Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:33:00.802846Z
Paper Citation Record · LEDGER
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy
As of 18 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2506.19792.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
29 of 29 outbound references displayed
- verified exact4
- verified fuzzy20
- unresolved5
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 59dc5ea7-4f46-40f6-bd63-42dfff87893e · outbound
This paper cites Quantum Hamiltonian complexity and the detectability lemma.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Quantum Hamiltonian complexity and the detectability lemma
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T18:33:00.676598Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 59e47b21-468f-4a77-8336-66e0a35902d6 · outbound
This paper cites The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T18:33:00.681621Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b701f401-3a14-43d4-a12a-bacfd22e552c · outbound
This paper cites Brand \ a o, and Or Sattath.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Brand \ a o, and Or Sattath
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.373769Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3696e7a2-0431-4d3f-b157-ec425edc62ae · outbound
This paper cites Quantum polynomial hierarchies: Karp-lipton, error reduction, and lower bounds.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Quantum polynomial hierarchies: Karp-lipton, error reduction, and lower bounds
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.359730Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 6cce9623-4f78-463a-a62a-7da1f0e645fa · outbound
This paper cites an unresolved cited work.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Unresolved cited work
Reference 5
- Resolution
- verified exact
- raw_fallback, observed 2026-08-15T18:33:01.009635Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 12421000-e90c-43ad-97dc-3c927afd3358 · outbound
This paper cites Proof verification and the hardness of approximation problems.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Proof verification and the hardness of approximation problems
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.346399Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fc1b2677-70f6-4ea5-aa62-150ca5c3220b · outbound
This paper cites Trading group theory for randomness.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Trading group theory for randomness
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.333147Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 76f6a4ea-0ee2-403e-865c-fb8ba4eb6f8c · outbound
This paper cites Non-deterministic exponential time has two-prover interactive protocols.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Non-deterministic exponential time has two-prover interactive protocols
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.319437Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ad293a2c-55be-45af-abd5-c7e3734f4bbb · outbound
This paper cites Classical versus quantum queries in quantum PCPs with classical proofs.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Classical versus quantum queries in quantum PCPs with classical proofs
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T18:33:00.925681Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dd593526-2f2d-41be-8113-611b6b35727d · outbound
This paper cites Quantum PCPs: on Adaptivity, Multiple Provers and Reductions to Local Hamiltonians.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Quantum PCPs: on Adaptivity, Multiple Provers and Reductions to Local Hamiltonians
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T18:33:00.716723Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1329368e-7bb6-43f0-8a39-eb58b0deab6f · outbound
This paper cites Interactive proofs and the hardness of approximating cliques.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Interactive proofs and the hardness of approximating cliques
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.304507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 76dfcafe-5115-4983-8e8f-22fa8377ca03 · outbound
This paper cites A Collapsible Polynomial Hierarchy for Promise Problems.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy A Collapsible Polynomial Hierarchy for Promise Problems
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T18:33:00.890336Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c70e702b-9cab-42c2-aafe-528e5d574b2a · outbound
This paper cites Hardness of approximation for quantum problems.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Hardness of approximation for quantum problems
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.290868Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 892b3346-a2ee-4bb6-bb3b-873014f091e9 · outbound
This paper cites The knowledge complexity of interactive proof-systems.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy The knowledge complexity of interactive proof-systems
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.276668Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 535afbd7-aff9-4f6d-88b9-7d024b52a060 · outbound
This paper cites Quantum generalizations of the polynomial hierarchy with applications to qma(2).
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Quantum generalizations of the polynomial hierarchy with applications to qma(2)
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.259939Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 23c77106-526a-4103-a7c2-e51fe9537d5d · outbound
This paper cites The entangled quantum polynomial hierarchy collapses.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy The entangled quantum polynomial hierarchy collapses
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.240331Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2929f435-7f92-4c6c-a079-98eed1bb86a8 · outbound
This paper cites Quantum search-to-decision reductions and the state synthesis problem.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Quantum search-to-decision reductions and the state synthesis problem
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.227971Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1970b282-3cdb-496b-9e9a-f6e840c485ec · outbound
This paper cites Mip* = re.
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.215294Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ef93d6ea-b5fc-494b-9594-20e98bb775f8 · outbound
This paper cites Parallel approximation of non-interactive zero-sum quantum games.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Parallel approximation of non-interactive zero-sum quantum games
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.198310Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 06fc7ec7-7d99-42e1-8900-196ed6a1a7db · outbound
This paper cites Karp and Richard J.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Karp and Richard J
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.182946Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 33306171-674c-47e7-96df-a075a89d0aec · outbound
This paper cites Quantum State Isomorphism.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Quantum State Isomorphism
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T18:33:00.765369Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 31a832f2-bd38-4207-ba55-7d10b46e0e10 · outbound
This paper cites Milman M.
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.165368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fc7ce858-b894-469e-8d8e-7f4d08bd5081 · outbound
This paper cites A parallel repetition theorem.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy A parallel repetition theorem
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.142735Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation db667a95-787f-4648-b46f-285beb1a5c82 · outbound
This paper cites Ip = pspace.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Ip = pspace
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.126827Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 01a53989-2763-4c80-b784-6f1db132a2da · outbound
This paper cites On general minimax theorems.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy On general minimax theorems
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.107735Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 520119d1-7a24-4ed7-9f48-171aaa09cda5 · outbound
This paper cites A quantum polynomial hierarchy and a simple proof of vyalyi's theorem.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy A quantum polynomial hierarchy and a simple proof of vyalyi's theorem
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.092620Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7c9fa91b-8f0c-45ee-9050-b71eb04f3e71 · outbound
This paper cites Valiant and Vijay V.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Valiant and Vijay V
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T18:33:01.071904Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 00a4717b-edfe-42ab-8c99-8d5f09f73087 · outbound
This paper cites The Theory of Quantum Information.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy The Theory of Quantum Information
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T18:33:00.797930Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 87e5b2fe-53d4-4045-95d9-3ac52177f45d · outbound
This paper cites Quantum NP and a Quantum Hierarchy.
Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy Quantum NP and a Quantum Hierarchy
Reference 29
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T18:33:00.854293Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
No inbound Pith citation observations are available.