Paper Citation Record · LEDGER

The Complexity of the Constructive Master Modality

As of 12 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2603.05131.

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

pith.paper-citation-record.v1
2603.05131 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T19:02:55.687165Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-09T15:09:25.177414Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T16:46:06.544719Z

Reference resolution

31 of 31 outbound references displayed

verified exact0
verified fuzzy0
unresolved31
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 01238296-00ee-496a-99a2-86091a1ae8fb · outbound

This paper cites Bellin, V.

The Complexity of the Constructive Master Modality Bellin, V

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:53.575164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ae04bad-fe9c-4c15-aa01-64ad5ffb50fd · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:53.679885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ded2eec8-2a7b-4230-ba61-bf0744bb0f7a · outbound

This paper cites Fischer and Richard E.

The Complexity of the Constructive Master Modality Fischer and Richard E

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:53.758352Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5471f4f-aed0-43a9-b122-e47bbc535012 · outbound

This paper cites Leigh, and Lukas Zenger, Intuitionistic master modality, InAdvances in Modal Logic, pages 19–39.

The Complexity of the Constructive Master Modality Leigh, and Lukas Zenger, Intuitionistic master modality, InAdvances in Modal Logic, pages 19–39

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:53.852506Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69a2d4d2-2919-4669-97a2-1383b42c4eac · outbound

This paper cites Schloss Dagstuhl, 2024.

The Complexity of the Constructive Master Modality Schloss Dagstuhl, 2024

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:53.967555Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5720a548-6344-45ca-be47-b7df3c201556 · outbound

This paper cites CSLI Publications, 1996.

The Complexity of the Constructive Master Modality CSLI Publications, 1996

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:53.998424Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e22da68a-480c-4e4b-ad70-cb8ba27126b0 · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.070417Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70e9b28a-dd45-4c8c-963c-d971d119053f · outbound

This paper cites Fitch,Intuitionistic modal logic with quantifiers.Portugaliae Mathematica, 7(2):113–118, 1948.

The Complexity of the Constructive Master Modality Fitch,Intuitionistic modal logic with quantifiers.Portugaliae Mathematica, 7(2):113–118, 1948

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.148251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78b6b03b-2a50-4f5f-bd50-837ca11c8248 · outbound

This paper cites Zakharyaschev,The relation between intuitionistic and classical modal logics.Algebra and Logic, 36(2):73–92, 1997.

The Complexity of the Constructive Master Modality Zakharyaschev,The relation between intuitionistic and classical modal logics.Algebra and Logic, 36(2):73–92, 1997

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.213382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20992421-f84c-4dbb-bd52-01c0f85d78e8 · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.288765Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a489a72f-8965-4c7f-8e59-df9d92f58b4a · outbound

This paper cites ACM, 1996.

The Complexity of the Constructive Master Modality ACM, 1996

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.361823Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16395d23-0922-4001-af81-fdaf167bdfd5 · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.450304Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80df6c6c-8124-4977-9db3-eda7eb5fbd51 · outbound

This paper cites Boudou, M.

The Complexity of the Constructive Master Modality Boudou, M

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.573056Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b8e65c6-f044-4886-b9ca-27e6ce6b9839 · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.623121Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1bac32b0-bbf6-4e86-b595-ec62faedb2cc · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.733116Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f54d2bf-3457-477c-a7d4-e7023922fc7c · outbound

This paper cites Pratt,A near-optimal method for reasoning about action, In Journal of Computer and System Sciences, 20(2):231–254, 1980.

The Complexity of the Constructive Master Modality Pratt,A near-optimal method for reasoning about action, In Journal of Computer and System Sciences, 20(2):231–254, 1980

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.793046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 268cf6a2-6f82-496b-971c-af8151c380b7 · outbound

This paper cites Nishimura,Semantical analysis of constructive PDL, InPublications of the Research Institute for Mathematical Sciences, 18:427–438, 1982.

The Complexity of the Constructive Master Modality Nishimura,Semantical analysis of constructive PDL, InPublications of the Research Institute for Mathematical Sciences, 18:427–438, 1982

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.913168Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a099d0cf-5e1b-4850-8277-1af69dde03a2 · outbound

This paper cites Degen and J.

The Complexity of the Constructive Master Modality Degen and J

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:54.997401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14b5ed68-4857-4ca1-af4a-472dbeae4fbc · outbound

This paper cites Springer, 2001.

The Complexity of the Constructive Master Modality Springer, 2001

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.039851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f143e37d-1835-40c3-ab0d-fed43495c5c6 · outbound

This paper cites IEEE, 2021.

The Complexity of the Constructive Master Modality IEEE, 2021

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.099944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4095a5b-401b-437c-a12e-da59cb4cd89a · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.184225Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a8ab7b7-9161-4db7-97df-8aa351bd0d5d · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.248804Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e661b6d-011e-411a-9efd-6995231f2e07 · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.300470Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70fca28e-d001-43a9-b5fb-1259ec377738 · outbound

This paper cites Oxford University Press, 2001.

The Complexity of the Constructive Master Modality Oxford University Press, 2001

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.346792Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49fc6054-7bb2-4fc7-a6f0-b348d385da18 · outbound

This paper cites an unresolved cited work.

The Complexity of the Constructive Master Modality Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.392584Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0ccc208-bb43-4887-80d9-96fcd1d35ea1 · outbound

This paper cites Constructive S4 modal logics with the finite birelational frame property.

The Complexity of the Constructive Master Modality Constructive S4 modal logics with the finite birelational frame property

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.451488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 100a2b6e-9755-49fc-871c-bd33a6a3dcb4 · outbound

This paper cites Appendix This appendix gathers the technical and straightforward proofs omitted from the main exposition.

The Complexity of the Constructive Master Modality Appendix This appendix gathers the technical and straightforward proofs omitted from the main exposition

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.510684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9178fdcc-27df-4050-949d-08294975d6ca · outbound

This paper cites Ifp /∈Var(φ), this holds trivially, since∥⊥∥ CK φ =∥ω P(φ) (⊥)∥=∥p∥ CK φ.

The Complexity of the Constructive Master Modality Ifp /∈Var(φ), this holds trivially, since∥⊥∥ CK φ =∥ω P(φ) (⊥)∥=∥p∥ CK φ

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.569825Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68b001f3-000d-408b-9f42-9bdfc1f589a3 · outbound

This paper cites Ifp∈Var(φ), thenw∈ ∥p∥ CK φ =∥p∥, and the atomic persistence ofMimpliesv∈ ∥p∥=∥p∥ CK φ.

The Complexity of the Constructive Master Modality Ifp∈Var(φ), thenw∈ ∥p∥ CK φ =∥p∥, and the atomic persistence ofMimpliesv∈ ∥p∥=∥p∥ CK φ

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.617999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01504ca6-df60-44a8-bab5-efc326962d6d · outbound

This paper cites By definition,w∈ ∥□ ∗(V P(φ)∧ ♢p⊥)∥implies that for allu, ifw(≼;R ∗)∗u, thenu∈ ∥ V P(φ)∧♢p ⊥∥.

The Complexity of the Constructive Master Modality By definition,w∈ ∥□ ∗(V P(φ)∧ ♢p⊥)∥implies that for allu, ifw(≼;R ∗)∗u, thenu∈ ∥ V P(φ)∧♢p ⊥∥

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.647034Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfd6a6dc-025c-4337-845a-f065721d1bfb · outbound

This paper cites 19 C Detailed proofs of the translation fromWK ∗ toPDL Proposition 5.3.LetMbe aWK-model andφ∈ L ∗.

The Complexity of the Constructive Master Modality 19 C Detailed proofs of the translation fromWK ∗ toPDL Proposition 5.3.LetMbe aWK-model andφ∈ L ∗

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-02T19:02:55.687165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 78e561f9-2269-47a6-b9fa-7fca17e7268f · inbound

Intuitionistic Common Knowledge cites this paper.

Intuitionistic Common Knowledge The Complexity of the Constructive Master Modality

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-22T03:22:05.647737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.