Pith Number

pith:6LR2QKZU

pith:2010:6LR2QKZUOVSW2XQVSQ6YMSUDFM

not attested not anchored not stored refs pending

Joint torsion of several commuting operators

Jens Kaad

arxiv:1011.0356 v2 · 2010-11-01 · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6LR2QKZUOVSW2XQVSQ6YMSUDFM}

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	2026-05-18T04:34:36.685617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2e3a82b3475656d5e15943d864a832b2b7c4ed9716236579fc736e75ded7c5f

Aliases

arxiv: 1011.0356 · arxiv_version: 1011.0356v2 · doi: 10.48550/arxiv.1011.0356 · pith_short_12: 6LR2QKZUOVSW · pith_short_16: 6LR2QKZUOVSW2XQV · pith_short_8: 6LR2QKZU

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/6LR2QKZUOVSW2XQVSQ6YMSUDFM \
  | 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: f2e3a82b3475656d5e15943d864a832b2b7c4ed9716236579fc736e75ded7c5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4939586f5315c26eaec3e2f8747bf2a920cd3297162705ed1e95cecd0147e62a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2010-11-01T15:49:44Z",
    "title_canon_sha256": "a4cb96138adb3e50e6ff2efd182e2cfa69e4c9f5c62ae31ead795397f342f216"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.0356",
    "kind": "arxiv",
    "version": 2
  }
}