Paper Citation Record · LEDGER

Arithmetic properties encoded in undermonoids

As of 13 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2412.11199.

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

pith.paper-citation-record.v1
2412.11199 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T15:23:58.174727Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

28 of 28 outbound references displayed

verified exact1
verified fuzzy9
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 06da378e-5dd1-4236-8078-4a5be0607cdf · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.021311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81a6ecb7-42f4-444b-8a07-7646462e94b8 · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.745633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 499dad20-f147-463b-8e09-435b7215f62f · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.724731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 53a508fb-5969-4aaa-a064-435eb2887380 · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.702901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8c4196fb-e91a-49a5-b3b0-7020f1d9014d · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.684702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ce2a74a9-28e3-430c-bbd8-bae5c9128018 · outbound

This paper cites Carlitz, A characterization of algebraic number ﬁelds with class num ber two , Proc.

Arithmetic properties encoded in undermonoids Carlitz, A characterization of algebraic number ﬁelds with class num ber two , Proc

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.666501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ed36412e-2ced-4569-9caf-70d2db02fcf0 · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.647574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bdc32019-2f1a-43fc-b608-3a9e68c234d8 · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.628654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e88fbb2c-3714-4973-9863-cc61e09c394d · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.601937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e4bbe1dc-25a7-488c-8d3d-abfdad21a6ac · outbound

This paper cites Coykendall and F.

Arithmetic properties encoded in undermonoids Coykendall and F

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.584188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 97be2d33-be9c-4dd5-9600-050e22212cc8 · outbound

This paper cites Coykendall and F.

Arithmetic properties encoded in undermonoids Coykendall and F

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.077705Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0349797c-0e62-42aa-93b8-e7c661753f63 · outbound

This paper cites Coykendall, F.

Arithmetic properties encoded in undermonoids Coykendall, F

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.554274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 97c34cd5-019b-4e20-8a90-270f748b6674 · outbound

This paper cites Coykendall and W.

Arithmetic properties encoded in undermonoids Coykendall and W

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.537323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4e32a007-dfa3-484a-87df-4d09fcef17b3 · outbound

This paper cites Geroldinger and F.

Arithmetic properties encoded in undermonoids Geroldinger and F

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.518686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f23d8dd7-9619-4001-a146-39561ab928c4 · outbound

This paper cites Geroldinger and Q.

Arithmetic properties encoded in undermonoids Geroldinger and Q

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.497934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e0b1e017-6292-4b71-8559-8c9115b7282f · outbound

This paper cites Hereditary atomicity and ACCP in abelian groups.

Arithmetic properties encoded in undermonoids Hereditary atomicity and ACCP in abelian groups

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:23:58.267230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 27ad5802-96da-45e7-bbbf-8488045d9913 · outbound

This paper cites Gotti, Increasing positive monoids of ordered ﬁelds are FF-monoid s, J.

Arithmetic properties encoded in undermonoids Gotti, Increasing positive monoids of ordered ﬁelds are FF-monoid s, J

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.111703Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0454bebc-6845-425a-97ec-f52705d74e2f · outbound

This paper cites Gotti, On semigroup algebras with rational exponents , Comm.

Arithmetic properties encoded in undermonoids Gotti, On semigroup algebras with rational exponents , Comm

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.117533Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddb93be9-07a9-4c1e-9637-f5ebf8b82c43 · outbound

This paper cites Gotti and B.

Arithmetic properties encoded in undermonoids Gotti and B

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.122962Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8aabfdd-319a-4812-8380-f38554d7feb3 · outbound

This paper cites Divisibility and a weak ascending chain condition on principal ideals.

Arithmetic properties encoded in undermonoids Divisibility and a weak ascending chain condition on principal ideals

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.127705Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 795f2f41-4112-4739-a0e6-ace89111822b · outbound

This paper cites Gotti and H.

Arithmetic properties encoded in undermonoids Gotti and H

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.135598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c7e045c8-7114-4096-8a9b-d8abe82c12f4 · outbound

This paper cites Gotti and J.

Arithmetic properties encoded in undermonoids Gotti and J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.403587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b42fa8fc-7f92-48a1-a4cd-21195c95f7f6 · outbound

This paper cites Grams, Atomic rings and the ascending chain condition for principa l ideals , Math.

Arithmetic properties encoded in undermonoids Grams, Atomic rings and the ascending chain condition for principa l ideals , Math

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.146157Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79325330-1f6f-48fe-a0e7-e26be581e966 · outbound

This paper cites Grams and H.

Arithmetic properties encoded in undermonoids Grams and H

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.151860Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eed33595-62b2-4036-bd24-d0b53a59eca8 · outbound

This paper cites an unresolved cited work.

Arithmetic properties encoded in undermonoids Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-11T15:23:58.349863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b7ec6432-5f2b-4a9f-8d5b-87e1c326e21e · outbound

This paper cites Halter-Koch, Finiteness theorems for factorizations , Semigroup Forum 44 (1992) 112–117.

Arithmetic properties encoded in undermonoids Halter-Koch, Finiteness theorems for factorizations , Semigroup Forum 44 (1992) 112–117

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T15:23:58.163181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3129378e-9547-4cd5-8cce-230c68026253 · outbound

This paper cites Zaks, Half-factorial domains , Bull.

Arithmetic properties encoded in undermonoids Zaks, Half-factorial domains , Bull

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.312835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cc832809-cc8e-427d-9358-4a776d293180 · outbound

This paper cites Zaks, Half-factorial domains , Israel J.

Arithmetic properties encoded in undermonoids Zaks, Half-factorial domains , Israel J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:23:58.290363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

No inbound Pith citation observations are available.