Paper Citation Record · LEDGER

Extending conceptual completeness via virtual ultracategories

As of 21 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 3 inbound Pith citation observations for arXiv:2506.23935.

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

pith.paper-citation-record.v1
2506.23935 v1

Coverage vector

measured 9 of 9 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:05:33.529758Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:37:40.707674Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T02:25:56.270106Z

Reference resolution

9 of 9 outbound references displayed

verified exact2
verified fuzzy2
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b6ecb050-b78b-4ab3-b686-27ae7fd33aca · outbound

This paper cites The classifying topos of a continuous groupoid. I.

Extending conceptual completeness via virtual ultracategories The classifying topos of a continuous groupoid. I

Reference 10

Resolution: verified exact; doi, observed 2026-08-06T22:05:33.738537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1be5ea89-9c8b-4d5d-9bd4-9ad9b434230c · outbound

This paper cites A unified framework for generalized multicategories.

Extending conceptual completeness via virtual ultracategories A unified framework for generalized multicategories

Reference 1970

Resolution: unresolved; no resolver link, observed 2026-08-06T22:05:32.969947Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7f11119-83f0-42e4-bb65-e00c10c573bc · outbound

This paper cites Functors which preserve elementary operations.

Extending conceptual completeness via virtual ultracategories Functors which preserve elementary operations

Reference 1977

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:05:34.439292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 40a3bc19-e6a7-4650-bf25-984281e5f00b · outbound

This paper cites Beck’s theorem for pseudo-monads.

Extending conceptual completeness via virtual ultracategories Beck’s theorem for pseudo-monads

Reference 2010

Resolution: unresolved; no resolver link, observed 2026-08-06T22:05:33.195329Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6af5900a-4d44-476b-8dd1-41538a864dff · outbound

This paper cites Stone duality for first order logic.

Extending conceptual completeness via virtual ultracategories Stone duality for first order logic

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:05:34.311212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a06d48cb-e9d1-431e-ac25-90f7d1156d1a · outbound

This paper cites The geometry of Coherent topoi and Ultrastructures.

Extending conceptual completeness via virtual ultracategories The geometry of Coherent topoi and Ultrastructures

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-06T22:05:33.011093Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec91aa26-d735-4ab7-8de1-246b2566425d · outbound

This paper cites On topological groupoids that represent theories.

Extending conceptual completeness via virtual ultracategories On topological groupoids that represent theories

Reference 2023

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T22:05:33.861254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0de58ee2-55fc-4990-b433-774da16a4eff · outbound

This paper cites Proper base change for separated locally proper maps.

Extending conceptual completeness via virtual ultracategories Proper base change for separated locally proper maps

Reference 2024

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T22:05:34.017619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b7e2cb47-1b38-4af8-b582-c0ecc60f5052 · outbound

This paper cites Ultracategories as colax algebras for a pseudo-monad on CAT.

Extending conceptual completeness via virtual ultracategories Ultracategories as colax algebras for a pseudo-monad on CAT

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:05:34.150802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation 1c9b6e4f-65dc-4263-bba5-adafdb662542 · inbound

Generalised ultracategories and conceptual completeness of geometric logic cites this paper.

Generalised ultracategories and conceptual completeness of geometric logic Extending conceptual completeness via virtual ultracategories

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T18:37:40.707674Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1470b4de-a811-4062-8e26-dfbbc849051b · inbound

A Lightweight Learned Cardinality Estimation Model cites this paper.

A Lightweight Learned Cardinality Estimation Model Extending conceptual completeness via virtual ultracategories

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-05T21:03:18.653854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03b729e8-fbc6-4567-a906-ce37f411642c · inbound

Duality theory for categorical theories cites this paper.

Duality theory for categorical theories Extending conceptual completeness via virtual ultracategories

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-22T02:25:56.272831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.