Pith Number

pith:UXPPJPCI

pith:2010:UXPPJPCIA3QYMMV5Y3EBXD36X5

not attested not anchored not stored refs pending

Fusion rules on a parametrized series of graphs

Marta Asaeda, Uffe Haagerup

arxiv:1008.5364 v2 · 2010-08-31 · math.OA · 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{UXPPJPCIA3QYMMV5Y3EBXD36X5}

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	2026-05-18T04:41:14.946789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5def4bc4806e18632bdc6c81b8f7ebf6af2943bc1c7d08b11c0b4c3b902a362

Aliases

arxiv: 1008.5364 · arxiv_version: 1008.5364v2 · doi: 10.48550/arxiv.1008.5364 · pith_short_12: UXPPJPCIA3QY · pith_short_16: UXPPJPCIA3QYMMV5 · pith_short_8: UXPPJPCI

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/UXPPJPCIA3QYMMV5Y3EBXD36X5 \
  | 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: a5def4bc4806e18632bdc6c81b8f7ebf6af2943bc1c7d08b11c0b4c3b902a362

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ad83f7f30fb6e94dd383aa61e49c4a581bfdc37a1694ff319b6b122964682a0",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-08-31T16:59:53Z",
    "title_canon_sha256": "201db4751f82e711189ca2824fee0258bf02a9694550ff864eafa0a1d7078e41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.5364",
    "kind": "arxiv",
    "version": 2
  }
}