Paper Citation Record · LEDGER

Galois groups of polynomials and neurosymbolic networks

As of 15 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2501.12978.

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

pith.paper-citation-record.v1
2501.12978 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T16:41:01.401815Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

22 of 22 outbound references displayed

verified exact5
verified fuzzy2
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 49f9ab0f-fd28-449b-acf1-cd9b78c20fbc · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 1

Resolution: verified exact; doi, observed 2026-08-10T16:41:01.470746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1756f701-5bcc-4b53-9016-303539499751 · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 2

Resolution: verified exact; doi, observed 2026-08-10T16:41:01.460618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cc081343-0bd2-4989-b7be-cd9593e43b79 · outbound

This paper cites Bialostocki and T.

Galois groups of polynomials and neurosymbolic networks Bialostocki and T

Reference 3

Resolution: verified exact; doi, observed 2026-08-10T16:41:01.448117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ebbec2c5-2661-4dfe-9400-f80e888da43e · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.789078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation aed2c189-bdc7-42df-bc46-b7e4f8b7c4aa · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T16:41:01.232449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9ebd1e9-de27-4f14-98c7-ffac66105f7f · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.779826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0765c051-9618-413e-ace3-92cb78b614c6 · outbound

This paper cites Hagedorn.

Galois groups of polynomials and neurosymbolic networks Hagedorn

Reference 7

Resolution: verified exact; raw_fallback, observed 2026-08-10T16:41:01.660307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 33e5d2a9-27fc-4736-b4ea-7b7e607fcbbd · outbound

This paper cites Bruce King.

Galois groups of polynomials and neurosymbolic networks Bruce King

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:41:01.770439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3f35b1ff-b17e-4f64-9dda-997aa136b33a · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.760174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f3851751-160e-4024-8bf0-5bdf145c4a7f · outbound

This paper cites Deep Learning for Symbolic Mathematics.

Galois groups of polynomials and neurosymbolic networks Deep Learning for Symbolic Mathematics

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T16:41:01.250839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dbc0edfc-2e21-4512-859e-b57d331c84f7 · outbound

This paper cites Pretrained Language Models are Symbolic Mathematics Solvers too!.

Galois groups of polynomials and neurosymbolic networks Pretrained Language Models are Symbolic Mathematics Solvers too!

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T16:41:01.255453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1e20e2f-937f-40dc-8218-063edfd039ce · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.748717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d92d9fb8-8237-4bfc-ab41-d7fa5eb89e60 · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.737526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c060a28d-7cde-4fc5-b8ce-c1c1c6b01a90 · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.726524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ca0cf291-103b-49de-bf2f-11c390bb9a7a · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.715111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation aa8e7996-68f6-4bb3-860a-fac2b66b96a6 · outbound

This paper cites Machine learning for moduli space of genus two curves and an application to isogeny based cryptography.

Galois groups of polynomials and neurosymbolic networks Machine learning for moduli space of genus two curves and an application to isogeny based cryptography

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-10T16:41:01.486786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 35f7edc8-106c-48fb-89ae-ae51796dd462 · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.703746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6f7d56cc-02b4-4c69-8dcc-b9b4836d52aa · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.692835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 771a0d9c-7e90-4719-94c2-8f15b9922bf9 · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:41:01.681891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6d4fe596-ca6f-4106-8e21-f7d7df0bd9a9 · outbound

This paper cites Shaska and L.

Galois groups of polynomials and neurosymbolic networks Shaska and L

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:41:01.670870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2d20a521-b885-46e2-b350-c211bacfb970 · outbound

This paper cites an unresolved cited work.

Galois groups of polynomials and neurosymbolic networks Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-10T16:41:01.401815Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51d35fa4-2e76-43b5-9a57-72a1c23e8b12 · outbound

This paper cites Symbolic Comput.

Galois groups of polynomials and neurosymbolic networks Symbolic Comput

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-10T16:41:01.263054Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.