Pith Number

pith:MUKWYQXH

pith:2009:MUKWYQXHEZDCJPXBOAB4YRFFFU

not attested not anchored not stored refs pending

Fixed points of commutative L\"uders operations

Liu Weihua, Wu Junde

arxiv:0908.2475 v6 · 2009-08-18 · math.OA · math-ph · math.MP · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MUKWYQXHEZDCJPXBOAB4YRFFFU}

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	2026-05-18T01:03:54.004595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65156c42e7264624bee17003cc44a52d127da891c3db8d1a396d94d1c60b6b22

Aliases

arxiv: 0908.2475 · arxiv_version: 0908.2475v6 · doi: 10.48550/arxiv.0908.2475 · pith_short_12: MUKWYQXHEZDC · pith_short_16: MUKWYQXHEZDCJPXB · pith_short_8: MUKWYQXH

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/MUKWYQXHEZDCJPXBOAB4YRFFFU \
  | 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: 65156c42e7264624bee17003cc44a52d127da891c3db8d1a396d94d1c60b6b22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "848c11fb69c53406bf59a712f9d1b11bcac71c33a91470af46c722ce748bd811",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-08-18T01:34:27Z",
    "title_canon_sha256": "3a4216efad3aa5e4bd45b87b2ccc1eaddec8189c7d3e099bb6b92b4c6acaaf10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.2475",
    "kind": "arxiv",
    "version": 6
  }
}