Pith Number

pith:IIGNEA7F

pith:2026:IIGNEA7FFHQLQ7RKTOTWUZMJ5V

not attested not anchored not stored refs pending

A path model for MV polytopes in type A_n

Zijun Li

Orientations of the fundamental alcove produce paths that exactly label the cluster variables in the initial seed of C[N].

arxiv:2603.28634 v2 · 2026-03-30 · math.RT

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\usepackage{pith}
\pithnumber{IIGNEA7FFHQLQ7RKTOTWUZMJ5V}

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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

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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

The paths given by an orientation of the fundamental alcove parameterize precisely the cluster variables in the initial seed of the coordinate ring C[N].

C2weakest assumption

That the newly defined one-skeleton paths faithfully capture the combinatorial and geometric structure of MV polytopes so that Minkowski sum equals path concatenation and the alcove orientations exactly match the cluster variables.

C3one line summary

Introduces a one-skeleton path model for MV polytopes in type A_n, proving Minkowski sums correspond to path concatenations and that alcove-oriented paths parameterize cluster variables in the initial seed of C[N].

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:37.227433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

420cd203e529e0b87e2a9ba76a6589ed7420c571e05888e012ae7198cc0da408

Aliases

arxiv: 2603.28634 · arxiv_version: 2603.28634v2 · doi: 10.48550/arxiv.2603.28634 · pith_short_12: IIGNEA7FFHQL · pith_short_16: IIGNEA7FFHQLQ7RK · pith_short_8: IIGNEA7F

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/IIGNEA7FFHQLQ7RKTOTWUZMJ5V \
  | 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: 420cd203e529e0b87e2a9ba76a6589ed7420c571e05888e012ae7198cc0da408

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c336a936a0833fa3e480df8d1d9304f2ca83511ae6a9a5efaa4382527c0f49b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-03-30T16:18:12Z",
    "title_canon_sha256": "1a6f1bc2105b129227222fddbdc4b78922c0e7a963178d9bdcd9d93ce15eac07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.28634",
    "kind": "arxiv",
    "version": 2
  }
}