Pith Number

pith:LKCLMI4A

pith:2011:LKCLMI4AW53C7CN5IOO3TTXM6Y

not attested not anchored not stored refs pending

Topological K-theory of the group C*-algebra of a semi-direct product Z^n rtimes Z/m for a free conjugation action

Martin Langer, Wolfgang Lueck

arxiv:1109.1440 v1 · 2011-09-07 · math.AT · math.KT · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LKCLMI4AW53C7CN5IOO3TTXM6Y}

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	2026-05-18T04:13:55.703665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a84b62380b7762f89bd439db9ceecf6316c8e9010da7566326a160cc91282a7

Aliases

arxiv: 1109.1440 · arxiv_version: 1109.1440v1 · doi: 10.48550/arxiv.1109.1440 · pith_short_12: LKCLMI4AW53C · pith_short_16: LKCLMI4AW53C7CN5 · pith_short_8: LKCLMI4A

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/LKCLMI4AW53C7CN5IOO3TTXM6Y \
  | 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: 5a84b62380b7762f89bd439db9ceecf6316c8e9010da7566326a160cc91282a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bf8b69b98c201828af29d3a2afe3077aeee0dec1c9606bb648bb9bf6f873c03",
    "cross_cats_sorted": [
      "math.KT",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-09-07T13:00:16Z",
    "title_canon_sha256": "469c1dcb0c2cec05dc3fe649f0365436ee005157af5b7b0c270b070c023daa4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1440",
    "kind": "arxiv",
    "version": 1
  }
}