Pith Number

pith:WLL5OKL5

pith:2005:WLL5OKL5NK3O2ETOYHPPDIVNZ2

not attested not anchored not stored refs pending

Symmetry of Quantum Torus with Crossed Product Algebra

Ee Chang-Young, Hoil Kim

arxiv:math-ph/0501007 v4 · 2005-01-04 · math-ph · hep-th · 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{WLL5OKL5NK3O2ETOYHPPDIVNZ2}

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	2026-05-18T01:05:30.177371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2d7d7297d6ab6ed126ec1def1a2adceb9c50d3505f49c895d4d5d4a62f58951

Aliases

arxiv: math-ph/0501007 · arxiv_version: math-ph/0501007v4 · doi: 10.48550/arxiv.math-ph/0501007 · pith_short_12: WLL5OKL5NK3O · pith_short_16: WLL5OKL5NK3O2ETO · pith_short_8: WLL5OKL5

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/WLL5OKL5NK3O2ETOYHPPDIVNZ2 \
  | 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: b2d7d7297d6ab6ed126ec1def1a2adceb9c50d3505f49c895d4d5d4a62f58951

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3395641d1656c512b6cbc7a40518205af86400ab5807d2e4be21c2ff17dab556",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-01-04T09:19:52Z",
    "title_canon_sha256": "d9b479b839a64742e861c503289dc236c3889e680e17bc8630496966438f4a95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0501007",
    "kind": "arxiv",
    "version": 4
  }
}