Paper Citation Record · LEDGER

Multiplicative Relationships of Subrings and their Applications to Factorization

As of 14 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 4 inbound Pith citation observations for arXiv:2506.24031.

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

pith.paper-citation-record.v1
2506.24031 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:37:41.501420Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:30:45.134326Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T22:22:49.408283Z

Reference resolution

21 of 21 outbound references displayed

verified exact1
verified fuzzy16
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3cb33777-9b51-4f32-b170-576980e9281a · outbound

This paper cites Elasticity in polynomial-type extensions.

Multiplicative Relationships of Subrings and their Applications to Factorization Elasticity in polynomial-type extensions

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:45.432769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 28eabfbe-a537-4723-9911-04fa3eee1a2c · outbound

This paper cites Overrings of half-factorial orders,.

Multiplicative Relationships of Subrings and their Applications to Factorization Overrings of half-factorial orders,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:45.232827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d3900132-2d7b-495b-87f6-c169680ca6be · outbound

This paper cites an unresolved cited work.

Multiplicative Relationships of Subrings and their Applications to Factorization Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:37:45.003309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a583fd66-b81b-444d-806b-127bd27f9348 · outbound

This paper cites Class group and factorization in orders of a PID.

Multiplicative Relationships of Subrings and their Applications to Factorization Class group and factorization in orders of a PID

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:44.832716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c375148d-d399-4897-86d9-79d5385e5c88 · outbound

This paper cites The conductor ideal of an order.

Multiplicative Relationships of Subrings and their Applications to Factorization The conductor ideal of an order

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:44.584662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d0e89d32-5be8-4c9c-884d-4f08327ed94d · outbound

This paper cites Elasticity in orders of an algebraic number field with radical conductor ideal and their rings of formal power series, 2025.

Multiplicative Relationships of Subrings and their Applications to Factorization Elasticity in orders of an algebraic number field with radical conductor ideal and their rings of formal power series, 2025

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:44.339632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 69fbe267-cdca-41d2-942e-ee381a9d8d39 · outbound

This paper cites A characterization of polynomial rings with the half-factorial property.

Multiplicative Relationships of Subrings and their Applications to Factorization A characterization of polynomial rings with the half-factorial property

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:44.128229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bf702ea7-d920-4308-9e71-4063c9a990f3 · outbound

This paper cites Half-factorial domains in quadratic fields.

Multiplicative Relationships of Subrings and their Applications to Factorization Half-factorial domains in quadratic fields

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:43.866910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f51b09b1-c338-4130-92e5-87bb84e43d75 · outbound

This paper cites Extensions of half-factorial domains: a survey.

Multiplicative Relationships of Subrings and their Applications to Factorization Extensions of half-factorial domains: a survey

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:43.667617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation afb26b42-e97b-46fb-9021-a03def5b50b5 · outbound

This paper cites Factorization of algebraic integers.

Multiplicative Relationships of Subrings and their Applications to Factorization Factorization of algebraic integers

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:43.412841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 60634a57-6575-4611-b10a-a9518905c6e2 · outbound

This paper cites Elasticity of orders in quadratic rings of integers.

Multiplicative Relationships of Subrings and their Applications to Factorization Elasticity of orders in quadratic rings of integers

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:43.274118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 04b9e09f-0cc3-4bdf-af74-f8ac776c14ea · outbound

This paper cites Elasticity of orders with prime conductor, 2025.

Multiplicative Relationships of Subrings and their Applications to Factorization Elasticity of orders with prime conductor, 2025

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:42.996894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5dd6e3a2-d839-4939-a5ba-88411055e0d3 · outbound

This paper cites Power series extensions of half-factorial domains.

Multiplicative Relationships of Subrings and their Applications to Factorization Power series extensions of half-factorial domains

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:42.690611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9a9c12f7-91eb-410a-97f1-55e9c0dac40d · outbound

This paper cites The HFD property in orders of a number field.

Multiplicative Relationships of Subrings and their Applications to Factorization The HFD property in orders of a number field

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:42.493177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b2252685-c664-4bc2-b8cf-26e74c8ee6cc · outbound

This paper cites Relating elasticity and other multiplicative properties among orders in number fields and related rings.

Multiplicative Relationships of Subrings and their Applications to Factorization Relating elasticity and other multiplicative properties among orders in number fields and related rings

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:42.282540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 607232e1-d567-42d7-8998-09738a47481f · outbound

This paper cites Associated Quadratic Orders, March 2025.

Multiplicative Relationships of Subrings and their Applications to Factorization Associated Quadratic Orders, March 2025

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:42.091361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6ca96b6e-df99-42bf-a0e2-98378e1ea955 · outbound

This paper cites A note on elasticity of factorizations.Journal of Number Theory, 51:46–47, 1995.

Multiplicative Relationships of Subrings and their Applications to Factorization A note on elasticity of factorizations.Journal of Number Theory, 51:46–47, 1995

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T21:37:41.113147Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 552a88a0-0e4e-4420-a302-acdb6024f2f2 · outbound

This paper cites Springer, 1999.

Multiplicative Relationships of Subrings and their Applications to Factorization Springer, 1999

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T21:37:41.236548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0d33c21-ec84-4f89-acb0-4a2a0b1409bf · outbound

This paper cites Half-factorial real quadratic orders.

Multiplicative Relationships of Subrings and their Applications to Factorization Half-factorial real quadratic orders

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:37:41.883182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 412895af-6c51-4fa1-a3b5-6dc178558ecd · outbound

This paper cites A characterization of half-factorial orders in algebraic number fields.

Multiplicative Relationships of Subrings and their Applications to Factorization A characterization of half-factorial orders in algebraic number fields

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T21:37:41.501420Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2e40f49-d60a-4ff8-9247-98cef167becb · outbound

This paper cites Overrings of half-factorial orders.

Multiplicative Relationships of Subrings and their Applications to Factorization Overrings of half-factorial orders

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:37:41.682564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation 0b5c0f7c-00f4-46b9-bb45-f90e9b54cca8 · inbound

On $q$-real and $q$-complex numbers cites this paper.

On $q$-real and $q$-complex numbers Multiplicative Relationships of Subrings and their Applications to Factorization

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T21:37:41.355887Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73ab3508-500d-48ca-8f49-2d21b6c5d716 · inbound

Elasticity of Orders from the $S$-relative Davenport Constant: an Arithmetic Application of a Number-Theoretic Investigation cites this paper.

Elasticity of Orders from the $S$-relative Davenport Constant: an Arithmetic Application of a Number-Theoretic Investigation Multiplicative Relationships of Subrings and their Applications to Factorization

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-19T22:22:49.409783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c3a6755a-5708-4ffd-bfb4-b4e34f6ee7bc · inbound

Elasticity of Orders from the $S$-relative Davenport Constant: an Arithmetic Application of a Number-Theoretic Investigation cites this paper.

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T14:10:38.145924Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 751e53c6-d0da-47b1-bf41-8ba9ebe59669 · inbound

(Locally) Associated Subrings in Polynomial and Power Series Extensions cites this paper.

(Locally) Associated Subrings in Polynomial and Power Series Extensions Multiplicative Relationships of Subrings and their Applications to Factorization

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T00:30:45.134326Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.