Pith Number

pith:ZTURQAV4

pith:2016:ZTURQAV4WB2WXFC32RRBTCUISR

not attested not anchored not stored refs pending

The complexity of a flat groupoid

David Rydh (KTH), Gabriel Zalamansky (IMJ-PRG), Matthieu Romagny (IRMAR)

arxiv:1609.00516 v4 · 2016-09-02 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTURQAV4WB2WXFC32RRBTCUISR}

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	2026-05-18T00:16:45.766619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cce91802bcb0756b945bd462198a889461104d1bea8eeb162c58399dd0471d04

Aliases

arxiv: 1609.00516 · arxiv_version: 1609.00516v4 · doi: 10.48550/arxiv.1609.00516 · pith_short_12: ZTURQAV4WB2W · pith_short_16: ZTURQAV4WB2WXFC3 · pith_short_8: ZTURQAV4

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/ZTURQAV4WB2WXFC32RRBTCUISR \
  | 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: cce91802bcb0756b945bd462198a889461104d1bea8eeb162c58399dd0471d04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9b24df525d77181b672fafe40ce019d491eebafa7f8198bf667404bffec0b66",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-09-02T09:23:42Z",
    "title_canon_sha256": "78ec93c6168496eb62706b98bb195e7eadb4edefafccd6f827df6b5040333f0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00516",
    "kind": "arxiv",
    "version": 4
  }
}