Pith Number

pith:IR27KQX7

pith:2011:IR27KQX7TNDJ2AFIKY2N2O4ACW

not attested not anchored not stored refs pending

The K-theory of free quantum groups

Christian Voigt, Roland Vergnioux

arxiv:1112.3291 v1 · 2011-12-14 · math.OA · 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{IR27KQX7TNDJ2AFIKY2N2O4ACW}

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	2026-05-18T03:14:08.842633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4475f542ff9b469d00a85634dd3b8015a342a54ab9d64156d0d6beadcc0abe04

Aliases

arxiv: 1112.3291 · arxiv_version: 1112.3291v1 · doi: 10.48550/arxiv.1112.3291 · pith_short_12: IR27KQX7TNDJ · pith_short_16: IR27KQX7TNDJ2AFI · pith_short_8: IR27KQX7

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/IR27KQX7TNDJ2AFIKY2N2O4ACW \
  | 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: 4475f542ff9b469d00a85634dd3b8015a342a54ab9d64156d0d6beadcc0abe04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c93a67014576b407582030c19f1dc3c5d69e1c8fb40f7e25442a2ee9683bc39a",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-12-14T18:00:15Z",
    "title_canon_sha256": "f6669f27b46664400d93da7900d4194f7c9953e56699b8175a673285bab59520"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3291",
    "kind": "arxiv",
    "version": 1
  }
}