Paper Citation Record · LEDGER

Extending orders to types

As of 8 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2509.09623.

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

pith.paper-citation-record.v1
2509.09623 v2

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T19:08:02.795252Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

14 of 14 outbound references displayed

verified exact0
verified fuzzy0
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation eaf67802-e9f7-47fa-bdc7-6a787d132c8c · outbound

This paper cites Countable ultraproducts without CH.

Extending orders to types Countable ultraproducts without CH

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.158583Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4b5f858-10a0-4286-a742-68aaffde97f3 · outbound

This paper cites Self-divisible ultrafilters and congruences in Z.

Extending orders to types Self-divisible ultrafilters and congruences in Z

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.189619Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6ce8272-533d-4afe-adb3-a04f7005dd00 · outbound

This paper cites Definably complete Baire structures.

Extending orders to types Definably complete Baire structures

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.329275Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 320c32bd-0530-433e-b8ef-4a56514c950e · outbound

This paper cites An analogue of the Baire category theorem.

Extending orders to types An analogue of the Baire category theorem

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.465595Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4525ef10-71e5-4d72-be79-b48b337222fd · outbound

This paper cites Definability patterns and their symmetries.

Extending orders to types Definability patterns and their symmetries

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.552047Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 683f0bc4-8abc-4fce-99bd-493c5c25c7f7 · outbound

This paper cites Algebra in the Stone- Cech Compactification : Theory and Applications.

Extending orders to types Algebra in the Stone- Cech Compactification : Theory and Applications

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.643787Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 97a0d184-91c9-4c34-be0f-b01549c2476c · outbound

This paper cites Nonstandard characterisations of tensor products and monads in the theory of ultrafilters.

Extending orders to types Nonstandard characterisations of tensor products and monads in the theory of ultrafilters

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.732804Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b59ad8d-8bac-4f06-be4e-6830d6dfeedd · outbound

This paper cites Expansions of dense linear orders with the intermediate value property.

Extending orders to types Expansions of dense linear orders with the intermediate value property

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.779338Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1dfcb147-d6f3-41e4-b0e0-a6f583a907cb · outbound

This paper cites Poliakov and Denis I.

Extending orders to types Poliakov and Denis I

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.782269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4fde3fc-2d97-4d0c-9a03-f4566b0a9fe2 · outbound

This paper cites Non-isomorphic hyper-real fields from non-isomorphic ultrapowers.

Extending orders to types Non-isomorphic hyper-real fields from non-isomorphic ultrapowers

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.784858Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 276286e6-f595-4d3d-9c05-4f26cebada11 · outbound

This paper cites Saveliev.

Extending orders to types Saveliev

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.787453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52263e41-1001-4d51-a869-6591ddaecbb9 · outbound

This paper cites Congruence of ultrafilters.

Extending orders to types Congruence of ultrafilters

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.789961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3beec030-d090-44d1-a79f-e9b27054bc28 · outbound

This paper cites $\widetilde{\mid}\hspace{1mm}$-divisibility of ultrafilters II: The big picture.

Extending orders to types $\widetilde{\mid}\hspace{1mm}$-divisibility of ultrafilters II: The big picture

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.792506Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 114c0e9e-abc5-4e24-9b5c-79dcf69be59a · outbound

This paper cites Divisibility classes of ultrafilters and their patterns.

Extending orders to types Divisibility classes of ultrafilters and their patterns

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T19:08:02.795252Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.