Paper Citation Record · LEDGER

Structural results on idealistic equivalence relations

As of 8 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2506.08217.

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

pith.paper-citation-record.v1
2506.08217 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:32:22.293302Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:08:57.416316Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T20:09:01.672749Z

Reference resolution

36 of 36 outbound references displayed

verified exact0
verified fuzzy24
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9f4cccea-9dde-441b-a803-4b8a7ca944ba · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.987836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dc39ed77-914d-43ff-992c-93aeb696d9fd · outbound

This paper cites Ash and Julia Knight.Computable structures and the hyperarithmetical hier- archy, volume 144 ofStudies in Logic and the Foundations of Mathematics.

Structural results on idealistic equivalence relations Ash and Julia Knight.Computable structures and the hyperarithmetical hier- archy, volume 144 ofStudies in Logic and the Foundations of Mathematics

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.953485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a2aecb8a-c2a0-418f-ab42-b1982ab633b0 · outbound

This paper cites Infinitary properties of abelian torsion groups.Ann.

Structural results on idealistic equivalence relations Infinitary properties of abelian torsion groups.Ann

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.915278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1d07e3c2-656c-4d1c-bbba-c27012ae448c · outbound

This paper cites The topological Vaught’s conjecture and minimal counterexamples.The Journal of Symbolic Logic, 59(3):757–784, 1994.

Structural results on idealistic equivalence relations The topological Vaught’s conjecture and minimal counterexamples.The Journal of Symbolic Logic, 59(3):757–784, 1994

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.866308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c61f4570-1741-4e60-87e5-60106416147e · outbound

This paper cites Idealistic equivalence relations.

Structural results on idealistic equivalence relations Idealistic equivalence relations

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.781395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0dfab223-c7c1-47d6-b2ea-b76f7f32ec9f · outbound

This paper cites Kechris.The descriptive set theory of Polish group actions, volume232ofLondon Mathematical Society Lecture Note Series.CambridgeUniversityPress, Cambridge, 1996.

Structural results on idealistic equivalence relations Kechris.The descriptive set theory of Polish group actions, volume232ofLondon Mathematical Society Lecture Note Series.CambridgeUniversityPress, Cambridge, 1996

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.760906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 90f454b2-b8f8-4b55-8868-1653d97cb32e · outbound

This paper cites The bi-embeddability relation for countable abelian groups.Trans.

Structural results on idealistic equivalence relations The bi-embeddability relation for countable abelian groups.Trans

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.745609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c16516b5-2f53-47dd-80a4-2c8e7a449487 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.732552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f45fc72d-cf3c-4e1e-89c2-a97dabad1d1d · outbound

This paper cites A Borel reducibility theory for classes of countable struc- tures.J.

Structural results on idealistic equivalence relations A Borel reducibility theory for classes of countable struc- tures.J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.719363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b0091193-4d74-4c28-ac2b-f8dba95ce3a2 · outbound

This paper cites Friedman.

Structural results on idealistic equivalence relations Friedman

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.705628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 73848d0d-8cc6-4798-ac1a-39370e549b4f · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.691878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 19aecb25-43c0-4e4a-a271-c9c633c4a58d · outbound

This paper cites Springer Monographs in Mathematics.

Structural results on idealistic equivalence relations Springer Monographs in Mathematics

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.677914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fe123b60-515a-4e45-abfc-352f5332dbf2 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.663748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0f4f8307-91cd-4abb-99a2-d8e58124ceb6 · outbound

This paper cites Somedichotomy theorems forisomorphism relations ofcountable models.J.

Structural results on idealistic equivalence relations Somedichotomy theorems forisomorphism relations ofcountable models.J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.649112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3e026bff-613a-4fdc-8b5c-7bfb1a0c7745 · outbound

This paper cites CRC Press, Boca Raton, FL, 2009.

Structural results on idealistic equivalence relations CRC Press, Boca Raton, FL, 2009

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.634561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2db5a14a-7eb1-4322-9a6e-108942fb4180 · outbound

This paper cites Analytic determinacy and0#.The Journal of Symbolic Logic, 43(4):685–693, 1978.

Structural results on idealistic equivalence relations Analytic determinacy and0#.The Journal of Symbolic Logic, 43(4):685–693, 1978

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.619308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1fa61342-2627-474c-ad47-e6984a0f5c8a · outbound

This paper cites American Mathematical Society, Providence, RI, 2000.

Structural results on idealistic equivalence relations American Mathematical Society, Providence, RI, 2000

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.603946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7f5b9a2b-89b2-4270-88b1-42900e374e11 · outbound

This paper cites Bi-Borel reducibility of essentially countable Borel equivalence relations.The Journal of Symbolic Logic, 70(3):979–992, 2005.

Structural results on idealistic equivalence relations Bi-Borel reducibility of essentially countable Borel equivalence relations.The Journal of Symbolic Logic, 70(3):979–992, 2005

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.589543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3cc895c9-c5b7-4a40-80d7-3034d8ae62b7 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.574626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 046b1e0a-036a-4207-9d65-0f4d0b401929 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.559410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9c940730-b0fb-4542-bd84-3c30d5d2220e · outbound

This paper cites Springer Monographs in Mathematics.

Structural results on idealistic equivalence relations Springer Monographs in Mathematics

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.544838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d7d456ac-3ea3-4253-87c8-f49b249b1523 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.519582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 359e6218-22d3-45dd-851c-c0a711b36c5d · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.506193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c0bac667-6a1f-4614-96f1-f5b1f8369cc6 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.491113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e3a6534d-c635-4d53-a5f6-2a2251cf8061 · outbound

This paper cites Kechris.Classical descriptive set theory, volume 156 ofGraduate Texts in Math- ematics.

Structural results on idealistic equivalence relations Kechris.Classical descriptive set theory, volume 156 ofGraduate Texts in Math- ematics

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.477536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 27ee9fbf-549d-4c3e-bd07-b7079c82e151 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.462888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fe483fb4-7967-464b-98f1-2bcf3a338cf4 · outbound

This paper cites Kechris and Alain Louveau.

Structural results on idealistic equivalence relations Kechris and Alain Louveau

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.448220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 040bcc4b-2aa0-4aee-9873-1d72e82a3182 · outbound

This paper cites Kechris and Henry L.

Structural results on idealistic equivalence relations Kechris and Henry L

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.433935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5c1a0218-c955-42d2-b21d-8a288dd10175 · outbound

This paper cites How to use Steel forcing.

Structural results on idealistic equivalence relations How to use Steel forcing

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.419099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 08f3c920-9785-49a3-9f13-60a9f491002a · outbound

This paper cites Moschovakis.Descriptive set theory, volume 100 ofStudies in Logic and the Foundations of Mathematics.

Structural results on idealistic equivalence relations Moschovakis.Descriptive set theory, volume 100 ofStudies in Logic and the Foundations of Mathematics

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.404393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e827962a-97b7-464e-b1f9-0fbaa740cd53 · outbound

This paper cites On the complexity of the relations of isomorphism and bi-embeddability.

Structural results on idealistic equivalence relations On the complexity of the relations of isomorphism and bi-embeddability

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.388449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a99f07c9-2b86-4aca-98c6-fa5282734233 · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:32:22.374184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 884d1db4-54e2-4ad0-b8d4-da08e25411b7 · outbound

This paper cites Analytic ideals and their applications.Ann.

Structural results on idealistic equivalence relations Analytic ideals and their applications.Ann

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.360186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 635f2a1b-77f3-4d34-902c-24cb5088e662 · outbound

This paper cites The coset equivalence relation and topologies on subgroups.American Journal of Mathematics, 131(3):571–605, 2009.

Structural results on idealistic equivalence relations The coset equivalence relation and topologies on subgroups.American Journal of Mathematics, 131(3):571–605, 2009

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.345443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9dafe244-0ca5-499b-9a06-2a3de4823422 · outbound

This paper cites Cambridge University Press, Cambridge, 2011.

Structural results on idealistic equivalence relations Cambridge University Press, Cambridge, 2011

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:32:22.330176Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3d22e67b-c54a-454b-b17c-1a3abaa3849b · outbound

This paper cites an unresolved cited work.

Structural results on idealistic equivalence relations Unresolved cited work

Reference 2003

Resolution: unresolved; no resolver link, observed 2026-08-07T05:32:22.236636Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 1bc119ff-0d27-4da2-9586-f89c94e2c5d2 · inbound

Componentwise Polish groupoids and equivalence relations cites this paper.

Componentwise Polish groupoids and equivalence relations Structural results on idealistic equivalence relations

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:09:01.823511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.