Pith Number

pith:JUAC4V4Y

pith:2012:JUAC4V4YDJTBAFPX66VJWR2C2U

not attested not anchored not stored refs pending

Stable equivalence of Morita type and Frobenius extensions

M. Beattie, S. Caenepeel, S. Raianu

arxiv:1202.2441 v1 · 2012-02-11 · 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{JUAC4V4YDJTBAFPX66VJWR2C2U}

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	2026-05-18T04:02:26.538358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d002e57981a661015f7f7aa9b4742d53590e35aed31de1e3606cae0e6f58a21

Aliases

arxiv: 1202.2441 · arxiv_version: 1202.2441v1 · doi: 10.48550/arxiv.1202.2441 · pith_short_12: JUAC4V4YDJTB · pith_short_16: JUAC4V4YDJTBAFPX · pith_short_8: JUAC4V4Y

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/JUAC4V4YDJTBAFPX66VJWR2C2U \
  | 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: 4d002e57981a661015f7f7aa9b4742d53590e35aed31de1e3606cae0e6f58a21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d3d6aeff27841b0a3d921aba54235b08095c3ff335d00b9e7d04633f1b772ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-02-11T13:05:23Z",
    "title_canon_sha256": "c21e3a1aaef2eff79c39abbb1322c91a27a4f19bd7872a3b37d7a2f60a993c13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2441",
    "kind": "arxiv",
    "version": 1
  }
}