Pith Number

pith:W4U7XB7X

pith:2009:W4U7XB7X4LEH3S5EYVWJNDOGH5

not attested not anchored not stored refs pending

$q$-exchangeability via quasi-invariance

Alexander Gnedin, Grigori Olshanski

arxiv:0907.3275 v2 · 2009-07-20 · math.PR · 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{W4U7XB7X4LEH3S5EYVWJNDOGH5}

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	2026-05-18T04:36:40.504754Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b729fb87f7e2c87dcba4c56c968dc63f7c06fed28df75b41aa26035bbb5598d0

Aliases

arxiv: 0907.3275 · arxiv_version: 0907.3275v2 · doi: 10.48550/arxiv.0907.3275 · pith_short_12: W4U7XB7X4LEH · pith_short_16: W4U7XB7X4LEH3S5E · pith_short_8: W4U7XB7X

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/W4U7XB7X4LEH3S5EYVWJNDOGH5 \
  | 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: b729fb87f7e2c87dcba4c56c968dc63f7c06fed28df75b41aa26035bbb5598d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e024fc511dcb513c2c33581cdb642fb73f4c58c3147bfccc40d3c47a42ef135c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-07-20T08:33:28Z",
    "title_canon_sha256": "bd2f4bed4899a5be0ba7133d195dfff0e8459f85781c0bdc10d4da5858167d96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.3275",
    "kind": "arxiv",
    "version": 2
  }
}