Pith Number

pith:BDYZV5LR

pith:2015:BDYZV5LRDF7SQ2ILPWKR5BIYZ4

not attested not anchored not stored refs pending

Group Extensions of the Co-type of a Crossed Module and Strict Categorical Groups

Nguyen Tien Quang

arxiv:1503.04379 v1 · 2015-03-15 · 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{BDYZV5LRDF7SQ2ILPWKR5BIYZ4}

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	2026-05-18T02:23:25.254996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08f19af571197f28690b7d951e8518cf3bbff9e19086134f11cfaf3653fed8ee

Aliases

arxiv: 1503.04379 · arxiv_version: 1503.04379v1 · doi: 10.48550/arxiv.1503.04379 · pith_short_12: BDYZV5LRDF7S · pith_short_16: BDYZV5LRDF7SQ2IL · pith_short_8: BDYZV5LR

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/BDYZV5LRDF7SQ2ILPWKR5BIYZ4 \
  | 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: 08f19af571197f28690b7d951e8518cf3bbff9e19086134f11cfaf3653fed8ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3af975a5a046e8ac6b70b648396e694b6bfb57e4a69e2dd2078fdd4aca603b17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-03-15T03:02:48Z",
    "title_canon_sha256": "0aa07806b8394487e22ca01fdf9afabd2b4061439b7bcca394f3e1c2b9415789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04379",
    "kind": "arxiv",
    "version": 1
  }
}