Pith Number

pith:YUJLD7QZ

pith:2026:YUJLD7QZQ5WGSWNIRF74RKH6OM

not attested not anchored not stored refs pending

Wug-snake graphs and Markov numbers of matrix semigroups

Oleg Karpenkov, Yefei Ma

Generalized Markov numbers from semigroups of reduced integer matrices are given by perfect matchings of wug-snake graphs.

arxiv:2604.17069 v2 · 2026-04-18 · math.CO · math.NT

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\usepackage{pith}
\pithnumber{YUJLD7QZQ5WGSWNIRF74RKH6OM}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

Generalized Markov numbers arising from semigroups of reduced integer matrices can be found by counting perfect matchings of wug-snake graphs.

C2weakest assumption

That the specific semigroup construction on reduced integer matrices produces objects that qualify as generalized Markov numbers and that the perfect-matching count on the associated wug-snake graphs exactly equals those numbers.

C3one line summary

Generalized Markov numbers from matrix semigroups equal the number of perfect matchings in wug-snake graphs.

Receipt and verification

First computed	2026-06-09T02:08:42.636898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c512b1fe19876c6959a8897fc8a8fe73361197e017dc7c37d7100449e605cb28

Aliases

arxiv: 2604.17069 · arxiv_version: 2604.17069v2 · doi: 10.48550/arxiv.2604.17069 · pith_short_12: YUJLD7QZQ5WG · pith_short_16: YUJLD7QZQ5WGSWNI · pith_short_8: YUJLD7QZ

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/YUJLD7QZQ5WGSWNIRF74RKH6OM \
  | 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: c512b1fe19876c6959a8897fc8a8fe73361197e017dc7c37d7100449e605cb28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "289ceafeeb13fac73330c371994c4c99a110cb20c717f4c4436e3ddaa4294138",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-04-18T17:06:37Z",
    "title_canon_sha256": "8c218d40abcb47b363d126f66347e441b759823ae0453b2070cc4cdf4a075d35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.17069",
    "kind": "arxiv",
    "version": 2
  }
}