dual to Two-dimensional Yang-Mills Theory Revisited

Receipt and verification

First computed	2026-07-04T14:34:28.338511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbecdffe3c0a3068890d405742fd36d9f60700667e4b3bc89e0b95b01198f266

Aliases

arxiv: math/0004128 · arxiv_version: math/0004128v1 · doi: 10.48550/arxiv.math/0004128 · pith_short_12: 7PWN77R4BIYG · pith_short_16: 7PWN77R4BIYGRCIN · pith_short_8: 7PWN77R4

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/7PWN77R4BIYGRCINIBLUF7JW3H \
  | 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: fbecdffe3c0a3068890d405742fd36d9f60700667e4b3bc89e0b95b01198f266

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6639a10acde2ad025d56cad2ad4981d991ba413100cbfc8b00ac9ed0dce89889",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP",
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-04-19T20:59:06Z",
    "title_canon_sha256": "dc3640864703a2d4346047e86b25f75e703ce796fe018d7fd4fb8e682dc331d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0004128",
    "kind": "arxiv",
    "version": 1
  }
}