Pith Number

pith:BQK6GCZH

pith:2010:BQK6GCZHUJ6KCEXYLGC5XD245W

not attested not anchored not stored refs pending

Vector Groupoids

Gheorghe Ivan, Vasile Poputa

arxiv:1012.4608 v1 · 2010-12-21 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BQK6GCZHUJ6KCEXYLGC5XD245W}

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	2026-05-18T04:32:54.027957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c15e30b27a27ca112f85985db8f5ceda2047af06be82149d4e44c0a0f49311d

Aliases

arxiv: 1012.4608 · arxiv_version: 1012.4608v1 · doi: 10.48550/arxiv.1012.4608 · pith_short_12: BQK6GCZHUJ6K · pith_short_16: BQK6GCZHUJ6KCEXY · pith_short_8: BQK6GCZH

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/BQK6GCZHUJ6KCEXYLGC5XD245W \
  | 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: 0c15e30b27a27ca112f85985db8f5ceda2047af06be82149d4e44c0a0f49311d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2a855a5140c92cb01714635f2c816677e5acb49212f9d568713cb9b2bc007fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-21T11:13:30Z",
    "title_canon_sha256": "3f9209d2eb99bb33784b5220f4acfffd6fe3e3110a8cd4bffdeedcdd8e5cf091"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4608",
    "kind": "arxiv",
    "version": 1
  }
}