Pith Number

pith:2PINHUCW

pith:2026:2PINHUCWS3IBSAZ7AQTMXYV4MH

not attested not anchored not stored refs pending

Additive Rigidity for Images of Rational Points on Abelian Varieties I: The Simple Case

Seokhyun Choi

Finite morphisms from abelian varieties to projective space make images of finite-rank rational point groups additively rigid.

arxiv:2603.24340 v3 · 2026-03-25 · math.NT · math.AG

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\usepackage{pith}
\pithnumber{2PINHUCWS3IBSAZ7AQTMXYV4MH}

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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

✓ 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 show that for any affine chart A^n ⊆ P^n and any finite subset X ⊆ f(Γ) ∩ A^n, the energy satisfies E(X) ≪ |X|^2 and the sumset satisfies |X+X| ≫ |X|^2. We then prove that this holds for arbitrary abelian varieties when f is compatible with the decomposition into simple factors, using the uniform Mordell-Lang conjecture.

C2weakest assumption

The uniform Mordell-Lang conjecture must hold; additionally the morphism f must be finite onto its image and, in the general case, compatible with the simple-factor decomposition of A.

C3one line summary

Images of rational points on abelian varieties under morphisms to projective space satisfy E(X) ≪ |X|^2 and |X+X| ≫ |X|^2 for finite subsets X in affine charts.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T02:04:16.582050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3d0d3d05696d019033f0426cbe2bc61d4fbefdd23cab8fef6bf33e85ea9bf83

Aliases

arxiv: 2603.24340 · arxiv_version: 2603.24340v3 · doi: 10.48550/arxiv.2603.24340 · pith_short_12: 2PINHUCWS3IB · pith_short_16: 2PINHUCWS3IBSAZ7 · pith_short_8: 2PINHUCW

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/2PINHUCWS3IBSAZ7AQTMXYV4MH \
  | 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: d3d0d3d05696d019033f0426cbe2bc61d4fbefdd23cab8fef6bf33e85ea9bf83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4674e00b8c1092f0d9d2965053149f7a8c123bc9b8d731ad1cb2188aebe5066",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-03-25T14:21:15Z",
    "title_canon_sha256": "3d8dc27a167bf555e34214c233ff1fc1cab9ddc65b866fbcf5739681c4315a41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.24340",
    "kind": "arxiv",
    "version": 3
  }
}