Pith Number

pith:WC6TQQTH

pith:2001:WC6TQQTHVGUZWJFQA7VX2GFVJQ

not attested not anchored not stored refs pending

Limit theorems for the hierarchy of freeness

Romuald Lenczewski, Uwe Franz

arxiv:math/0103032 v1 · 2001-03-06 · math.QA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WC6TQQTHVGUZWJFQA7VX2GFVJQ}

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	2026-05-18T02:46:38.154760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0bd384267a9a99b24b007eb7d18b54c16ef087c9c0406b6f888300bb4a97c6b

Aliases

arxiv: math/0103032 · arxiv_version: math/0103032v1 · doi: 10.48550/arxiv.math/0103032 · pith_short_12: WC6TQQTHVGUZ · pith_short_16: WC6TQQTHVGUZWJFQ · pith_short_8: WC6TQQTH

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/WC6TQQTHVGUZWJFQA7VX2GFVJQ \
  | 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: b0bd384267a9a99b24b007eb7d18b54c16ef087c9c0406b6f888300bb4a97c6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4430557b4d7fd93ac3d1a36628936f5d0571215293cb50b463940865f4b3267c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2001-03-06T10:29:31Z",
    "title_canon_sha256": "6dfbe354d46200fca236b35c91148ffd4fd1e95ed6997c4e34b9c3de4fb131bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0103032",
    "kind": "arxiv",
    "version": 1
  }
}