Paper Citation Record · LEDGER

Learning Euler Factors of Elliptic Curves

As of 8 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 5 inbound Pith citation observations for arXiv:2502.10357.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2502.10357 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T18:32:13.714607Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:28:19.721141Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-18T01:35:36.403165Z

Reference resolution

27 of 27 outbound references displayed

verified exact1
verified fuzzy20
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b18735c1-6324-4f0b-ae6d-93179b718e2a · outbound

This paper cites Amir, Y.-H.

Learning Euler Factors of Elliptic Curves Amir, Y.-H

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.815062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eeb921a1-614c-4c6d-abfa-1758a556101f · outbound

This paper cites Pca plotting for int2int.

Learning Euler Factors of Elliptic Curves Pca plotting for int2int

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.799061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c9c6f054-d98c-4d21-8165-ea293fea86ed · outbound

This paper cites Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curves.

Learning Euler Factors of Elliptic Curves Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curves

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:13.039713Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12c2bb11-19bd-4d73-b6c6-2c5c15b9b0c3 · outbound

This paper cites An application of the effective sato-tate conjecture.

Learning Euler Factors of Elliptic Curves An application of the effective sato-tate conjecture

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.783394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3d1305b6-c9a5-4a1e-8812-8693734037a6 · outbound

This paper cites A toy model of universality: Reverse engineering how networks learn group operations.

Learning Euler Factors of Elliptic Curves A toy model of universality: Reverse engineering how networks learn group operations

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.766917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 05f96294-b8c0-482f-8448-72c5b4a5ca6d · outbound

This paper cites an unresolved cited work.

Learning Euler Factors of Elliptic Curves Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T18:32:14.749002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ddee2056-8967-452b-9b53-582b6a566c79 · outbound

This paper cites Learning the greatest common divisor: explaining transformer predictions.

Learning Euler Factors of Elliptic Curves Learning the greatest common divisor: explaining transformer predictions

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:13.078022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bea8ccff-6caf-479f-959f-d40092a43d7a · outbound

This paper cites A mathematical framework for transformer circuits.

Learning Euler Factors of Elliptic Curves A mathematical framework for transformer circuits

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.731213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 33692695-4325-4cd5-b278-09217fa188e6 · outbound

This paper cites Comparing two k-category assignments by a k-category correlation coefficient.

Learning Euler Factors of Elliptic Curves Comparing two k-category assignments by a k-category correlation coefficient

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.714073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 96e361b1-3954-4f30-ade2-12690e1b7d64 · outbound

This paper cites Machine-learning number fields.

Learning Euler Factors of Elliptic Curves Machine-learning number fields

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.696034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3b97c417-0c0f-4b35-bf23-d72c09b34a3f · outbound

This paper cites Machine-learning the S ato- T ate conjecture.

Learning Euler Factors of Elliptic Curves Machine-learning the S ato- T ate conjecture

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.679330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 55dee601-c837-4ce8-ba02-4ecb8461edd9 · outbound

This paper cites Machine learning invariants of arithmetic curves.

Learning Euler Factors of Elliptic Curves Machine learning invariants of arithmetic curves

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.662355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 993dc140-52fd-4ca9-9fb5-a222d2fb1573 · outbound

This paper cites Murmurations of elliptic curves.

Learning Euler Factors of Elliptic Curves Murmurations of elliptic curves

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.644290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5c01800e-58e2-4f01-a947-e18033d041e7 · outbound

This paper cites How does gpt-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model.

Learning Euler Factors of Elliptic Curves How does gpt-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.587239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 04816052-2eac-423e-8206-92cccc54e8e7 · outbound

This paper cites Ranks of elliptic curves and deep neural networks.

Learning Euler Factors of Elliptic Curves Ranks of elliptic curves and deep neural networks

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.517322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 71c193c7-2a7f-4651-bdbd-89e3df5ddb1e · outbound

This paper cites Towards understanding grokking: An effective theory of representation learning.

Learning Euler Factors of Elliptic Curves Towards understanding grokking: An effective theory of representation learning

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.471204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 32176073-bc21-4c2a-b290-201edea2e807 · outbound

This paper cites The L -functions and modular forms database.

Learning Euler Factors of Elliptic Curves The L -functions and modular forms database

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.399723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4fb561cf-97da-46de-8fac-9559f39a8788 · outbound

This paper cites Comparison of the predicted and observed secondary structure of t4 phage lysozyme.

Learning Euler Factors of Elliptic Curves Comparison of the predicted and observed secondary structure of t4 phage lysozyme

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.338221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a86ca024-e958-4c82-a04d-9b3618d1d4fa · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

Learning Euler Factors of Elliptic Curves Progress measures for grokking via mechanistic interpretability

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:13.462936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39718c85-140c-4cf1-81e7-dffa71dd02e0 · outbound

This paper cites Predicting root numbers with neural networks.

Learning Euler Factors of Elliptic Curves Predicting root numbers with neural networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:13.481182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 601c39fe-7a89-4767-8142-bb0be25c4437 · outbound

This paper cites Understanding Addition in Transformers.

Learning Euler Factors of Elliptic Curves Understanding Addition in Transformers

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:13.542776Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 958cc109-b283-466e-9da0-8e67bacf8ced · outbound

This paper cites Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic.

Learning Euler Factors of Elliptic Curves Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-07T18:32:13.917949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ebdc4666-a4a4-4990-8346-e5c995406983 · outbound

This paper cites Quelques applications du th \'e oreme de densit \'e de chebotarev.

Learning Euler Factors of Elliptic Curves Quelques applications du th \'e oreme de densit \'e de chebotarev

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.291045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a5dfe090-f7ec-4ad5-8b37-175907a7a102 · outbound

This paper cites Sutherland.

Learning Euler Factors of Elliptic Curves Sutherland

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.233965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 18a28ad8-d3ce-4351-9256-38bd57a92e92 · outbound

This paper cites Stein and Mark Watkins.

Learning Euler Factors of Elliptic Curves Stein and Mark Watkins

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.202041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9e62f1e9-285e-40b2-8038-966f3307aad5 · outbound

This paper cites Attention is all you need.

Learning Euler Factors of Elliptic Curves Attention is all you need

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.118468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 36045a1c-52e1-42f0-ba46-eb98893bd417 · outbound

This paper cites The clock and the pizza: Two stories in mechanistic explanation of neural networks.

Learning Euler Factors of Elliptic Curves The clock and the pizza: Two stories in mechanistic explanation of neural networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T18:32:14.056482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation beb9daef-4c54-4b3a-8f6c-0f7ac5b8fa8b · inbound

Improving elliptic curve rank classification using multi-value and learned Mestre-Nagao sums cites this paper.

Improving elliptic curve rank classification using multi-value and learned Mestre-Nagao sums Learning Euler Factors of Elliptic Curves

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T05:28:19.721141Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8fdc6b3-853e-4360-b61e-41fc02f480cb · inbound

Large Lemma Miners: Can LLMs do Induction Proofs for Hardware? cites this paper.

Large Lemma Miners: Can LLMs do Induction Proofs for Hardware? Learning Euler Factors of Elliptic Curves

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-18T01:35:36.406259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b04cc5c3-7360-4eb2-ba3c-db919dac7598 · inbound

Large Lemma Miners: Can LLMs do Induction Proofs for Hardware? cites this paper.

Large Lemma Miners: Can LLMs do Induction Proofs for Hardware? Learning Euler Factors of Elliptic Curves

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T00:14:48.113296Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4efd678-0d79-4912-b0a2-2be2d4afdf71 · inbound

Computer vision and converse theorems cites this paper.

Computer vision and converse theorems Learning Euler Factors of Elliptic Curves

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-10T10:04:06.224179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fd3c03ef-1868-4fd4-90cb-47f322116a8e · inbound

Emergent Latent-State Computation under Stochastic Volatility cites this paper.

Emergent Latent-State Computation under Stochastic Volatility Learning Euler Factors of Elliptic Curves

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-01T02:27:04.632780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.