Paper Citation Record · LEDGER

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods

As of 12 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2607.07723.

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

pith.paper-citation-record.v1
2607.07723 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T22:36:35.074344Z

measured 25 of 25 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 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

25 of 25 outbound references displayed

verified exact0
verified fuzzy0
unresolved24
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0909728a-8159-4265-8fd3-4f5f3f39fb89 · outbound

This paper cites Algebrization: A new barrier in com- plexity theory.ACM Transactions on Computation Theory, 1(1):2:1–2:54, 2009.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Algebrization: A new barrier in com- plexity theory.ACM Transactions on Computation Theory, 1(1):2:1–2:54, 2009

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5525dc70-819c-42fa-a360-6b8533a49f5d · outbound

This paper cites Cambridge University Press, 2009.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Cambridge University Press, 2009

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d963cc4-064c-4ede-8d5f-0f4180c9e2db · outbound

This paper cites Relativizations of the p = ? np question.SIAM Journal on Computing, 4(4):431–442, 1975.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Relativizations of the p = ? np question.SIAM Journal on Computing, 4(4):431–442, 1975

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c8401fe-f624-49fe-b7f1-4b2870cb4ae6 · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4803f53e-cb85-4eef-93d2-71520d0d1f3a · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7d1d299-b0b2-46a4-8334-52ae3b0519ae · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7450ce1b-300b-4943-9b29-a66fa112c21c · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 222c1990-fcad-4eca-90c2-0663793d8b3b · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da948800-0ef1-4c3f-b434-55ccdc6b86de · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f323529-d9f3-4648-ab13-a81286c67c08 · outbound

This paper cites The status of the p versus np problem.Communications of the ACM, 52(9):78–86, 2009.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods The status of the p versus np problem.Communications of the ACM, 52(9):78–86, 2009

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation faff940e-d94f-43c8-80cb-06add80fe2c9 · outbound

This paper cites Cambridge University Press, 2008.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Cambridge University Press, 2008

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfa88d1b-1a58-4574-a423-c2eabe32151d · outbound

This paper cites Hopcroft, Rajeev Motwani, and Jeffrey D.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Hopcroft, Rajeev Motwani, and Jeffrey D

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 434bc4af-bf35-45b6-a1d1-a39971a3df7c · outbound

This paper cites A personal view of average-case complexity.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods A personal view of average-case complexity

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9e4aacb-7dd7-41fd-bfdd-fd1954743f35 · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a07dc8dd-e10a-4c29-9784-38f79dc5afcc · outbound

This paper cites Papadimitriou.Computational Complexity.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Papadimitriou.Computational Complexity

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c01137a-909c-476b-bf3b-20149af59421 · outbound

This paper cites Razborov and Steven Rudich.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Razborov and Steven Rudich

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f16402e-988d-4d2f-85a5-1616493e6725 · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fb6411e-a141-4479-93ba-38ee5e65338b · outbound

This paper cites MIT Press, 1987.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods MIT Press, 1987

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5c63f09-4b70-481d-b520-9c8cbff8db99 · outbound

This paper cites Cengage Learn- ing, 3rd edition, 2012.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Cengage Learn- ing, 3rd edition, 2012

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 147aabc3-ec9b-461d-8985-000eb3050d17 · outbound

This paper cites Rice applies to arbitrary programs given as input, but a proof about a single fixed programx 0 does not analyse arbitrary programs.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Rice applies to arbitrary programs given as input, but a proof about a single fixed programx 0 does not analyse arbitrary programs

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1da3fe66-7615-4a29-8037-78beafb37405 · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7fec17ba-e281-46c9-bb5e-529987c3eba5 · outbound

This paper cites The barrier identifies the same structural condition as for relativisa- tion, applied to a richer class of non-simulable resources.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods The barrier identifies the same structural condition as for relativisa- tion, applied to a richer class of non-simulable resources

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36e5d53c-465e-44f6-85f4-17f351aa0a23 · outbound

This paper cites an unresolved cited work.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 693777ee-9203-413f-8d32-2018168eb885 · outbound

This paper cites The barrier identifies this directly.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods The barrier identifies this directly

Reference 24

Resolution: malformed identifier; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 993a2e35-6d03-4c57-b057-cd63b7712cb5 · outbound

This paper cites A 31 perfect observer would need to refine each indistinguishability class into indi- vidually discriminable behaviours.

Limits of Uniform Certification in the Standard Turing Model -- Semantic Invariants and Admissible Methods A 31 perfect observer would need to refine each indistinguishability class into indi- vidually discriminable behaviours

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-11T22:36:35.074344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.