Paper Citation Record · LEDGER

Complexity of Unambiguous Problems in $\Sigma^P_2$

As of 12 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2510.19084.

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

pith.paper-citation-record.v1
2510.19084 v3

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T08:53:07.433451Z

measured 41 of 41 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.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

41 of 41 outbound references displayed

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unresolved41
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 51f15471-d191-4995-8322-34846cfef350 · outbound

This paper cites The computational complexity of structure-based causality.

Complexity of Unambiguous Problems in $\Sigma^P_2$ The computational complexity of structure-based causality

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:02.939202Z

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Observation 63f05231-64c9-45ca-91fc-f519f81cfe28 · outbound

This paper cites Generalized intransitive dice: Mimicking an arbitrary tournament.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Generalized intransitive dice: Mimicking an arbitrary tournament

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.007697Z

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Observation b65ed237-0b87-41c5-9e5c-1ba156024692 · outbound

This paper cites Trading group theory for randomness.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Trading group theory for randomness

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.092369Z

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Observation a8ea4812-9c3a-4677-b62a-30d1bc45a670 · outbound

This paper cites Finding and recognizing popular coalition structures.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Finding and recognizing popular coalition structures

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.166270Z

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Observation d321ed16-918f-40fc-b65a-751ad015b4ae · outbound

This paper cites On the unique satisfiability problem.

Complexity of Unambiguous Problems in $\Sigma^P_2$ On the unique satisfiability problem

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.260147Z

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Observation 7bfd7497-7ce0-4f79-91c3-a5e06cacc698 · outbound

This paper cites Settling the complexity of popularity in additively separable and fractional hedonic games.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Settling the complexity of popularity in additively separable and fractional hedonic games

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.361937Z

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Observation 8edcb165-fe61-41d5-a95c-38510a3a4631 · outbound

This paper cites Does co-np have short interactive proofs? Information Processing Letters , 25(2):127--132, 1987.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Does co-np have short interactive proofs? Information Processing Letters , 25(2):127--132, 1987

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.423674Z

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Observation b59dacbe-37c7-4319-a3a0-8e9fd22f396d · outbound

This paper cites The stability of hedonic coalition structures.

Complexity of Unambiguous Problems in $\Sigma^P_2$ The stability of hedonic coalition structures

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.470177Z

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Observation 9da5ea63-5c6c-49c1-bf2f-cbd04bdf4fae · outbound

This paper cites S ^p_2 ZPP ^ NP.

Complexity of Unambiguous Problems in $\Sigma^P_2$ S ^p_2 ZPP ^ NP

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.538269Z

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Observation 5443f105-80ba-4a34-bfd4-021d281c1722 · outbound

This paper cites More on BPP and the polynomial-time hierarchy.

Complexity of Unambiguous Problems in $\Sigma^P_2$ More on BPP and the polynomial-time hierarchy

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.596362Z

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Observation 5ca8b879-80cb-4d21-ac18-5b96d1c34a37 · outbound

This paper cites A central limit theorem for intransitive dice.

Complexity of Unambiguous Problems in $\Sigma^P_2$ A central limit theorem for intransitive dice

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.699403Z

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Observation 0c8e318b-83d8-4e4d-8b3b-5e65dd601ec1 · outbound

This paper cites Intransitive dice tournament is not quasirandom.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Intransitive dice tournament is not quasirandom

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.772379Z

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Observation 7f5efb14-dd17-430e-b17d-1fedf139c10d · outbound

This paper cites Symmetric exponential time requires near-maximum circuit size.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Symmetric exponential time requires near-maximum circuit size

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.871990Z

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Observation a945b2a6-af31-49b9-b2c7-7c741ab777ac · outbound

This paper cites The complexity of theorem-proving procedures.

Complexity of Unambiguous Problems in $\Sigma^P_2$ The complexity of theorem-proving procedures

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:03.957211Z

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Observation fc2d1007-7559-438a-95ec-b66af6322cd3 · outbound

This paper cites Essai sur l'application de l'analyse \`a la probabilit \'e des d \'e cisions rendues \`a la pluralit \'e des voix.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Essai sur l'application de l'analyse \`a la probabilit \'e des d \'e cisions rendues \`a la pluralit \'e des voix

Reference 15

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Observation 9e21702d-924b-4b64-93ab-4316c41cdd40 · outbound

This paper cites On the representation of directed graphs as unions of orderings.

Complexity of Unambiguous Problems in $\Sigma^P_2$ On the representation of directed graphs as unions of orderings

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:04.108210Z

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Observation 321967db-4419-431b-af7e-deb9186eee45 · outbound

This paper cites Paradox of nontransitive dice and elusive principle of indifference.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Paradox of nontransitive dice and elusive principle of indifference

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:04.299245Z

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Observation a6a1dbea-b0d0-46ac-9cee-bfd8876b5da5 · outbound

This paper cites Match making: assignments based on bilateral preferences.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Match making: assignments based on bilateral preferences

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:04.453280Z

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Observation e32d3710-29cb-416f-b47f-84cfb394cd04 · outbound

This paper cites Complexity measures for public-key cryptosystems.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Complexity measures for public-key cryptosystems

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:04.636457Z

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Observation 9db96e4c-ba94-4f4b-b065-c3447de8d8e9 · outbound

This paper cites On isomorphisms and density of NP and other complete sets.

Complexity of Unambiguous Problems in $\Sigma^P_2$ On isomorphisms and density of NP and other complete sets

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:04.722872Z

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Observation 5be3d1f6-066a-4d35-afe7-3185b8d16bea · outbound

This paper cites A game of nontransitive dice.

Complexity of Unambiguous Problems in $\Sigma^P_2$ A game of nontransitive dice

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:04.793335Z

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Observation 2211aa3c-08d8-4d51-9b03-c3864c409f01 · outbound

This paper cites Deciding the winner in parity games is in UP co- UP.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Deciding the winner in parity games is in UP co- UP

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:04.915785Z

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Observation e5dc1f7a-6cf7-4831-8a77-9e26debc93ad · outbound

This paper cites Total functions in the polynomial hierarchy.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Total functions in the polynomial hierarchy

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:05.013257Z

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Observation 2ce52f1f-9321-48c6-90f1-8b24e18f80db · outbound

This paper cites Range avoidance and the complexity of explicit constructions.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Range avoidance and the complexity of explicit constructions

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:05.100062Z

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Observation 8918e15e-2e17-40fd-9842-d634467f5639 · outbound

This paper cites The complexity of optimization problems.

Complexity of Unambiguous Problems in $\Sigma^P_2$ The complexity of optimization problems

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:05.284532Z

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Observation a475b21d-03ab-4893-ac72-9ad5d6ca3db1 · outbound

This paper cites Symmetric exponential time requires near-maximum circuit size: Simplified, truly uniform.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Symmetric exponential time requires near-maximum circuit size: Simplified, truly uniform

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:05.426373Z

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Observation cb1ef772-d7e0-4340-8965-130547cd008a · outbound

This paper cites Unambiguous polynomial hierarchies and exponential size.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Unambiguous polynomial hierarchies and exponential size

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:05.546727Z

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Observation fa73017e-c5e5-440c-9f50-65fead9d9bf9 · outbound

This paper cites Unambiguous computations and locally definable acceptance types.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Unambiguous computations and locally definable acceptance types

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:05.654631Z

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Observation 2a09e7ec-76aa-4695-8a74-34f0253fd11c · outbound

This paper cites On the complexity of unique solutions.

Complexity of Unambiguous Problems in $\Sigma^P_2$ On the complexity of unique solutions

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:05.768459Z

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Observation a6af9ac6-a01c-4def-9e18-5f67eab944d5 · outbound

This paper cites Computational Complexity.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Computational Complexity

Reference 30

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Observation 2d80a908-5098-4b78-bf0c-dfe065c0e820 · outbound

This paper cites The complexity of facets (and some facets of complexity).

Complexity of Unambiguous Problems in $\Sigma^P_2$ The complexity of facets (and some facets of complexity)

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:06.052535Z

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Observation 3260e62b-40dc-4f5d-88e9-2482d044a2af · outbound

This paper cites Domination and irredundance in tournaments.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Domination and irredundance in tournaments

Reference 32

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Observation b1b0ea68-ce4e-4332-8804-1c7b5a4c4aaf · outbound

This paper cites Symmetric alternation captures BPP.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Symmetric alternation captures BPP

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:06.304735Z

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Observation db604a3a-d32b-4170-8abb-53360784e0d5 · outbound

This paper cites Balanced Non-Transitive Dice II: Tournaments.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Balanced Non-Transitive Dice II: Tournaments

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:06.449164Z

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Observation 246206a7-561c-4cc0-aed5-32c69f9203c3 · outbound

This paper cites On the difference between one and many: preliminary version.

Complexity of Unambiguous Problems in $\Sigma^P_2$ On the difference between one and many: preliminary version

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:06.543210Z

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Observation e96ccaeb-e604-4065-92e3-9787cc8b6ce8 · outbound

This paper cites The voting problem.

Complexity of Unambiguous Problems in $\Sigma^P_2$ The voting problem

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:06.710090Z

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Observation 517a8d4f-7d78-4cd2-8fbb-ccde36ce531f · outbound

This paper cites The polynomial-time hierarchy.

Complexity of Unambiguous Problems in $\Sigma^P_2$ The polynomial-time hierarchy

Reference 37

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Observation 6f136885-3ad5-407c-a85b-ff818889c54e · outbound

This paper cites A reduction from satisfiability to hamiltonian circuits that preserves the number of solutions.

Complexity of Unambiguous Problems in $\Sigma^P_2$ A reduction from satisfiability to hamiltonian circuits that preserves the number of solutions

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:07.030650Z

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Observation fde15dbb-5941-448a-8ad9-32822ec2910d · outbound

This paper cites Relative complexity of checking and evaluating.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Relative complexity of checking and evaluating

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:07.161705Z

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Observation 9164ec6d-c78c-49ba-9121-a5f78666aa65 · outbound

This paper cites NP is as easy as detecting unique solutions.

Complexity of Unambiguous Problems in $\Sigma^P_2$ NP is as easy as detecting unique solutions

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T08:53:07.326670Z

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Observation 34115b94-01f6-4183-bbcf-4ef7bc68853e · outbound

This paper cites Complete sets and the polynomial-time hierarchy.

Complexity of Unambiguous Problems in $\Sigma^P_2$ Complete sets and the polynomial-time hierarchy

Reference 41

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