Paper Citation Record · LEDGER

A unified framework for classical and quantum uncertainty relations using stochastic representations

As of 13 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 4 inbound Pith citation observations for arXiv:2412.04988.

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

pith.paper-citation-record.v1
2412.04988 v2

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T21:13:15.823849Z

measured 58 of 58 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:53:44.886819Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T00:02:54.078294Z

Reference resolution

54 of 54 outbound references displayed

verified exact0
verified fuzzy24
unresolved30
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f1a3ca00-cafd-4d74-a12f-e2b462ad452b · outbound

This paper cites (13) Without loss of generality, we set t ≥ t′.

A unified framework for classical and quantum uncertainty relations using stochastic representations (13) Without loss of generality, we set t ≥ t′

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:13:16.727506Z

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Observation ba02bcc5-00a8-47e2-8d78-e9e8af66012a · outbound

This paper cites an unresolved cited work.

A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 2

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Observation d6006fe7-be86-4c38-83a3-4fd02c19012e · outbound

This paper cites (37) The first step in deriving Eq.

A unified framework for classical and quantum uncertainty relations using stochastic representations (37) The first step in deriving Eq

Reference 3

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This paper cites (43) Expanding Eq.

A unified framework for classical and quantum uncertainty relations using stochastic representations (43) Expanding Eq

Reference 4

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Observation 8886a0e9-cc6f-463e-856c-864af20d0a32 · outbound

This paper cites (B7) Using the same formulation as in Appendix B 1, we ob- tain ∆k,k′(t, t′) = ⟨tr [LkU (t, t′) {Lk′ψt′ − ψt′tr(Lk′ψt′)}]⟩ , (B8) where ψt′ ≡ ρc(t′).

A unified framework for classical and quantum uncertainty relations using stochastic representations (B7) Using the same formulation as in Appendix B 1, we ob- tain ∆k,k′(t, t′) = ⟨tr [LkU (t, t′) {Lk′ψt′ − ψt′tr(Lk′ψt′)}]⟩ , (B8) where ψt′ ≡ ρc(t′)

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:13:16.671745Z

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Observation ee8bf3c0-7d5d-43fa-9cd2-ecf9f7d974d7 · outbound

This paper cites (D1) The steady-state density matrix of this system can be evaluated as ρss = γ2(n+1)(2n+1)+4∆2 γ2(2n+1)2+8∆2 2iγ∆ γ2(2n+1)2+8∆2 − 2iγ∆ γ2(2n+1)2+8∆2 γ2n(2n+1)+4∆2 γ2(2n+1)2+8∆2 !.

A unified framework for classical and quantum uncertainty relations using stochastic representations (D1) The steady-state density matrix of this system can be evaluated as ρss = γ2(n+1)(2n+1)+4∆2 γ2(2n+1)2+8∆2 2iγ∆ γ2(2n+1)2+8∆2 − 2iγ∆ γ2(2n+1)2+8∆2 γ2n(2n+1)+4∆2 γ2(2n+1)2+8∆2 !

Reference 6

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Observation e8d75f52-3066-4764-b327-d91d9aa71e7e · outbound

This paper cites an unresolved cited work.

A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 7

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Observation 6676d376-bf57-481f-a9b4-277b271df72c · outbound

This paper cites B 2, Lk|ψ⟩ = |Lk|ψ⟩||ψk⟩, where |ψk⟩ is the ket corresponding to the pure density matrix φk ∈ S.

A unified framework for classical and quantum uncertainty relations using stochastic representations B 2, Lk|ψ⟩ = |Lk|ψ⟩||ψk⟩, where |ψk⟩ is the ket corresponding to the pure density matrix φk ∈ S

Reference 8

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This paper cites an unresolved cited work.

A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 9

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 10

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 11

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Observation 32f6f06a-ed2d-40b4-b0ea-9283ff9db807 · outbound

This paper cites Dechant and S.

A unified framework for classical and quantum uncertainty relations using stochastic representations Dechant and S

Reference 12

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Observation 28ade73d-25f7-45d7-a5fc-aad8e6eb95e8 · outbound

This paper cites Koyuk and U.

A unified framework for classical and quantum uncertainty relations using stochastic representations Koyuk and U

Reference 13

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Observation d0646654-ecaa-48c7-adbd-79053c48f87d · outbound

This paper cites Hasegawa and T.

A unified framework for classical and quantum uncertainty relations using stochastic representations Hasegawa and T

Reference 14

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Observation ff1c05d4-d5c9-4947-9352-bc9f335a44ea · outbound

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 15

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Observation eaab165c-e955-4403-a40b-5b2873869c47 · outbound

This paper cites an unresolved cited work.

A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 16

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Observation c4c5e8c2-42c0-47f0-8271-0ece61fbdbaf · outbound

This paper cites Dieball and A.

A unified framework for classical and quantum uncertainty relations using stochastic representations Dieball and A

Reference 17

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Observation a24c7bbd-c1e3-4f30-bedf-7c340b46a09a · outbound

This paper cites Kwon, J.-M.

A unified framework for classical and quantum uncertainty relations using stochastic representations Kwon, J.-M

Reference 18

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 19

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 20

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Observation ae3a38f4-9a78-4c36-a18e-6608c2e90d82 · outbound

This paper cites Maggi, F.

A unified framework for classical and quantum uncertainty relations using stochastic representations Maggi, F

Reference 21

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 22

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Observation d9549663-fd26-421d-87bc-6675de935250 · outbound

This paper cites Otsubo, S.

A unified framework for classical and quantum uncertainty relations using stochastic representations Otsubo, S

Reference 23

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Observation 20344104-7391-494a-8921-b6207442a73f · outbound

This paper cites an unresolved cited work.

A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 24

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Observation 8bbf102d-c8a2-4b93-83eb-8f309c8c28bd · outbound

This paper cites Hasegawa, Unifying speed limit, thermodynamic un- certainty relation and heisenberg principle via bulk- boundary correspondence, Nature Communications 14, 2828 (2023).

A unified framework for classical and quantum uncertainty relations using stochastic representations Hasegawa, Unifying speed limit, thermodynamic un- certainty relation and heisenberg principle via bulk- boundary correspondence, Nature Communications 14, 2828 (2023)

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:13:16.378345Z

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Observation 3acc201d-fffa-48cc-85f3-6aa289159370 · outbound

This paper cites Shiraishi, K.

A unified framework for classical and quantum uncertainty relations using stochastic representations Shiraishi, K

Reference 26

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Observation b9910f63-0a18-41c4-a091-8070a2533753 · outbound

This paper cites Pietzonka and U.

A unified framework for classical and quantum uncertainty relations using stochastic representations Pietzonka and U

Reference 27

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Observation 8f2aa66a-7f3f-4662-a33d-1088af14cf02 · outbound

This paper cites Shiraishi, K.

A unified framework for classical and quantum uncertainty relations using stochastic representations Shiraishi, K

Reference 28

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 29

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Observation 50645134-1a74-4282-be97-fc8f914272a0 · outbound

This paper cites Dechant and S.-i.

A unified framework for classical and quantum uncertainty relations using stochastic representations Dechant and S.-i

Reference 30

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Observation cd8cecb7-9924-454a-a9c9-7eb5682fb696 · outbound

This paper cites Lee, D.-K.

A unified framework for classical and quantum uncertainty relations using stochastic representations Lee, D.-K

Reference 31

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Observation 77615e0e-1d43-4585-87d0-ca5f994dc1d7 · outbound

This paper cites Dechant and S.-i.

A unified framework for classical and quantum uncertainty relations using stochastic representations Dechant and S.-i

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:13:16.296397Z

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Observation 76412222-61d6-435e-81c9-5eddd3454805 · outbound

This paper cites Dechant and S.-i.

A unified framework for classical and quantum uncertainty relations using stochastic representations Dechant and S.-i

Reference 33

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Observation 16296e77-b470-42da-a607-d69524506a44 · outbound

This paper cites Shiraishi, Optimal thermodynamic uncertainty rela- tion in markov jump processes, Journal of Statistical Physics 185, 19 (2021).

A unified framework for classical and quantum uncertainty relations using stochastic representations Shiraishi, Optimal thermodynamic uncertainty rela- tion in markov jump processes, Journal of Statistical Physics 185, 19 (2021)

Reference 34

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Observation 4e7c3d5e-6dfb-4797-bac8-f189eb13f3e0 · outbound

This paper cites Kwon, H.-M.

A unified framework for classical and quantum uncertainty relations using stochastic representations Kwon, H.-M

Reference 35

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Observation e4a4195a-255a-4cc3-8c50-4ab42b22b954 · outbound

This paper cites Hasegawa, Quantum thermodynamic uncertainty re- lation for continuous measurement, Phys.

A unified framework for classical and quantum uncertainty relations using stochastic representations Hasegawa, Quantum thermodynamic uncertainty re- lation for continuous measurement, Phys

Reference 36

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Observation c6cc429a-294a-495e-9a51-dcab1ba68b54 · outbound

This paper cites Hasegawa, Thermodynamic uncertainty relation for general open quantum systems, Phys.

A unified framework for classical and quantum uncertainty relations using stochastic representations Hasegawa, Thermodynamic uncertainty relation for general open quantum systems, Phys

Reference 37

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Observation 1ace0209-53a7-417c-8795-a48e70ef9491 · outbound

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A unified framework for classical and quantum uncertainty relations using stochastic representations Van Vu and K

Reference 38

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Observation 7efbf319-5f56-43b7-903d-8fc6bda58493 · outbound

This paper cites Role of Quantum Coherence in Kinetic Uncertainty Relations.

A unified framework for classical and quantum uncertainty relations using stochastic representations Role of Quantum Coherence in Kinetic Uncertainty Relations

Reference 39

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 40

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 41

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A unified framework for classical and quantum uncertainty relations using stochastic representations Manzano, J

Reference 42

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A unified framework for classical and quantum uncertainty relations using stochastic representations Carollo, R

Reference 43

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 44

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 45

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A unified framework for classical and quantum uncertainty relations using stochastic representations Menczel, E

Reference 46

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 47

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Observation ad9fe4d4-ce41-4fcf-9621-dd33afd390e3 · outbound

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A unified framework for classical and quantum uncertainty relations using stochastic representations Singh and C

Reference 48

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Observation 42fe0fb8-c32b-4fce-9946-8619362f8ead · outbound

This paper cites Singh, V.

A unified framework for classical and quantum uncertainty relations using stochastic representations Singh, V

Reference 49

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Observation d5acee35-7815-4739-9f01-3668c87bbfe4 · outbound

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 50

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Observation 1444160d-3116-4268-8757-faa8e4d0c391 · outbound

This paper cites Hiura and S.-i.

A unified framework for classical and quantum uncertainty relations using stochastic representations Hiura and S.-i

Reference 51

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Observation 5b91ecc2-8e62-4ae9-95d1-0bdc572f7d72 · outbound

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A unified framework for classical and quantum uncertainty relations using stochastic representations Unresolved cited work

Reference 52

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:13:16.079909Z

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Observation 87045c74-0035-4a67-8a9b-fa45343a4b1d · outbound

This paper cites Hasegawa, Thermodynamic uncertainty relation for quantum first-passage processes, Phys.

A unified framework for classical and quantum uncertainty relations using stochastic representations Hasegawa, Thermodynamic uncertainty relation for quantum first-passage processes, Phys

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:13:16.065451Z

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Observation 49e22631-1992-4a6a-85dd-4154d001f350 · outbound

This paper cites Pietzonka and F.

A unified framework for classical and quantum uncertainty relations using stochastic representations Pietzonka and F

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:13:16.049626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation 546629b9-20c6-417c-8f5e-a30f4efbd34d · inbound

Effects of noise-induced coherence on the performance of a four-level laser heat engine cites this paper.

Effects of noise-induced coherence on the performance of a four-level laser heat engine A unified framework for classical and quantum uncertainty relations using stochastic representations

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T04:53:44.886819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76ce92b4-0488-4fb6-b62f-a2c2111a2be9 · inbound

Thermodynamic Uncertainty Relations for Coherent Transport cites this paper.

Thermodynamic Uncertainty Relations for Coherent Transport A unified framework for classical and quantum uncertainty relations using stochastic representations

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:55.337793Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e406c470-64c8-40cc-8f1a-81ef05db8384 · inbound

Stochastic Calculus for Pathwise Observables of Markov-Jump Processes: Unification of Diffusion and Jump Dynamics cites this paper.

Stochastic Calculus for Pathwise Observables of Markov-Jump Processes: Unification of Diffusion and Jump Dynamics A unified framework for classical and quantum uncertainty relations using stochastic representations

Reference 73

Resolution: verified exact; arxiv_id, observed 2026-05-19T00:02:54.081060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2bc8a3ea-a3c3-4e14-90c0-8866f1014da9 · inbound

Universal Precision Limits in General Open Quantum Systems cites this paper.

Universal Precision Limits in General Open Quantum Systems A unified framework for classical and quantum uncertainty relations using stochastic representations

Reference 47

Resolution: verified exact; arxiv_id, observed 2026-05-18T20:46:51.778061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.