Pith Number

pith:T54T43CB

pith:2012:T54T43CBSLXKWPLFRE5HXYUCJL

not attested not anchored not stored refs pending

On universal gradings, versal gradings and Schurian generated categories

Andrea Solotar, Claude Cibils, Maria Julia Redondo

arxiv:1210.4098 v2 · 2012-10-15 · math.CT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T54T43CBSLXKWPLFRE5HXYUCJL}

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	2026-05-18T03:31:29.367948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f793e6c4192eeab3d65893a7be2824ae6c651abf4e008608b8421b27efaf7f4

Aliases

arxiv: 1210.4098 · arxiv_version: 1210.4098v2 · doi: 10.48550/arxiv.1210.4098 · pith_short_12: T54T43CBSLXK · pith_short_16: T54T43CBSLXKWPLF · pith_short_8: T54T43CB

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/T54T43CBSLXKWPLFRE5HXYUCJL \
  | 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: 9f793e6c4192eeab3d65893a7be2824ae6c651abf4e008608b8421b27efaf7f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64dc6dbffa94ba0d669d31559404660fceb5eef3f7f46dbe7bd687d3f224355e",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2012-10-15T16:39:44Z",
    "title_canon_sha256": "6cbd1d12f8ad5118e50044c06c39fbc95a582910db64ce8527f7900d68d9b4cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4098",
    "kind": "arxiv",
    "version": 2
  }
}