Pith Number

pith:KPW5RUE3

pith:2025:KPW5RUE33TO25HV2Y3RSA22CJG

not attested not anchored not stored refs pending

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Esther Banaian, Yasuaki Gyoda

arxiv:2507.06900 v2 · 2025-07-09 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KPW5RUE33TO25HV2Y3RSA22CJG}

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.

Cited by

7 papers in Pith

Cluster Expansions from Punctured Orbifolds

Words for generalized Markov numbers

Orderings of k-Markov Numbers

Generalized discrete Markov spectra

Fractal phenomenon in $c$- and $g$-vectors of the Markov quiver

Receipt and verification

First computed	2026-07-05T11:41:26.436736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53edd8d09bdcddae9ebac6e3206b4249a4238a5293fe799cf2a20452286b766c

Aliases

arxiv: 2507.06900 · arxiv_version: 2507.06900v2 · doi: 10.48550/arxiv.2507.06900 · pith_short_12: KPW5RUE33TO2 · pith_short_16: KPW5RUE33TO25HV2 · pith_short_8: KPW5RUE3

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/KPW5RUE33TO25HV2Y3RSA22CJG \
  | 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: 53edd8d09bdcddae9ebac6e3206b4249a4238a5293fe799cf2a20452286b766c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ef7b3dd42916bfb12fcefb934db94adc6f534a9a26dc0fef17c053a51fceb62",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-09T14:36:31Z",
    "title_canon_sha256": "752ce9638ebf0d8f717997fa6e834a460094dfdde8080e8f79379bdbc0369a0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06900",
    "kind": "arxiv",
    "version": 2
  }
}