Pith Number

pith:W44SH4E4

pith:2026:W44SH4E4BKMGZD2MM7BR3OXST7

not attested not anchored not stored refs resolved

How Twist Class Redundancy Drives the Prediction of Traces of Frobenius of Elliptic Curves

Angelica Babei, Malick Kebe, Ujjawal Shah

Redundancy within quadratic twist classes of elliptic curves suffices for highly accurate machine learning predictions of their Frobenius traces.

arxiv:2605.14288 v1 · 2026-05-14 · math.NT

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\pithnumber{W44SH4E4BKMGZD2MM7BR3OXST7}

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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

We demonstrate that the underlying datasets contain significant redundancy within quadratic twist classes, which alone is sufficient to produce highly accurate predictions.

C2weakest assumption

That the performance drop on the new unique-twist-class dataset is caused by removal of redundancy rather than by changes in data distribution or model capacity.

C3one line summary

Redundancy within quadratic twist classes in elliptic curve datasets is sufficient to produce highly accurate machine learning predictions of Frobenius traces.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] M. Amir, Y.-H. He, K.-H. Lee, T. Oliver, and E. Sultanow. Machine learning class numbers of real quadratic fields.https://arxiv.org/pdf/2209.09283, 2022. arXiv:math.NT:2209.09283 2022

[2] Frobenius traces for a set of (quadratic) twist classes of elliptic curves of conductor up to 10 7, May 2026 2026

[3] Banwait, AJ Fing, Xiaoyu Huang, and Deependra Singh 2025

[4] Learning euler factors of elliptic curves.Advances in Theoretical and Math- ematical Physics, 29(8):2327–2351, 2025 2025

[5] Booker, Min Lee, and David Lowry-Duda 2023

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:10.222818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b73923f09c0a986c8f4c67c31dbaf29fea10a198baf7c94b8bd39b7260976007

Aliases

arxiv: 2605.14288 · arxiv_version: 2605.14288v1 · doi: 10.48550/arxiv.2605.14288 · pith_short_12: W44SH4E4BKMG · pith_short_16: W44SH4E4BKMGZD2M · pith_short_8: W44SH4E4

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W44SH4E4BKMGZD2MM7BR3OXST7 \
  | 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: b73923f09c0a986c8f4c67c31dbaf29fea10a198baf7c94b8bd39b7260976007

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23dc8d0f43048df97734b5a41a32bf8c1ababc548d1801cc79a5843ebe78174b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-14T02:46:39Z",
    "title_canon_sha256": "db6ea7874007f084739821fbc8f3ccf197deb6df57e3e5dbd40281be9b6b685e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14288",
    "kind": "arxiv",
    "version": 1
  }
}