Paper Citation Record · LEDGER

Additive systems for $\mathbb{Z}$ are undecidable

As of 17 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2508.17285.

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

pith.paper-citation-record.v1
2508.17285 v2

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

12 of 12 outbound references displayed

verified exact4
verified fuzzy7
unresolved0
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f22247c5-34a3-4f50-b35a-e7338854a97f · outbound

This paper cites Deciding stability and mortality of piecewise affine dynamical systems.

Additive systems for $\mathbb{Z}$ are undecidable Deciding stability and mortality of piecewise affine dynamical systems

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T21:51:52.947434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4508f1df-48f7-4c32-9d50-268b0e1ac74d · outbound

This paper cites On number systems.

Additive systems for $\mathbb{Z}$ are undecidable On number systems

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T21:51:52.964287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c3b66ff8-dcc7-482e-b893-c241e58d73be · outbound

This paper cites A 3 x + 1 survey: Number theory and dynamical systems.

Additive systems for $\mathbb{Z}$ are undecidable A 3 x + 1 survey: Number theory and dynamical systems

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T21:51:52.958661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 10cd8d5b-9370-49a3-a647-057ead9739ed · outbound

This paper cites FRACTRAN: A Simple Universal Programming Language for Arith- metic.

Additive systems for $\mathbb{Z}$ are undecidable FRACTRAN: A Simple Universal Programming Language for Arith- metic

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T21:51:52.961639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 87ba6b3d-08e7-4e97-9a05-0a825448a033 · outbound

This paper cites Chapter 7. Integer Tilings.

Additive systems for $\mathbb{Z}$ are undecidable Chapter 7. Integer Tilings

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T21:51:52.955469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 94e1530c-d2f8-49c7-861b-dabfb4360599 · outbound

This paper cites Undecidability of translational monotilings.

Additive systems for $\mathbb{Z}$ are undecidable Undecidability of translational monotilings

Reference 6

Resolution: verified exact; doi, observed 2026-05-18T21:51:51.489122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ecadd5d3-764d-4113-b646-25db851d842c · outbound

This paper cites Tiling the integers with aperiodic tiles.

Additive systems for $\mathbb{Z}$ are undecidable Tiling the integers with aperiodic tiles

Reference 7

Resolution: verified exact; doi, observed 2026-05-18T21:51:51.481470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8aeb9c90-4364-4319-8f00-0386d88cca92 · outbound

This paper cites Translational tilings of the integers with long periods.

Additive systems for $\mathbb{Z}$ are undecidable Translational tilings of the integers with long periods

Reference 8

Resolution: malformed identifier; doi_truncated, observed 2026-05-18T21:51:51.485538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 697a1f78-19ff-4235-961d-a945ed4bba1b · outbound

This paper cites Multifactorisations and Divisor Functions.

Additive systems for $\mathbb{Z}$ are undecidable Multifactorisations and Divisor Functions

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-18T21:51:52.107767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d74820b5-0942-4d28-8e61-81b5dce3d5ad · outbound

This paper cites Additive systems and a theorem of de Bruijn.

Additive systems for $\mathbb{Z}$ are undecidable Additive systems and a theorem of de Bruijn

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-05-18T21:51:51.475270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 356ba143-841e-4ccb-8855-30c5e4a14eec · outbound

This paper cites Puzzle #4 — The n-Category Caf´ e (comment).

Additive systems for $\mathbb{Z}$ are undecidable Puzzle #4 — The n-Category Caf´ e (comment)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T21:51:52.950332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 45e7e0ce-d7f7-45f7-aa0a-12506a351d03 · outbound

This paper cites 7.3 Tiling the integers.

Additive systems for $\mathbb{Z}$ are undecidable 7.3 Tiling the integers

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T21:51:52.952872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.