Pith Number

pith:7GL3QROV

pith:2001:7GL3QROVEZ22PUYYBLK4DM27BV

not attested not anchored not stored refs pending

Unification of independence in quantum probability

Romuald Lenczewski

arxiv:math/0103031 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{7GL3QROVEZ22PUYYBLK4DM27BV}

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	2026-05-18T02:46:38.161831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f997b845d52675a7d3180ad5c1b35f0d65e33073765cd646eed26b0288fdfcd2

Aliases

arxiv: math/0103031 · arxiv_version: math/0103031v1 · doi: 10.48550/arxiv.math/0103031 · pith_short_12: 7GL3QROVEZ22 · pith_short_16: 7GL3QROVEZ22PUYY · pith_short_8: 7GL3QROV

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/7GL3QROVEZ22PUYYBLK4DM27BV \
  | 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: f997b845d52675a7d3180ad5c1b35f0d65e33073765cd646eed26b0288fdfcd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b27e312ff1fda007f5f2bb3fad137ce39a4325c058d2418575f7952c0f7a4be",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2001-03-06T10:24:19Z",
    "title_canon_sha256": "6e9480baa1a70e86addbbb998e12b08572d465b4fa02ade17ee3b6849c97c283"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0103031",
    "kind": "arxiv",
    "version": 1
  }
}