Paper Citation Record · LEDGER

Generalised ultracategories and conceptual completeness of geometric logic

As of 11 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2507.07922.

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

pith.paper-citation-record.v1
2507.07922 v3

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:37:40.710819Z

measured 27 of 27 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 2026-08-05T21:03:18.642818Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T02:25:56.279446Z

Reference resolution

25 of 25 outbound references displayed

verified exact1
verified fuzzy23
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f14feec1-b15b-44e1-b02a-7d30cc6aeec0 · outbound

This paper cites Relational algebras.

Generalised ultracategories and conceptual completeness of geometric logic Relational algebras

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.970419Z

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 03e84093-798d-488b-aa00-4cdb10794697 · outbound

This paper cites Th´ eorie formelle des bicat´ egories.Esquisses Math´ emataiques 25, 1976.

Generalised ultracategories and conceptual completeness of geometric logic Th´ eorie formelle des bicat´ egories.Esquisses Math´ emataiques 25, 1976

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.958543Z

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 d8a297e4-aaab-4ff9-8c61-03cc0d2b4040 · outbound

This paper cites Fibred 2-categories and bicategories.Journal of pure and applied algebra, 218(6):1034–1074, 2014.

Generalised ultracategories and conceptual completeness of geometric logic Fibred 2-categories and bicategories.Journal of pure and applied algebra, 218(6):1034–1074, 2014

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.946873Z

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 4cc55c32-dafc-4963-8692-3d65a8ab99fe · outbound

This paper cites Representation of topoi by topological spaces.Journal of Pure and Applied algebra 130 223-235, 1998.

Generalised ultracategories and conceptual completeness of geometric logic Representation of topoi by topological spaces.Journal of Pure and Applied algebra 130 223-235, 1998

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.935549Z

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 bc45b049-4d1d-4429-afd9-2f9461d65ea4 · outbound

This paper cites Topological representation of sheaf cohomology of sites.

Generalised ultracategories and conceptual completeness of geometric logic Topological representation of sheaf cohomology of sites

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.926004Z

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 9a3677cd-a49c-43d7-b9d3-f4199478b4c8 · outbound

This paper cites Oxford University Press, 2018.

Generalised ultracategories and conceptual completeness of geometric logic Oxford University Press, 2018

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.916474Z

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 cdb8c234-c830-4129-864e-6f2b729ddc6a · outbound

This paper cites Homotopy theory and calculus of fraction.Ergebnisse der Mathematik, Bd, 35.

Generalised ultracategories and conceptual completeness of geometric logic Homotopy theory and calculus of fraction.Ergebnisse der Mathematik, Bd, 35

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.906501Z

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 613d2588-fd2a-4902-9c5a-4e4f16cf33bd · outbound

This paper cites Lax colimits and free fibrations in ∞-categories.Documenta Mathematica, 22:1255–1266, 2017.

Generalised ultracategories and conceptual completeness of geometric logic Lax colimits and free fibrations in ∞-categories.Documenta Mathematica, 22:1255–1266, 2017

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.897684Z

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 8e539fba-7300-45e3-a762-c38032a80758 · outbound

This paper cites Bundles of metric structures as left ultrafunctors.arxiv preprinthttps: // arxiv.

Generalised ultracategories and conceptual completeness of geometric logic Bundles of metric structures as left ultrafunctors.arxiv preprinthttps: // arxiv

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.888274Z

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 cfbf1776-7f88-47ad-a330-4aa61cbb56bc · outbound

This paper cites Ultracategories as colax algebras for a pseudo-monad on cat.https: // arxiv.

Generalised ultracategories and conceptual completeness of geometric logic Ultracategories as colax algebras for a pseudo-monad on cat.https: // arxiv

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.877702Z

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 157bde3e-ec31-4a27-9d2c-c5a8bfed04ff · outbound

This paper cites Notes on Lax Ends.

Generalised ultracategories and conceptual completeness of geometric logic Notes on Lax Ends

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:37:40.746256Z

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 e531e33c-dc91-4569-a631-63138472ac6e · outbound

This paper cites When do kan extensions preserve limits/colimits? MathOverflow.

Generalised ultracategories and conceptual completeness of geometric logic When do kan extensions preserve limits/colimits? MathOverflow

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.868102Z

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 dee6556d-0d0f-41df-a119-9a9dc7b8e37f · outbound

This paper cites Oxford University Press, 2002.

Generalised ultracategories and conceptual completeness of geometric logic Oxford University Press, 2002

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.860752Z

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 d8ed727e-c104-4a26-b16e-0c32d797196a · outbound

This paper cites Discrete 2-fibrations.Higher structures Volume 8, Issue 1, 2024.

Generalised ultracategories and conceptual completeness of geometric logic Discrete 2-fibrations.Higher structures Volume 8, Issue 1, 2024

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.852782Z

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 655ca663-d704-432a-8ece-c1b653b975eb · outbound

This paper cites Cambridge University Press, 2021.

Generalised ultracategories and conceptual completeness of geometric logic Cambridge University Press, 2021

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.845652Z

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 56f924aa-cd5c-4cdc-9910-dea4418889b8 · outbound

This paper cites Ultracategories.Preprint available athttps: // www.

Generalised ultracategories and conceptual completeness of geometric logic Ultracategories.Preprint available athttps: // www

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.837560Z

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 e2ecf974-a418-4d4f-a5f4-29e537653ee4 · outbound

This paper cites Sheaves in geometry and logic: A first introduction to topos theory.Universitext.

Generalised ultracategories and conceptual completeness of geometric logic Sheaves in geometry and logic: A first introduction to topos theory.Universitext

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.827272Z

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 203fe849-a7b2-460c-9169-6cf16e80340e · outbound

This paper cites Stone duality for first order logic.Advances in Mathematics, 65(2):97–170, 1987.

Generalised ultracategories and conceptual completeness of geometric logic Stone duality for first order logic.Advances in Mathematics, 65(2):97–170, 1987

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.818624Z

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 98c9d5c5-f77f-48b9-9bf9-b218e46ee605 · outbound

This paper cites Strong conceptual completeness for first-order logic.Annals of Pure and Applied Logic, 40(2):167–215, 1988.

Generalised ultracategories and conceptual completeness of geometric logic Strong conceptual completeness for first-order logic.Annals of Pure and Applied Logic, 40(2):167–215, 1988

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.808921Z

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 0f05b255-9ec3-4864-8a94-94806c3a5ee9 · outbound

This paper cites The classifying topos of a continuous groupoid.

Generalised ultracategories and conceptual completeness of geometric logic The classifying topos of a continuous groupoid

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.798771Z

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 fbf69085-e32f-4459-a8ef-60d750fe51e2 · outbound

This paper cites On product and change of base for toposes.Cahiers de Topologie et G´ eom´ etrie Diff´ erentielle Cat´ egoriques, 26(1):43–61, 1985.

Generalised ultracategories and conceptual completeness of geometric logic On product and change of base for toposes.Cahiers de Topologie et G´ eom´ etrie Diff´ erentielle Cat´ egoriques, 26(1):43–61, 1985

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.789123Z

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 6d16b12c-ccfa-4898-ad22-9d50b51f3fdc · outbound

This paper cites Springer, 1977.

Generalised ultracategories and conceptual completeness of geometric logic Springer, 1977

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.778730Z

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 0d85f0e6-919a-4e40-a4fd-89bc32f836df · outbound

This paper cites Structures in Foundations of Mathematics Padova.

Generalised ultracategories and conceptual completeness of geometric logic Structures in Foundations of Mathematics Padova

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.768486Z

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 1c9b6e4f-65dc-4263-bba5-adafdb662542 · outbound

This paper cites Extending conceptual completeness via virtual ultracategories.

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 58bc5940-7ba8-4689-a173-e479cf701699 · outbound

This paper cites commutativity of products with directed colimits.

Generalised ultracategories and conceptual completeness of geometric logic commutativity of products with directed colimits

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:37:40.758422Z

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.

Pith citing papers

Observation 660c0b71-9d2f-4ff3-b9b6-4f4258249eed · inbound

A Lightweight Learned Cardinality Estimation Model cites this paper.

A Lightweight Learned Cardinality Estimation Model Generalised ultracategories and conceptual completeness of geometric logic

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-05T21:03:18.642818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bacd338-3a6a-4fcf-bd48-dd09cbe7f50d · inbound

Duality theory for categorical theories cites this paper.

Duality theory for categorical theories Generalised ultracategories and conceptual completeness of geometric logic

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-06-09T03:08:00.484291Z

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.