Paper Citation Record · LEDGER

Computable Scott Sentences and the Friedman-Stanley embedding

As of 4 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2605.04404.

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

pith.paper-citation-record.v1
2605.04404 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-08T17:26:09.981455Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+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

27 of 27 outbound references displayed

verified exact3
verified fuzzy23
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 03de177f-0e2f-4021-a89b-2ca640ffa5b9 · outbound

This paper cites On the computability of optimal Scott sentences.

Computable Scott Sentences and the Friedman-Stanley embedding On the computability of optimal Scott sentences

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.282630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 821c217d-c5a2-4654-b764-91e82ffcfbfb · outbound

This paper cites Complexity of Scott sen- tences.

Computable Scott Sentences and the Friedman-Stanley embedding Complexity of Scott sen- tences

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.250739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1f0b984e-a573-4ea4-8f8e-e2830e68dba9 · outbound

This paper cites Pairs of Recursive Structures.

Computable Scott Sentences and the Friedman-Stanley embedding Pairs of Recursive Structures

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.304120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 07ae800d-03e9-4b3e-ac31-31daea835a41 · outbound

This paper cites an unresolved cited work.

Computable Scott Sentences and the Friedman-Stanley embedding Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-05-26T07:46:55.255577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a303f5be-85a7-41c9-bfbd-6fd87fd54c74 · outbound

This paper cites Recursive labeling systems and stability of recursive structures in hyperarithmetical degrees.

Computable Scott Sentences and the Friedman-Stanley embedding Recursive labeling systems and stability of recursive structures in hyperarithmetical degrees

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.300398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 7798d0c9-7d1e-4104-8e79-f1894314fbf8 · outbound

This paper cites Comparing classes of finite structures.

Computable Scott Sentences and the Friedman-Stanley embedding Comparing classes of finite structures

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.291450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 9c5cee98-4ac8-4cb6-9d87-c2d9aae721d0 · outbound

This paper cites Optimal Syn- tactic Definitions of Back-and-Forth Types.

Computable Scott Sentences and the Friedman-Stanley embedding Optimal Syn- tactic Definitions of Back-and-Forth Types

Reference 7

Resolution: verified exact; doi, observed 2026-05-08T20:04:07.696265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 910ff7c8-a75a-496d-8771-3ca4ae479bca · outbound

This paper cites Cohen,Set Theory and the Continuum Hypothesis, Dover, Garden City.

Computable Scott Sentences and the Friedman-Stanley embedding Cohen,Set Theory and the Continuum Hypothesis, Dover, Garden City

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.260632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d64eddcf-03b1-4e4a-8fc4-75a54225b820 · outbound

This paper cites A Borel reducibility theory for classes of countable structures.

Computable Scott Sentences and the Friedman-Stanley embedding A Borel reducibility theory for classes of countable structures

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.269380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 055576da-b6fb-479a-9c0f-2cdb89fab380 · outbound

This paper cites Some dichotomy theorems for isomorphism relations of countable models.

Computable Scott Sentences and the Friedman-Stanley embedding Some dichotomy theorems for isomorphism relations of countable models

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.314146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1741def2-d52e-4584-9d95-ff6ef9ea40bc · outbound

This paper cites Enumerations in computable structure theory.

Computable Scott Sentences and the Friedman-Stanley embedding Enumerations in computable structure theory

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.273840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 9c4b7fcb-2fff-4da5-bd2f-9f2207a7429c · outbound

This paper cites Scott Spectral Gaps are Bounded for Linear Orderings.

Computable Scott Sentences and the Friedman-Stanley embedding Scott Spectral Gaps are Bounded for Linear Orderings

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-11T17:36:05.311509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a88113a8-4493-45f4-8f8c-1d06119b2a22 · outbound

This paper cites Scott sentence complexities of linear or- derings.

Computable Scott Sentences and the Friedman-Stanley embedding Scott sentence complexities of linear or- derings

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.278494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation af31ee04-6974-4012-bd17-78708f1c1a06 · outbound

This paper cites Complexity of well-ordered sets in an Abelian group.

Computable Scott Sentences and the Friedman-Stanley embedding Complexity of well-ordered sets in an Abelian group

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.287445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4a2cf58d-69fc-4eed-b3ec-77fd199ec47f · outbound

This paper cites Relative to any non-arithmetic set.

Computable Scott Sentences and the Friedman-Stanley embedding Relative to any non-arithmetic set

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-11T17:36:05.303800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0e1b09c5-2888-4cb0-a0fa-33d247e7ff28 · outbound

This paper cites The tree of tuples of a struc- ture.

Computable Scott Sentences and the Friedman-Stanley embedding The tree of tuples of a struc- ture

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.295740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation dc239e72-79db-4892-b214-8d90c2d528f5 · outbound

This paper cites Around non-classifiability for countable torsion-free Abelian groups.

Computable Scott Sentences and the Friedman-Stanley embedding Around non-classifiability for countable torsion-free Abelian groups

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.308746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0c05bb16-bb80-4f1f-8dcb-1687ffa97628 · outbound

This paper cites Finite-quantifier equivalence.

Computable Scott Sentences and the Friedman-Stanley embedding Finite-quantifier equivalence

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.264805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 9f1428e8-9b0d-4738-b2d4-36345db071c2 · outbound

This paper cites Turing computable em- beddings.

Computable Scott Sentences and the Friedman-Stanley embedding Turing computable em- beddings

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.228128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation f2d26aeb-b215-45a4-ba5a-b86a1be854fd · outbound

This paper cites Coding in graphs and linear orderings.

Computable Scott Sentences and the Friedman-Stanley embedding Coding in graphs and linear orderings

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.210710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1f5bce4e-61fb-4b61-b979-7d74beeec287 · outbound

This paper cites Maher,On Embeddings of Computable Structures, Classes of Struc- tures, and Computable Isomorphism, PhD Dissertation, University of Notre Dame.

Computable Scott Sentences and the Friedman-Stanley embedding Maher,On Embeddings of Computable Structures, Classes of Struc- tures, and Computable Isomorphism, PhD Dissertation, University of Notre Dame

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.215382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 5a8b116b-5ad9-4979-876c-75946658d8e7 · outbound

This paper cites A robuster Scott rank.

Computable Scott Sentences and the Friedman-Stanley embedding A robuster Scott rank

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.219258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation da1584d1-7f33-4b02-86a5-7c4f53e33b8a · outbound

This paper cites Computable Structure Theory: Within the Arithmetic.

Computable Scott Sentences and the Friedman-Stanley embedding Computable Structure Theory: Within the Arithmetic

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.246827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c3c6d2e9-bef2-4eb4-bf9f-9ddc630b13a7 · outbound

This paper cites Computable Structure Theory: Beyond the Arithmetic.

Computable Scott Sentences and the Friedman-Stanley embedding Computable Structure Theory: Beyond the Arithmetic

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.236974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 7272257e-41db-4b3c-96c4-ac5a01d9ecd3 · outbound

This paper cites Torsion-free abelian groups are Borel com- plete.

Computable Scott Sentences and the Friedman-Stanley embedding Torsion-free abelian groups are Borel com- plete

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.241641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 70725609-9558-40ea-a28d-86cc2dc7bc92 · outbound

This paper cites Logic with denumerably long formulas and finite strings of quantifiers.

Computable Scott Sentences and the Friedman-Stanley embedding Logic with denumerably long formulas and finite strings of quantifiers

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.232625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 99e95fec-6b75-4ae9-896f-a448855a4fca · outbound

This paper cites The classification problem for torsion-free Abelian groups of finite rank.

Computable Scott Sentences and the Friedman-Stanley embedding The classification problem for torsion-free Abelian groups of finite rank

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T07:46:55.223730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Pith citing papers

No inbound Pith citation observations are available.