Pith Number

pith:K4XX7KG3

pith:2026:K4XX7KG3CU6B6AZYVDE3AUDFMT

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On the finite transcendence of Frobenius traces for abelian varieties over $\mathbb{Q}$

Yuto Tsuruta

Frobenius traces for elliptic curves over the rationals remain finitely transcendental even without complex multiplication.

arxiv:2605.17674 v1 · 2026-05-17 · math.NT

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\usepackage{pith}
\pithnumber{K4XX7KG3CU6B6AZYVDE3AUDFMT}

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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 finite transcendence of Frobenius traces for elliptic curves over Q without the assumption of complex multiplication.

C2weakest assumption

That the method developed by Luca and Zudilin for the CM case extends directly to the non-CM setting and to higher-dimensional abelian varieties.

C3one line summary

Establishes finite transcendence of Frobenius traces for non-CM elliptic curves over Q and extends the result to some abelian varieties over Q.

References

14 extracted · 14 resolved · 2 Pith anchors

[1] A. Aizenbud, and N. Avni,Counting points of schemes over finite rings and counting represen- tations of arithmetic lattices, Duke Math. J.,167(2018), no. 14, 2721–2743 2018

[2] T. Anzawa, and H. Funakura,Congruences of the𝑞-Fibonacci sequence related with its tran- scendence, Ramanujan J.,63, No.4 (2024) 1057–1072 2024

[3] T. Barnet-Lamb, D. Geraghty, M. Harris, and R. Taylor,A family of Calabi-Yau varieties and potential automorphy II., Publ. Res. Inst. Math. Sci.,47(2011) no. 1, 29–98 2011

[4] Deligne,La conjecture de Weil.I., Inst 1974

[5] F. Luca, and W. Zudilin,Irrationality and transcendence questions in the ‘poor man’s adèle ring’, Ramanujan J.,67, No.88 (2025) 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:52.079234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

572f7fa8db153c1f0338a8c9b0506564c9132509a5e651cc4be8a72da1f9a02f

Aliases

arxiv: 2605.17674 · arxiv_version: 2605.17674v1 · doi: 10.48550/arxiv.2605.17674 · pith_short_12: K4XX7KG3CU6B · pith_short_16: K4XX7KG3CU6B6AZY · pith_short_8: K4XX7KG3

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/K4XX7KG3CU6B6AZYVDE3AUDFMT \
  | 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: 572f7fa8db153c1f0338a8c9b0506564c9132509a5e651cc4be8a72da1f9a02f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71cc4a47c7b6b7dd4d505819eb7eeebebf89b677862c40aced665ac851ce08dd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-17T22:06:39Z",
    "title_canon_sha256": "471b4e7b5b2855f72238197f923136bfef42d755d525362fba9eb296df35eb5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17674",
    "kind": "arxiv",
    "version": 1
  }
}