Pith Number

pith:Q6QM4EFT

pith:2007:Q6QM4EFTBVNS4FD5B5BZTBDPOY

not attested not anchored not stored refs pending

On the properties of the exchange graph of a cluster algebra

Alek Vainshtein, Michael Gekhtman, Michael Shapiro

arxiv:math/0703151 v2 · 2007-03-06 · math.CO · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q6QM4EFTBVNS4FD5B5BZTBDPOY}

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	2026-05-18T01:14:29.900969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87a0ce10b30d5b2e147d0f4399846f7606dc85d11e16b1d405649cfdbb5a074e

Aliases

arxiv: math/0703151 · arxiv_version: math/0703151v2 · doi: 10.48550/arxiv.math/0703151 · pith_short_12: Q6QM4EFTBVNS · pith_short_16: Q6QM4EFTBVNS4FD5 · pith_short_8: Q6QM4EFT

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/Q6QM4EFTBVNS4FD5B5BZTBDPOY \
  | 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: 87a0ce10b30d5b2e147d0f4399846f7606dc85d11e16b1d405649cfdbb5a074e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e9dea350adbd5fcce0649050cb35c92aec8dd4192c216c29786d2eae2899721",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2007-03-06T13:02:13Z",
    "title_canon_sha256": "915763dba0177243811bd83df94130800a1c7176236d97748f104163248424a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703151",
    "kind": "arxiv",
    "version": 2
  }
}