Paper Citation Record · LEDGER

On the notion of a patterning property in model theory

As of 12 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 2 inbound Pith citation observations for arXiv:2606.18533.

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

pith.paper-citation-record.v1
2606.18533 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T21:29:54.129942Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-12T11:20:25.093177Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-06-30T08:54:29.481188Z

Reference resolution

36 of 36 outbound references displayed

verified exact12
verified fuzzy0
unresolved20
parse uncertain0
malformed identifier0
metadata mismatch4

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8dd26440-172f-4608-aea1-99228b3b8915 · outbound

This paper cites Annals of Pure and Applied Logic , year =.

On the notion of a patterning property in model theory Annals of Pure and Applied Logic , year =

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1151f130-0983-4912-978e-88e44e718cde · outbound

This paper cites manuscript , year =.

On the notion of a patterning property in model theory manuscript , year =

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23c2041c-74fb-44d9-b902-36a453ee3cc5 · outbound

This paper cites 2020 , school=.

On the notion of a patterning property in model theory 2020 , school=

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29b14050-a3ab-4fe7-982c-25db5a9b29d7 · outbound

This paper cites , title =.

On the notion of a patterning property in model theory , title =

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-07-04T00:09:14.260994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e8fb034a-21ab-4d62-b079-ef969a133c83 · outbound

This paper cites an unresolved cited work.

On the notion of a patterning property in model theory Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db7a2ac5-3f08-48df-af1d-d112a7426f36 · outbound

This paper cites an unresolved cited work.

On the notion of a patterning property in model theory Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 668d6ceb-81e5-470b-a18c-6a1dbf3ce303 · outbound

This paper cites Binary simple homogeneous structures are supersimple with finite rank , urldate =.

On the notion of a patterning property in model theory Binary simple homogeneous structures are supersimple with finite rank , urldate =

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0754b4d7-7242-4446-8fad-32ea4d9aeff3 · outbound

This paper cites Simple Homogeneous Structures and Indiscernible Sequence Invariants.

On the notion of a patterning property in model theory Simple Homogeneous Structures and Indiscernible Sequence Invariants

Reference 8

Resolution: metadata mismatch; local_arxiv, observed 2026-07-04T00:09:14.273278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b388c220-a21c-49a9-b143-d4b22be65771 · outbound

This paper cites 1988 , publisher=.

On the notion of a patterning property in model theory 1988 , publisher=

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fcb7f6dd-700b-4d8e-bd41-6d0e76623fb6 · outbound

This paper cites Annals of Pure and Applied Logic , volume =.

On the notion of a patterning property in model theory Annals of Pure and Applied Logic , volume =

Reference 10

Resolution: verified exact; doi, observed 2026-06-26T21:30:02.534376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a274db74-d7bc-4396-9be1-6b1dbd7cf1f4 · outbound

This paper cites Notre Dame Journal of Formal Logic , volume =.

On the notion of a patterning property in model theory Notre Dame Journal of Formal Logic , volume =

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-06-26T21:30:02.540105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 982ed07d-e827-48f2-a660-3cc85e734959 · outbound

This paper cites Proceedings of the American Mathematical Society , volume=.

On the notion of a patterning property in model theory Proceedings of the American Mathematical Society , volume=

Reference 12

Resolution: verified exact; doi, observed 2026-06-26T21:30:02.539042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f496a005-20a0-4821-b896-a520970c2aa9 · outbound

This paper cites Taking model-complete cores.

On the notion of a patterning property in model theory Taking model-complete cores

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-29T02:24:13.612455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9f1ac0ef-fa27-4a39-b020-6cb516b13a15 · outbound

This paper cites Properties of independence in $\mathrm{NSOP}_3$ theories.

On the notion of a patterning property in model theory Properties of independence in $\mathrm{NSOP}_3$ theories

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-07-04T00:09:14.268942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation db6c9565-d64c-4605-a1b6-9feebbab1349 · outbound

This paper cites 2023 , month =.

On the notion of a patterning property in model theory 2023 , month =

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e93868ee-8508-49e4-b5d7-0af280fe11cf · outbound

This paper cites Annals of Pure and Applied Logic , year =.

On the notion of a patterning property in model theory Annals of Pure and Applied Logic , year =

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24c4a927-25d2-4fc8-86c8-bccef5e38285 · outbound

This paper cites 1990 , publisher=.

On the notion of a patterning property in model theory 1990 , publisher=

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2862a109-f89b-4ee3-b547-45de9edad43c · outbound

This paper cites Results on Colored Tree Properties.

On the notion of a patterning property in model theory Results on Colored Tree Properties

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-04T00:09:14.256951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 68347ddd-bcd8-47cc-933c-a99544ef00ff · outbound

This paper cites an unresolved cited work.

On the notion of a patterning property in model theory Unresolved cited work

Reference 19

Resolution: verified exact; doi, observed 2026-06-26T21:30:02.541818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation cf66ce9d-01b1-4492-bf41-78ea6b8648d6 · outbound

This paper cites Archive for Mathematical Logic , volume=.

On the notion of a patterning property in model theory Archive for Mathematical Logic , volume=

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56c166fe-4380-4051-a31a-a26d89be7277 · outbound

This paper cites Journal of the European Mathematical Society 28 (2026), no.

On the notion of a patterning property in model theory Journal of the European Mathematical Society 28 (2026), no

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e878133c-bea5-4fc1-899a-19fd80762ef9 · outbound

This paper cites On what I do not understand (and have something to say), model theory.

On the notion of a patterning property in model theory On what I do not understand (and have something to say), model theory

Reference 22

Resolution: metadata mismatch; local_arxiv, observed 2026-07-04T00:09:14.252938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a0f3c88d-6ad0-4f6a-a6f7-996d8b8b19d3 · outbound

This paper cites Mathematical Logic Quarterly , volume=.

On the notion of a patterning property in model theory Mathematical Logic Quarterly , volume=

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0dfb067c-6727-4d0d-9370-640b6e61760f · outbound

This paper cites Hypergraph regularity and higher arity VC-dimension.

On the notion of a patterning property in model theory Hypergraph regularity and higher arity VC-dimension

Reference 24

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T00:09:14.282889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fc028226-d093-44f6-a635-bfd4dd75ef7f · outbound

This paper cites Higher-order generalizations of stability and arithmetic regularity.

On the notion of a patterning property in model theory Higher-order generalizations of stability and arithmetic regularity

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T00:09:14.265326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f04829ef-53f0-447b-8019-bd258351b43c · outbound

This paper cites Fundamenta Mathematicae , author =.

On the notion of a patterning property in model theory Fundamenta Mathematicae , author =

Reference 26

Resolution: verified exact; doi, observed 2026-06-26T21:30:02.536801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3d2baa86-159a-432d-bc3f-721c1c1109ce · outbound

This paper cites Model-theoretic dividing lines via posets.

On the notion of a patterning property in model theory Model-theoretic dividing lines via posets

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-07-04T00:09:14.286640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 84008e3d-89c2-45ad-b45a-77a8f6131f86 · outbound

This paper cites Trace definability.

On the notion of a patterning property in model theory Trace definability

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a489d96-a4b9-4a3b-a4ab-4409bc80bdd0 · outbound

This paper cites Forum of Mathematics, Sigma , volume=.

On the notion of a patterning property in model theory Forum of Mathematics, Sigma , volume=

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d24b1345-fa16-4f0f-bdc9-4257a45c91fb · outbound

This paper cites an unresolved cited work.

On the notion of a patterning property in model theory Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bc36289-b52e-46c7-bae0-1e77788b8aeb · outbound

This paper cites Definable groups for dependent and 2-dependent theories.

On the notion of a patterning property in model theory Definable groups for dependent and 2-dependent theories

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-07-04T00:09:14.248965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 98a1a822-06b2-46ae-b4f8-b4c3a93e727b · outbound

This paper cites Selecta Mathematica , volume=.

On the notion of a patterning property in model theory Selecta Mathematica , volume=

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d1f72bd-782b-4644-ab3f-66f5b897fb88 · outbound

This paper cites Mathematical Logic Quarterly , author =.

On the notion of a patterning property in model theory Mathematical Logic Quarterly , author =

Reference 33

Resolution: verified exact; doi, observed 2026-06-26T21:30:02.531235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a00975c7-8301-4f08-bfbb-d333fbd1f457 · outbound

This paper cites The Journal of Symbolic Logic , pages=.

On the notion of a patterning property in model theory The Journal of Symbolic Logic , pages=

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13759066-fdcb-45fe-ba16-425cd120add3 · outbound

This paper cites Notre Dame Journal of Formal Logic , year=.

On the notion of a patterning property in model theory Notre Dame Journal of Formal Logic , year=

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6048e603-29b1-42e3-9408-75917d0cf3f6 · outbound

This paper cites Characterization of.

On the notion of a patterning property in model theory Characterization of

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-26T21:29:54.129942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation a381bd3e-79ad-405d-b9fa-a59b30637fd0 · inbound

Some applications of the real strict order property hierarchy cites this paper.

Some applications of the real strict order property hierarchy On the notion of a patterning property in model theory

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-06-30T08:54:29.482719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8c664706-14fd-4c3d-859f-0cdb3503625a · inbound

Some applications of the real strict order property hierarchy cites this paper.

Some applications of the real strict order property hierarchy On the notion of a patterning property in model theory

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-12T11:20:25.093177Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.