Pith Number

pith:IAAPXCOX

pith:2026:IAAPXCOXNDT5Y2NODWLBQLSD7J

not attested not anchored not stored refs pending

Edge Ideals of Prime Ideal Graphs over Finite Rings: Ordinary Powers, Fiber Cones, and Linear Powers

Tabinda Rasheed, Wang Yao

Prime ideal graphs of finite rings are complete split graphs whose edge ideal powers have explicit generators and are polymatroidal.

arxiv:2604.19408 v3 · 2026-04-21 · math.AC · math.CO

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\usepackage{pith}
\pithnumber{IAAPXCOXNDT5Y2NODWLBQLSD7J}

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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.

Claims

C1strongest claim

We prove that Γ_P(R) ≅ K_{|P|-1} ∨ K-bar_{|R|-|P|}, and a monomial x^α y^β belongs to the minimal generators of I(Γ_P(R))^n if and only if |α| + |β| = 2n, |β| ≤ n, and 0 ≤ α_i ≤ n for all i.

C2weakest assumption

R is a finite commutative ring with identity and P is a proper prime ideal; this finiteness and the prime property are used to obtain the explicit isomorphism and the counting formulas.

C3one line summary

Prime ideal graphs are complete split graphs whose edge ideal powers have explicit minimal monomial generators satisfying exponent conditions, are polymatroidal with linear resolutions, and have computable analytic spread.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-09T01:05:17.545916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4000fb89d768e7dc69ae1d96182e43fa4b5d0eb9106a45c9a647f4fe057571e7

Aliases

arxiv: 2604.19408 · arxiv_version: 2604.19408v3 · doi: 10.48550/arxiv.2604.19408 · pith_short_12: IAAPXCOXNDT5 · pith_short_16: IAAPXCOXNDT5Y2NO · pith_short_8: IAAPXCOX

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/IAAPXCOXNDT5Y2NODWLBQLSD7J \
  | 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: 4000fb89d768e7dc69ae1d96182e43fa4b5d0eb9106a45c9a647f4fe057571e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32bb321b4508c4102d50ddf81532f045bb4901c4ff2fe51d21591bad35e18baa",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-04-21T12:35:40Z",
    "title_canon_sha256": "4ec064539a17e8148b399603ddfc945a1bf100085426c8000e288d39c575d70b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.19408",
    "kind": "arxiv",
    "version": 3
  }
}