Pith Number

pith:VK5LDVO6

pith:2012:VK5LDVO6I6H7JLEC2FVI36HMC5

not attested not anchored not stored refs pending

On the graded center of graded categories

Alexis Virelizier, Vladimir Turaev

arxiv:1208.5696 v1 · 2012-08-28 · math.QA · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VK5LDVO6I6H7JLEC2FVI36HMC5}

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	2026-05-18T03:46:57.982524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aabab1d5de478ff4ac82d16a8df8ec17520ea9fb69b986db681cd9a427d1d298

Aliases

arxiv: 1208.5696 · arxiv_version: 1208.5696v1 · doi: 10.48550/arxiv.1208.5696 · pith_short_12: VK5LDVO6I6H7 · pith_short_16: VK5LDVO6I6H7JLEC · pith_short_8: VK5LDVO6

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/VK5LDVO6I6H7JLEC2FVI36HMC5 \
  | 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: aabab1d5de478ff4ac82d16a8df8ec17520ea9fb69b986db681cd9a427d1d298

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "592f992183fa30fd081752cba33bbd0f613764da1d7689f3e02e7574dfc1c3f7",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-08-28T15:57:27Z",
    "title_canon_sha256": "60a76f188aa2c9cca14317cbb2f6d87da293e256d06c49f404ed728e0d167c41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5696",
    "kind": "arxiv",
    "version": 1
  }
}