Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T21:43:17.092404Z
Paper Citation Record · LEDGER
As of 21 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 0 inbound Pith citation observations for arXiv:2505.09282.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T21:43:17.092404Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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
68 of 68 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 41014f5d-edfa-4798-a126-fbaead01b371 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 1
Source-reported events for the cited work
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Observation 337b4c6f-f374-41d7-82a2-17fe7b9d8f9a · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 2
Source-reported events for the cited work
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Observation 303c1c03-080c-4c58-94bb-9a243ead59c9 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 3
Source-reported events for the cited work
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Observation 2bd9ff31-3a3c-4803-afe8-5ad386f8aeda · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets This can occur, however, only for at most an exponentially small fraction of strings
Reference 4
Source-reported events for the cited work
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Observation 3134bfd5-5022-413a-a330-73d4cf1a2361 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 5
Source-reported events for the cited work
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Observation a6786f07-39b2-4ec2-aea5-a4e40fe8e968 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Example Functions Meeting the Requirements ofPoly The condition in Eqn
Reference 6
Source-reported events for the cited work
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Observation 8c15cc25-1856-4583-aa93-ccac92d6d484 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 7
Source-reported events for the cited work
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Observation 27285e9c-6d6a-4aa8-a1b2-55dfb8d7bc28 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 8
Source-reported events for the cited work
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Observation 98364264-5ff8-4fed-91f9-a1e06738a9b7 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Call the outputs{S j} |Pp| j=1 and assumeS 0 is the BQP-device’s solution top
Reference 9
Source-reported events for the cited work
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Observation fb0c33fa-d9cf-4cac-b098-40438ac7416e · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets ACKNOWLEDGEMENTS The author acknowledges the support of the Quantum Ad- vantage Pathfinder (EP/X026167/1)
Reference 10
Source-reported events for the cited work
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Observation 15000058-c65c-465d-ad95-dd3bcb299135 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Arora and B
Reference 11
Source-reported events for the cited work
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Observation f8ea87cb-8563-4aaf-82ad-b0a9e2b4ba71 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Dean, Computational Complexity Theory, inThe Stanford Encyclopedia of Philosophy, edited by E
Reference 12
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 03e90b87-53c6-4c0f-855c-7abed2a0161a · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 13
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 4697b77b-3c66-48bb-a334-d77b47afbf2b · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Bernstein and U
Reference 14
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 9a24da6f-4798-4066-b689-24ce5eaacacf · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets BQP and the Polynomial Hierarchy
Reference 15
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 2a3e71b0-71ce-491f-a35e-65194910e847 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Edmonds, Paths, trees, and flowers, Canadian Journal of Mathematics17, 449–467 (1965)
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ce585f24-9128-431e-944a-27da8c86ef53 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Cobham, The intrinsic computational difficulty of functions, inLogic, methodology and philosophy of science, edited by Y
Reference 17
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 a20b77a5-b9b9-4f5e-b4d4-44daf8a7c66d · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Sipser, Introduction to the theory of computation (Course Technology, Boston, MA, 1997) pp
Reference 18
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 bf1c986c-b467-4cfa-9c3b-5bfc68b29216 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Sipser, Introduction to the theory of computation (Course Technology, Boston, MA, 1997) pp
Reference 19
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 1a9a3099-c4d6-4b98-a800-c07a5552066f · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Sipser, Introduction to the theory of computation (Course Technology, Boston, MA, 1997) pp
Reference 20
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 a400b077-9890-4616-a99c-c81ed1a75c17 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Dempsey and C
Reference 21
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 2d7926c6-fcaa-492c-ae70-e851a3ed8fad · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Achlioptas and E
Reference 22
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 fc24de48-5edd-48c1-9650-a15e9999577b · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 23
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 855cee97-f218-4452-bdef-15a1a99a8650 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 24
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 cf570edc-08d1-4ae7-871e-fbb6f7203d53 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Galam, Y
Reference 25
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 5bfc543c-ac73-4f0c-aff0-252afcd26d11 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Explaining the Ubiquity of Phase Transitions in Decision Problems
Reference 26
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 cac7dd40-6364-4bfc-a677-d6fd7c4c7281 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Schawe, R
Reference 27
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 d8211632-85c4-432e-a33b-718a0e7d1600 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 28
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 8c2b2a77-fdf0-4f22-9566-310a461f4502 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 29
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 109ed836-5f94-4bdb-b44f-68403d253357 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Hook and H
Reference 30
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 6a3e8974-8b1e-4f5f-9811-a58abe9cd741 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 31
Source-reported events for the cited work
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Observation aa8199e9-fe92-425f-808a-9c11971d1697 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Hook and H
Reference 32
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 3d6cdecd-12ac-40ad-a478-00b01ed0f8f8 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Hook and H
Reference 33
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 edfc1473-5f1b-4318-a380-21c7945e7f30 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 34
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 3e2ba56b-b317-4e3f-913b-c44efe23911a · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 35
Source-reported events for the cited work
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Observation 18a40a83-f995-46c3-b895-5c020099cc23 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Farag ´o and R
Reference 36
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 bb2e71b6-7da1-43c6-9985-8a45647ff0a3 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Cai, Cs 810: Introduction to complexity theory
Reference 37
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 150c29d6-53e8-42a8-a65a-cd58b1cd713f · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 38
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 c7b077ce-384e-4efa-9baa-13b0a8494396 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Extensively Not P-Bi-Immune promiseBQP-Complete Languages
Reference 39
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 f81c7842-bb56-47be-a1f4-f46ece5e78c7 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 40
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 c15c6adf-64aa-49c6-822b-d8c639e7f39c · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets McKague, Interactive proofs forBQPvia self-tested graph states, Theory of Computing12, 1 (2016)
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0b48b629-748a-44f4-b990-86edf6b987b6 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Hangleiter, M
Reference 42
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 a13819bd-0e4c-4eed-8fa3-dced4932d401 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Kashefi and P
Reference 43
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 f656085b-b6cc-48eb-8511-87b3b9c63019 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Gheorghiu, T
Reference 44
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 0c041f32-cf55-4534-a670-f256b6187c8f · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Ferracin, T
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e9b4b5e1-8bcb-487d-b267-517ddeaa7996 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Markham and A
Reference 46
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 055ed986-ab3d-4c35-a65c-245391ed7300 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Ferracin, S
Reference 47
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 6fb8d578-fa52-4be9-a999-15c12f80145b · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Jackson, Accreditation against limited adversarial noise (2025), arXiv:2409.03995 [quant-ph]
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2160e144-e263-4c29-bc60-754a439e6f68 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Shaffer, E
Reference 49
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 d897774b-ec5f-465a-a8e1-7368ff989e75 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Jackson, T
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d3108016-b2b8-46d3-a64c-b27f611061b3 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Improved Accreditation of Analogue Quantum Simulation and Establishing Quantum Advantage
Reference 51
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f953b2d9-726e-4a29-817f-538b5f688ac8 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Arora and B
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a8e6e785-88c4-4353-a213-16f784d3c5fc · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 53
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 199d3a3f-c9e9-48f0-85c3-c6d91f6aaa8a · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets B3, is zero-indexing
Reference 54
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 67db85fc-3427-49ae-9060-9a4896e7ffe7 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 55
Source-reported events for the cited work
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Observation 19401c4b-58a3-421c-9684-8efd39fa4795 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 56
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 af48f1d5-5d58-470e-b3b6-28d813c55ad7 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets 4 suffices as the key point is the symmetry of the relationship
Reference 57
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 37bfeb9d-1032-41e7-9583-80401f48bfd6 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 58
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 e8087a69-995d-4f9e-ad33-2735cca3c2e2 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 59
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 557761a9-fe09-4350-97dc-2ec9c4c5c890 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 60
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 1866ba08-9963-46a6-9be5-73dee78c66e9 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 61
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 bf479088-d7fd-4444-bbe5-9eb7f01a9c30 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 62
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 7aa880d9-8d37-4529-bdef-f5b1048b2376 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Antonopoulos, Computational complexity graduate course
Reference 63
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 4b8e228c-7f8a-4c82-81e4-630a6fb84907 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets additional property
Reference 64
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 2b29199b-ac8c-49a7-9dd7-118005eaf036 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets does not return⊥ for)
Reference 65
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 410272c7-f924-4b9a-8bd8-680c5ab6c8b6 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets Unresolved cited work
Reference 66
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 475c1c87-40b4-4ea6-ac27-ce72ec3cdc4b · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets B33, lete 0∈B ϕ
Reference 67
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 732353cc-dcf7-4301-a134-134d68226d51 · outbound
Phase Transitions in Decision Problems Over Odd-Sized Alphabets filling up
Reference 68
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.
No inbound Pith citation observations are available.