Pith Number

pith:VBJE27OJ

pith:2026:VBJE27OJEC7BFQKFYW42NJUHIB

not attested not anchored not stored refs pending

On Arithmetic Mirror Symmetry for smooth Fano fourfolds

Mikhail Ovcharenko

An explicit class of tempered Laurent polynomials provides Landau-Ginzburg models for smooth Fano threefolds and several fourfolds, enabling two arithmetic mirror symmetry examples.

arxiv:2604.26592 v3 · 2026-04-29 · math.AG · 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{VBJE27OJEC7BFQKFYW42NJUHIB}

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.

Claims

C1strongest claim

We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n ≤ 4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds ... Using the partial case of Arithmetic Mirror Symmetry conjecture proved by Kerr, we construct two examples of a Mirror Symmetry correspondence between specific algebraic classes.

C2weakest assumption

That the newly introduced explicit class of tempered Laurent polynomials indeed contains the correct Landau-Ginzburg models for the listed Fano fourfolds (complete intersections in toric varieties, Grassmannians of planes, and quiver flag zero loci), as asserted by the 'checks' performed.

C3one line summary

An explicit class of tempered Laurent polynomials is introduced that includes Landau-Ginzburg models for smooth Fano threefolds and various Fano fourfolds, enabling two new examples of arithmetic mirror symmetry correspondences.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T02:04:11.535886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8524d7dc920be12c145c5b9a6a6874065d9f4cb3bdd33b517a0f1849fb1ccba

Aliases

arxiv: 2604.26592 · arxiv_version: 2604.26592v3 · doi: 10.48550/arxiv.2604.26592 · pith_short_12: VBJE27OJEC7B · pith_short_16: VBJE27OJEC7BFQKF · pith_short_8: VBJE27OJ

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/VBJE27OJEC7BFQKFYW42NJUHIB \
  | 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: a8524d7dc920be12c145c5b9a6a6874065d9f4cb3bdd33b517a0f1849fb1ccba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e149c14d4761fc496cdb7d8e28e293b45c35dcbe245a32b44a691281481a9555",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-29T12:18:00Z",
    "title_canon_sha256": "53aca40e76fc59247eba9df86db204ccac02cbcadc6f6644cd9d7ca459b4bd07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26592",
    "kind": "arxiv",
    "version": 3
  }
}