Paper Citation Record · LEDGER

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic

As of 22 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2606.01163.

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

pith.paper-citation-record.v1
2606.01163 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T16:13:04.789491Z

measured 29 of 29 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 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

29 of 29 outbound references displayed

verified exact5
verified fuzzy0
unresolved23
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

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Outbound references

Observation 0008d5ca-f44d-4efd-a673-589ec1421184 · outbound

This paper cites Oxford Univer- sity Press (2018).https://doi.org/10.1093/oso/9780198814788.001.0001.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Oxford Univer- sity Press (2018).https://doi.org/10.1093/oso/9780198814788.001.0001

Reference 1

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T16:22:22.685141Z

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 d133ed02-e85f-4d24-bde3-13ccec5470f7 · outbound

This paper cites an unresolved cited work.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Unavailable: canonical work link unavailable.

Observation ff9724bf-3618-4c20-9261-cd19845dbc41 · outbound

This paper cites 2024 , eprint=.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 2024 , eprint=

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation ea300634-4b0e-4f52-9aab-f9d70883e65a · outbound

This paper cites 2025 , eprint=.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 2025 , eprint=

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation 0d596e30-8ea9-48ee-b043-1a7d557ef5f0 · outbound

This paper cites 1963 , journal =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 1963 , journal =

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation 8179fcce-5484-4ab4-808c-93ad61e09591 · outbound

This paper cites 1988 , journal =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 1988 , journal =

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7139b856-6ede-4b2d-8db4-903f60352554 · outbound

This paper cites 1987 , school =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 1987 , school =

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1729ecb-713d-43ce-98dd-f9547107f3a0 · outbound

This paper cites Proceedings of the IEEE 29th Annual Symposium on Foundations of Computer Science , year =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Proceedings of the IEEE 29th Annual Symposium on Foundations of Computer Science , year =

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70e3568b-856b-4d98-8714-7967def85d94 · outbound

This paper cites 1995 , journal =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 1995 , journal =

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a12ed00-5ed9-4bd3-8d63-d80719a2f29b · outbound

This paper cites and Skelley, A.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Skelley, A

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee1dc389-3007-444d-a696-91b523a0fce0 · outbound

This paper cites and Krajíček, J.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Krajíček, J

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e724eca3-2f10-4b7f-9cd3-57a615ff9059 · outbound

This paper cites 1993 , journal =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 1993 , journal =

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Unavailable: canonical work link unavailable.

Observation 19a64753-dbbe-4936-8049-96e056530502 · outbound

This paper cites Feasible mathematics , publisher =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Feasible mathematics , publisher =

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation a76fe8e3-24d3-49e6-bc08-5d0f6960d7f9 · outbound

This paper cites and Wilkie, A.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Wilkie, A

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f51eeb7f-e874-4acc-b035-2b0d0b4083be · outbound

This paper cites an unresolved cited work.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6328b1d7-dddb-4f13-918a-70ba26b947fc · outbound

This paper cites 2019 , publisher=.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic 2019 , publisher=

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a593c49f-85cc-4e34-a9d6-d867689779a6 · outbound

This paper cites A simple proof of the.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic A simple proof of the

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59fd868b-9985-43d1-96d5-4331b6f42bbc · outbound

This paper cites and Krajíček, J.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Krajíček, J

Reference 18

Resolution: verified exact; doi, observed 2026-06-28T16:22:22.681800Z

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 1f75e660-60aa-4f6a-a2fe-5dae1f8b5f05 · outbound

This paper cites Arithmetic, proof theory and computational complexity , pages=.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Arithmetic, proof theory and computational complexity , pages=

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation ce6b62c9-43f8-434d-9b0e-0b3f572980bf · outbound

This paper cites , title =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic , title =

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ab32a1b-b10a-47bc-a507-a4cce9d92451 · outbound

This paper cites and Müller, M.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Müller, M

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6d652fa-2831-4938-a606-530814471b7a · outbound

This paper cites and Vishkin, U.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Vishkin, U

Reference 22

Resolution: verified exact; doi, observed 2026-06-28T16:22:22.671080Z

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 786a80d5-842f-4d42-b625-188c74895d6b · outbound

This paper cites , title =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic , title =

Reference 23

Resolution: verified exact; doi, observed 2026-06-28T16:22:22.678285Z

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 e0866a30-5074-4dc2-b455-4e7ee72e3d7b · outbound

This paper cites On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence

Reference 24

Resolution: verified exact; doi, observed 2026-06-28T16:22:22.673483Z

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 357a9d54-39a2-4d1c-b6ff-ac149931037d · outbound

This paper cites and Thapen, N.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Thapen, N

Reference 25

Resolution: verified exact; doi, observed 2026-06-28T16:22:22.669440Z

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 9242abe0-c575-4158-87c3-b8c24b8d6ec1 · outbound

This paper cites an unresolved cited work.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation b2dfb4ed-7b81-4969-b4c8-baa2c71dc7f3 · outbound

This paper cites Journal of Symbolic Logic , number =.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Journal of Symbolic Logic , number =

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation 3b58614f-fa3a-46b7-b7df-3463cce3c52d · outbound

This paper cites and Ježil, O.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic and Ježil, O

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Observation d99eea8a-ec35-4e94-b987-bd19d8ee4b82 · outbound

This paper cites an unresolved cited work.

Minimization Principle for Polynomial-Time Predicates and Forcing in Bounded Arithmetic Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-28T16:13:04.789491Z

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Pith citing papers

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