Paper Citation Record · LEDGER

Geometric Generality of Transformer-Based Gr\"obner Basis Computation

As of 24 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2504.12465.

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

pith.paper-citation-record.v1
2504.12465 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:40:41.686565Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

38 of 38 outbound references displayed

verified exact0
verified fuzzy22
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a308f748-8a42-4783-9156-ff020c9ce31e · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.382540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7d1e0141-747b-48a8-b956-62b78cbe44c2 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.359948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 71872bfc-f28a-4110-a29f-df3634c616cc · outbound

This paper cites ACC (IEEE Cat.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation ACC (IEEE Cat

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.345051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 13caaae8-1eb2-469e-b36a-9f60a074ad36 · outbound

This paper cites B \^o cher, Introduction to Higher Algebra , Macmillan, 1907.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation B \^o cher, Introduction to Higher Algebra , Macmillan, 1907

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.329624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e22ed5a8-10e7-4557-813f-9b56d2191806 · outbound

This paper cites Proceedings, Springer, 2006, pp.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Proceedings, Springer, 2006, pp

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.312650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7c32269e-9ad0-4257-a8f7-80a50e6d90c1 · outbound

This paper cites Buchberger, A theoretical basis for the reduction of polynomials to canonical forms, SIGSAM Bull.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Buchberger, A theoretical basis for the reduction of polynomials to canonical forms, SIGSAM Bull

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.294339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation cee957d4-6aaf-4d2d-a747-97a93d2c5885 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.277815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a3b7a965-3b1e-4250-8489-d2a56af9baef · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.263005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 856525a8-38a2-479e-9c52-fc5b11fa675a · outbound

This paper cites Cox, John B.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Cox, John B

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.247342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 09c280c6-43cf-4ce7-8843-df9445abb068 · outbound

This paper cites 345--359.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 345--359

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.229582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 35e2169c-1cc2-4259-86b7-b6d0b84e42c7 · outbound

This paper cites 150, Springer-Verlag, New York, 1995.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 150, Springer-Verlag, New York, 1995

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.212422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4c52111a-3704-4c49-aec3-c13233f4d329 · outbound

This paper cites 1, 61--88.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 1, 61--88

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.196596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 74a83fae-a999-42cb-8362-5ed96eccbd74 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.181541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c3fd7bf5-d0f6-45d9-8134-2027bfb71b81 · outbound

This paper cites Fried and Moshe Jarden, Field Arithmetic , 4th corrected edition ed., Ergeb.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Fried and Moshe Jarden, Field Arithmetic , 4th corrected edition ed., Ergeb

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.165405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f736bc99-40af-407f-838c-7f8bca4b6a5d · outbound

This paper cites Towards Empirical Interpretation of Internal Circuits and Properties in Grokked Transformers on Modular Polynomials.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Towards Empirical Interpretation of Internal Circuits and Properties in Grokked Transformers on Modular Polynomials

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:41.553945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9903b680-5166-41a0-a94b-1dee27d71686 · outbound

This paper cites 247--257.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 247--257

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.146639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a4b94824-7dc0-4bd9-8217-2fc7cad32038 · outbound

This paper cites Grokking modular arithmetic.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Grokking modular arithmetic

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:41.563972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52b88600-14a3-4f2b-b5bd-3a8b5318ad9c · outbound

This paper cites 2-3, 149--167.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 2-3, 149--167

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.129507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 66212dfc-ba68-4ce2-bbff-d8fd30bdbc95 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.113753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d82ce9fb-f93c-43b0-bab9-3470d72d8dc6 · outbound

This paper cites Why are Sensitive Functions Hard for Transformers?.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Why are Sensitive Functions Hard for Transformers?

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:41.585215Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79536d11-60f2-42f9-bffb-6bf9c7485809 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.096527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f216917d-94a5-4292-a11f-f18ed7aa01db · outbound

This paper cites 206--222.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 206--222

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.078774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4308c795-739c-47a0-b870-e4b8cd1c351c · outbound

This paper cites ed., Grad.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation ed., Grad

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.060389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 630a61d7-2a3e-4ed3-8e8f-4db15fdf2f2f · outbound

This paper cites Deep Learning for Symbolic Mathematics.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Deep Learning for Symbolic Mathematics

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-16T12:40:41.607231Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a54a62e-727b-429d-8897-910a07e46e7a · outbound

This paper cites Available at https://pq-crystals.org/.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Available at https://pq-crystals.org/

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.043368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 52fcd541-8578-446e-abc0-85696bd6482f · outbound

This paper cites 10, 882--891.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 10, 882--891

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:42.026561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 24454237-923d-4096-96a9-da12e4b840e4 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:42.006800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 41705778-2fa1-4197-935e-e8d5e74d20da · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:41.990150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8dac82f7-1e3f-47e0-aee8-77fbfe47e814 · outbound

This paper cites 3, 305--329.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 3, 305--329

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:41.972794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 25f428c6-bdfc-47e1-b155-067f147ac935 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:41.954029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e884e7cc-42b4-414d-b7bb-cdac32d0b29b · outbound

This paper cites 4, 579--590.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 4, 579--590

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:41.934988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fa7a209b-7d18-4d0c-b8e4-61a81ce7f93b · outbound

This paper cites 6, 1--40.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 6, 1--40

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:41.913532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5e7d7961-de0e-4be9-a129-76f93f11b41f · outbound

This paper cites o bner bases using gr \.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation o bner bases using gr \

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:41.890830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b7594cbf-2586-4a22-a281-b2d6f9b6c833 · outbound

This paper cites 2, 221--238.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 2, 221--238

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:41.871527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6571b3c0-6e02-4a3f-9d5a-fb8755b90a86 · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:41.853031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d68dad82-aa1d-46ab-9525-977210181f8c · outbound

This paper cites an unresolved cited work.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:40:41.834129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 211e7fbc-c8f8-4f00-8b41-b9bca43d9183 · outbound

This paper cites 1, 1--29.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 1, 1--29

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:41.813626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5c9eff79-97f5-4a7e-a412-19ff41f327e4 · outbound

This paper cites 393--419.

Geometric Generality of Transformer-Based Gr\"obner Basis Computation 393--419

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:40:41.795305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.