Pith Number

pith:CPXQLYAC

pith:2012:CPXQLYACVOK6DD25U3EGKMMQSK

not attested not anchored not stored refs pending

Grothendieck quantaloids for allegories of enriched categories

Hans Heymans, Isar Stubbe

arxiv:1206.5975 v1 · 2012-06-26 · 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{CPXQLYACVOK6DD25U3EGKMMQSK}

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	2026-05-18T03:52:37.457109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13ef05e002ab95e18f5da6c865319092b22715b5dcc9d2eac397c5abece77073

Aliases

arxiv: 1206.5975 · arxiv_version: 1206.5975v1 · doi: 10.48550/arxiv.1206.5975 · pith_short_12: CPXQLYACVOK6 · pith_short_16: CPXQLYACVOK6DD25 · pith_short_8: CPXQLYAC

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/CPXQLYACVOK6DD25U3EGKMMQSK \
  | 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: 13ef05e002ab95e18f5da6c865319092b22715b5dcc9d2eac397c5abece77073

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18b456f305c512c3e3d9fff5c2efac041a9a70eb6a5e03439afa92eed0de0c8d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2012-06-26T12:54:36Z",
    "title_canon_sha256": "9ca86e3cb43b1349fb5f1b5e333340497e82954a298bc6c000dbf9670009b3c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.5975",
    "kind": "arxiv",
    "version": 1
  }
}