Pith Number

pith:QJS3TKAJ

pith:1999:QJS3TKAJ5HRSWCMZMXCWYURTNY

not attested not anchored not stored refs pending

Asymptotics of Plancherel measures for symmetric groups

Alexei Borodin, Andrei Okounkov, Grigori Olshanski

arxiv:math/9905032 v2 · 1999-05-05 · math.CO · 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{QJS3TKAJ5HRSWCMZMXCWYURTNY}

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

Multicritical Scaling Limit of Shifted Schur Measure

Receipt and verification

First computed	2026-07-04T15:09:54.670733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8265b9a809e9e32b099965c56c52336e0fdb806258a0db56aff44da884899726

Aliases

arxiv: math/9905032 · arxiv_version: math/9905032v2 · doi: 10.48550/arxiv.math/9905032 · pith_short_12: QJS3TKAJ5HRS · pith_short_16: QJS3TKAJ5HRSWCMZ · pith_short_8: QJS3TKAJ

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/QJS3TKAJ5HRSWCMZMXCWYURTNY \
  | 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: 8265b9a809e9e32b099965c56c52336e0fdb806258a0db56aff44da884899726

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b22ee382c0b81562bfd276af9c64e315317a675c76724549a0d74d69696db4da",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1999-05-05T17:52:57Z",
    "title_canon_sha256": "6450c13df283709e42f02d6aefd0130e780532c536f801ffbc52415ec6c5057f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9905032",
    "kind": "arxiv",
    "version": 2
  }
}