Paper Citation Record · LEDGER

Graded Keller maps and the Jacobian Conjecture

As of 12 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2607.20210.

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

pith.paper-citation-record.v1
2607.20210 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:40:22.987402Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

17 of 17 outbound references displayed

verified exact0
verified fuzzy0
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 44c4c6ee-03a2-41bd-a26e-284032a0c5ce · outbound

This paper cites Alp¨ oge, announcement, July 19, 2026,https://x.com/alpoge/status/ 2079028340955197566.

Graded Keller maps and the Jacobian Conjecture Alp¨ oge, announcement, July 19, 2026,https://x.com/__alpoge__/status/ 2079028340955197566

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.897918Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6833047f-e3ca-4ada-abfd-5aaf6edaca47 · outbound

This paper cites Beshaj, J.

Graded Keller maps and the Jacobian Conjecture Beshaj, J

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.904237Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec5f642f-ad24-4d11-9ba7-619cf8ec653c · outbound

This paper cites de Bondt and A.

Graded Keller maps and the Jacobian Conjecture de Bondt and A

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.908761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0ea64ac-acaa-4608-9260-47962b2ec8d0 · outbound

This paper cites an unresolved cited work.

Graded Keller maps and the Jacobian Conjecture Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.914703Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4cce9212-3273-44ec-8199-aec9e4499b05 · outbound

This paper cites Gutwirth,The action of an algebraic torus on the affine plane, Trans.

Graded Keller maps and the Jacobian Conjecture Gutwirth,The action of an algebraic torus on the affine plane, Trans

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.920798Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4178dfff-8f9c-4880-87ed-c071510e2031 · outbound

This paper cites Kaliman, M.

Graded Keller maps and the Jacobian Conjecture Kaliman, M

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.925721Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e6ab5505-7bd1-4fbd-8402-e4abb02c1d15 · outbound

This paper cites an unresolved cited work.

Graded Keller maps and the Jacobian Conjecture Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.930934Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7efae4e-1385-43c5-8030-3855c8a228be · outbound

This paper cites Pate and C.

Graded Keller maps and the Jacobian Conjecture Pate and C

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.935911Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56066581-36e0-4b92-86da-af28ad4c11d2 · outbound

This paper cites Rudin,Injective polynomial maps are automorphisms, Amer.

Graded Keller maps and the Jacobian Conjecture Rudin,Injective polynomial maps are automorphisms, Amer

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.941381Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c17422e-0084-46f8-b516-ec70768fe2b6 · outbound

This paper cites Serre,Topics in Galois theory, Notes written by Henri Darmon, 2nd ed., Research Notes in Mathematics, Vol.

Graded Keller maps and the Jacobian Conjecture Serre,Topics in Galois theory, Notes written by Henri Darmon, 2nd ed., Research Notes in Mathematics, Vol

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.946438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d652917c-4f50-421c-9dc0-5130dd598eb5 · outbound

This paper cites Arithmetic Sparsity and Obstructions in Weighted Projective Spaces.

Graded Keller maps and the Jacobian Conjecture Arithmetic Sparsity and Obstructions in Weighted Projective Spaces

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.951566Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ce2ff72-24bb-4b31-8a1a-af4dd5a8e614 · outbound

This paper cites Shaska,Artificial neural networks on graded vector spaces, Contemp.

Graded Keller maps and the Jacobian Conjecture Shaska,Artificial neural networks on graded vector spaces, Contemp

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.957438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6cfd6ccb-3c87-4de2-a257-710c6028bc45 · outbound

This paper cites Graded Neural Networks.

Graded Keller maps and the Jacobian Conjecture Graded Neural Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.962187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 095bcdcf-dadb-423e-960f-0cb3aaedf0eb · outbound

This paper cites Shaska,Quantum Weighted Algebraic Geometry Codes, Des.

Graded Keller maps and the Jacobian Conjecture Shaska,Quantum Weighted Algebraic Geometry Codes, Des

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.968266Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dbe08280-e42a-47e1-bb06-5aa5b2e47730 · outbound

This paper cites Graded Transformers.

Graded Keller maps and the Jacobian Conjecture Graded Transformers

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.973762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57f5d540-e9ab-4eb6-ae0d-211347ac1aa7 · outbound

This paper cites an unresolved cited work.

Graded Keller maps and the Jacobian Conjecture Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.979662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c36abfa-45fe-42f4-b6c6-b389f94ecd5b · outbound

This paper cites an unresolved cited work.

Graded Keller maps and the Jacobian Conjecture Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T10:40:22.987402Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.