Pith Number

pith:2TUCEZ2B

pith:2010:2TUCEZ2B5EE4NTPOY27YK3INL2

not attested not anchored not stored refs pending

The multiplication theorem and bases in finite and affine quantum cluster algebras

Fan Xu, Ming Ding

arxiv:1006.3928 v4 · 2010-06-20 · math.RT · math.QA · 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{2TUCEZ2B5EE4NTPOY27YK3INL2}

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	2026-05-18T04:36:51.205898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4e8226741e909c6cdeec6bf856d0d5eba63fc3182e84e007609a58aa9112e5d

Aliases

arxiv: 1006.3928 · arxiv_version: 1006.3928v4 · doi: 10.48550/arxiv.1006.3928 · pith_short_12: 2TUCEZ2B5EE4 · pith_short_16: 2TUCEZ2B5EE4NTPO · pith_short_8: 2TUCEZ2B

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/2TUCEZ2B5EE4NTPOY27YK3INL2 \
  | 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: d4e8226741e909c6cdeec6bf856d0d5eba63fc3182e84e007609a58aa9112e5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "798ef8f149df09de92c89b9aee884f5e0b196e84d918931780eb46b5610b3af7",
    "cross_cats_sorted": [
      "math.QA",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2010-06-20T11:29:15Z",
    "title_canon_sha256": "b5a9018a2992f23024274837f664b1ca5807866fbf9d6fd660fb04c3580f129f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3928",
    "kind": "arxiv",
    "version": 4
  }
}