Pith Number

pith:N7F2MTHL

pith:2008:N7F2MTHLWVPA5FOB6B5Z4DHXWR

not attested not anchored not stored refs pending

Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

Aidan Sims, Mark Tomforde, Paul S. Muhly, Takeshi Katsura

arxiv:0809.0164 v2 · 2008-09-01 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N7F2MTHLWVPA5FOB6B5Z4DHXWR}

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	2026-07-04T15:33:27.153742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fcba64cebb55e0e95c1f07b9e0cf7b4421ffdf9e3e0c7629462f235327b8dfd

Aliases

arxiv: 0809.0164 · arxiv_version: 0809.0164v2 · doi: 10.48550/arxiv.0809.0164 · pith_short_12: N7F2MTHLWVPA · pith_short_16: N7F2MTHLWVPA5FOB · pith_short_8: N7F2MTHL

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/N7F2MTHLWVPA5FOB6B5Z4DHXWR \
  | 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: 6fcba64cebb55e0e95c1f07b9e0cf7b4421ffdf9e3e0c7629462f235327b8dfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8039bd862da184eb6d6c7f4999ae21bf2a9305795e6966b454a1b3fb9fb921b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2008-09-01T01:23:40Z",
    "title_canon_sha256": "0d8732ea96292f29fd70ef54ec6b438954890a971b86fac622b142a431777692"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.0164",
    "kind": "arxiv",
    "version": 2
  }
}