Pith Number

pith:56CQ5MUB

pith:2012:56CQ5MUBX4L45LOAMK33ORL7S2

not attested not anchored not stored refs pending

Cluster algebras: an introduction

Lauren K. Williams

arxiv:1212.6263 v3 · 2012-12-26 · math.RA · math-ph · math.CO · math.MP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{56CQ5MUBX4L45LOAMK33ORL7S2}

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	2026-05-18T03:30:41.213716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef850eb281bf17ceadc062b7b7457f969077b8a2f8c2baf6a5c555871d5e54de

Aliases

arxiv: 1212.6263 · arxiv_version: 1212.6263v3 · doi: 10.48550/arxiv.1212.6263 · pith_short_12: 56CQ5MUBX4L4 · pith_short_16: 56CQ5MUBX4L45LOA · pith_short_8: 56CQ5MUB

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/56CQ5MUBX4L45LOAMK33ORL7S2 \
  | 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: ef850eb281bf17ceadc062b7b7457f969077b8a2f8c2baf6a5c555871d5e54de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "682ac191c6986a6959248ffda89e79aff1f7018df221d9ab34ed6ed206a3f87b",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-12-26T21:00:02Z",
    "title_canon_sha256": "82b5df5c9e5b35a193619bc43e94bf37385379e89362278ba0ed2cb86dbb5cb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6263",
    "kind": "arxiv",
    "version": 3
  }
}