Pith Number

pith:YXGJRNLX

pith:2001:YXGJRNLXQUBPVYD5K5S3PBQM2I

not attested not anchored not stored refs pending

Multiple noncommutative tori and Hopf algebras

Andrzej Sitarz, Mario Paschke, Markus Debert

arxiv:math-ph/0103034 v2 · 2001-03-25 · math-ph · math.MP · math.QA · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YXGJRNLXQUBPVYD5K5S3PBQM2I}

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	2026-05-18T00:14:23.517385Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5cc98b5778502fae07d5765b7860cd23ef164e1e4b7e03879e67efbdf6a9378

Aliases

arxiv: math-ph/0103034 · arxiv_version: math-ph/0103034v2 · doi: 10.48550/arxiv.math-ph/0103034 · pith_short_12: YXGJRNLXQUBP · pith_short_16: YXGJRNLXQUBPVYD5 · pith_short_8: YXGJRNLX

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/YXGJRNLXQUBPVYD5K5S3PBQM2I \
  | 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: c5cc98b5778502fae07d5765b7860cd23ef164e1e4b7e03879e67efbdf6a9378

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1d78f88573074b12afc88086af742cc2b3e568f805879ec2a507a1a3d941618",
    "cross_cats_sorted": [
      "math.MP",
      "math.QA",
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2001-03-25T16:46:30Z",
    "title_canon_sha256": "58ffe3b5a60335bc83f9a372dfb81013b316c18499e410b003111c141083bf60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0103034",
    "kind": "arxiv",
    "version": 2
  }
}