Pith Number

pith:GOFOKEM2

pith:2013:GOFOKEM2HCGQ2GDCAXG37U3XFV

not attested not anchored not stored refs pending

Wodzicki residue and minimal operators on a noncommutative 4-dimensional torus

Andrzej Sitarz

arxiv:1306.3705 v1 · 2013-06-16 · math.QA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GOFOKEM2HCGQ2GDCAXG37U3XFV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:14:29.446241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

338ae5119a388d0d186205cdbfd3772d53843ec155f0b61824b5cbb351901c44

Aliases

arxiv: 1306.3705 · arxiv_version: 1306.3705v1 · doi: 10.48550/arxiv.1306.3705 · pith_short_12: GOFOKEM2HCGQ · pith_short_16: GOFOKEM2HCGQ2GDC · pith_short_8: GOFOKEM2

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/GOFOKEM2HCGQ2GDCAXG37U3XFV \
  | 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: 338ae5119a388d0d186205cdbfd3772d53843ec155f0b61824b5cbb351901c44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67f4eedd37edbe0addca90884e303b5369b2ade847408b787536ce56ee73e15b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2013-06-16T21:08:17Z",
    "title_canon_sha256": "6a3551c47f4f63c88beac975028574fabedcb7852beb13a69c1147bbf8c92347"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3705",
    "kind": "arxiv",
    "version": 1
  }
}