Pith Number

pith:T2FMDZYD

pith:2005:T2FMDZYDFH52UHR4O5C7WUNPUQ

not attested not anchored not stored refs pending

Cluster-tilted algebras are Gorenstein and stably Calabi-Yau

Bernhard Keller, Idun Reiten

arxiv:math/0512471 v4 · 2005-12-20 · math.RT · 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{T2FMDZYDFH52UHR4O5C7WUNPUQ}

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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.

Cited by

1 paper in Pith

From green mutation to $\mathrm{X}$-evolution: flows and foliations on cluster complexes

Receipt and verification

First computed	2026-07-04T14:52:16.658963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e8ac1e70329fbaa1e3c7745fb51afa40e40cdbebcc74eeb55d1707f050aa8c3

Aliases

arxiv: math/0512471 · arxiv_version: math/0512471v4 · doi: 10.48550/arxiv.math/0512471 · pith_short_12: T2FMDZYDFH52 · pith_short_16: T2FMDZYDFH52UHR4 · pith_short_8: T2FMDZYD

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/T2FMDZYDFH52UHR4O5C7WUNPUQ \
  | 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: 9e8ac1e70329fbaa1e3c7745fb51afa40e40cdbebcc74eeb55d1707f050aa8c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52703ea76166d9131064cbef534b44af687160d059ef4ff879e69ce534a2f7d1",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math.RT",
    "submitted_at": "2005-12-20T16:23:01Z",
    "title_canon_sha256": "a554c6367d6385143bab2a9883f861f5af08c12f7d9778028944f146992e156b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512471",
    "kind": "arxiv",
    "version": 4
  }
}