Paper Citation Record · LEDGER

Statistical inference for quantum singular models

As of 20 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2411.16396.

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

pith.paper-citation-record.v1
2411.16396 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T13:15:54.552644Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:58:15.495590Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T12:58:16.788990Z

Reference resolution

33 of 33 outbound references displayed

verified exact0
verified fuzzy19
unresolved14
parse uncertain0
malformed identifier0
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External citation measurements

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Outbound references

Observation 54f2296f-566b-47c1-80c2-ec052ad1b774 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:55.288938Z

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Observation 7fc08996-3aa1-4cc8-9a31-9ac024621096 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:55.265671Z

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Observation ee17982a-ece6-4f7b-a521-149c9133c692 · outbound

This paper cites homogeneous.

Statistical inference for quantum singular models homogeneous

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:55.248927Z

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Observation bc5832d9-6cb9-4a09-bb51-a8e0534e5955 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:55.228951Z

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Observation 4b32e7fa-93dd-4ce3-9fb2-0a830ca7deee · outbound

This paper cites In particular, under Assumption R1, Assumption R2 is equivalent to Assumption S2.

Statistical inference for quantum singular models In particular, under Assumption R1, Assumption R2 is equivalent to Assumption S2

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:55.210192Z

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Observation 83eb7759-c85c-4b94-ad23-53be369f38bf · outbound

This paper cites Before introducing the real log canonical thresholds, let us briefly recall the results on the log resolution of singularities, originally proved by Hironaka [88, 89].

Statistical inference for quantum singular models Before introducing the real log canonical thresholds, let us briefly recall the results on the log resolution of singularities, originally proved by Hironaka [88, 89]

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:55.192787Z

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Observation 8b77634c-1d2a-469e-94b1-181d6341fc77 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:55.151912Z

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Observation a6a09f2e-7c6b-460a-a1c9-96b5c28d3685 · outbound

This paper cites 31 For our purposes, we refer to an alternative version of this theorem that is more directly applicable to our context, as Atiyah wrote [86].

Statistical inference for quantum singular models 31 For our purposes, we refer to an alternative version of this theorem that is more directly applicable to our context, as Atiyah wrote [86]

Reference 9

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Observation ce7467a1-c2b2-4598-a4f3-a1991d39ba78 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:55.110848Z

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Observation c44450b4-da09-4999-bca5-052e3016616f · outbound

This paper cites Moreover, if f(x)≥ 0 for any x, then the integers κ1,··· ,κd are even.

Statistical inference for quantum singular models Moreover, if f(x)≥ 0 for any x, then the integers κ1,··· ,κd are even

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:55.089667Z

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Observation b87d7e3e-700b-4964-bec7-c7e16a99b65a · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:55.067453Z

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Observation 6e53ff3d-08de-482e-9112-dde6a493f537 · outbound

This paper cites It is known that the smallerλ is, the worse the singularity in algebraic geometry.

Statistical inference for quantum singular models It is known that the smallerλ is, the worse the singularity in algebraic geometry

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:55.038553Z

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Observation 8882135a-3306-4b2a-b4fe-76bf4a16f068 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:55.018927Z

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Observation cd2dc810-0cb6-482a-9c2f-813966eaf590 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:54.994697Z

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Observation 9b272230-ded9-4d08-bd02-0b1a43077a3b · outbound

This paper cites We denote by I := I(θ0) and J := J(θ0).

Statistical inference for quantum singular models We denote by I := I(θ0) and J := J(θ0)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.972928Z

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Observation 76feb433-9f14-4244-a682-9c9ac0aafde1 · outbound

This paper cites Definition B.9.

Statistical inference for quantum singular models Definition B.9

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.950482Z

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Observation f53236e3-be03-4658-9259-00d897b680ba · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:54.930406Z

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Observation 4c83cbaf-7602-4461-9772-df6fb468664f · outbound

This paper cites all models are wrong.

Statistical inference for quantum singular models all models are wrong

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.907492Z

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Observation e6a45e8b-39ae-47a8-bb5a-d0f364e5eb86 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:54.878484Z

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Observation e01e843f-4cbc-4cff-a597-882f79ea68e1 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:54.855473Z

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Observation 588a9225-c50b-4907-a346-d6297322899d · outbound

This paper cites Remark C.7.

Statistical inference for quantum singular models Remark C.7

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.838179Z

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Observation 01e7955d-9a13-4262-96f7-56b1dd31223f · outbound

This paper cites In such cases, the Hessian of the KL divergence degenerates, which hinders the formulation of a learning theory in the same way as in regular cases.

Statistical inference for quantum singular models In such cases, the Hessian of the KL divergence degenerates, which hinders the formulation of a learning theory in the same way as in regular cases

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.820617Z

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Observation 7b71306a-3307-437f-8c1e-8f71632e6d2c · outbound

This paper cites In other words, λ := min i {2ki + 1 hi } , where ki and hi are defined through a log resolution of singularities Eq.

Statistical inference for quantum singular models In other words, λ := min i {2ki + 1 hi } , where ki and hi are defined through a log resolution of singularities Eq

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.801399Z

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Observation 7f0d0258-2c24-4b39-ba66-89b93c178cf2 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:54.782531Z

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Observation 4d8fe7b9-1a39-4977-9669-c1a8e2007b68 · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:54.762289Z

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Observation aa36649f-e7b5-4034-ab42-772ecf0ea4f0 · outbound

This paper cites The origin of this is the state density formula and the Mellin transformation.

Statistical inference for quantum singular models The origin of this is the state density formula and the Mellin transformation

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.745484Z

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Observation 29aa5b61-8866-4450-9657-3bfd1a9b6d15 · outbound

This paper cites Note that V (ξn) is a functional of ξn because Vθ[·] depends on ξn.

Statistical inference for quantum singular models Note that V (ξn) is a functional of ξn because Vθ[·] depends on ξn

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.718874Z

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Observation e44e5d30-b4e3-4ef2-81a9-de2b507b47cb · outbound

This paper cites an unresolved cited work.

Statistical inference for quantum singular models Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:15:54.698624Z

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Observation f430c079-ec8a-491a-89a6-6d28adc8db44 · outbound

This paper cites Now, though we omit the details of the proof here, let us state that WAIC is a generalization of AIC in the following sense.

Statistical inference for quantum singular models Now, though we omit the details of the proof here, let us state that WAIC is a generalization of AIC in the following sense

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.678457Z

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Observation a3c43dab-f145-44f3-a4e6-5dd5add3a547 · outbound

This paper cites Definition D.1.

Statistical inference for quantum singular models Definition D.1

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.655190Z

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Observation 66ec114c-e962-4147-88ac-869686fd3cff · outbound

This paper cites This assumption allows us to utilize the benefits coming from the classical and quantum statistics in view of the Fisher information matrix.

Statistical inference for quantum singular models This assumption allows us to utilize the benefits coming from the classical and quantum statistics in view of the Fisher information matrix

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.634870Z

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Observation 9d5a20bc-d089-496b-8d03-578277c85cae · outbound

This paper cites To define WAIC, one had to assume an L2 and finiteness property of the classical log-likelihood ratio function.

Statistical inference for quantum singular models To define WAIC, one had to assume an L2 and finiteness property of the classical log-likelihood ratio function

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:54.614067Z

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Observation 937b1c8d-23e7-4777-9b3a-71f5ad15e945 · outbound

This paper cites We present the theorem relevant to our discussion: Theorem B.1.

Statistical inference for quantum singular models We present the theorem relevant to our discussion: Theorem B.1

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:15:55.173748Z

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Pith citing papers

Observation 1ccb47dd-8d10-440d-afe7-9101edcb40af · inbound

On Quantum and Quantum-Inspired Maximum Likelihood Estimation and Filtering of Stochastic Volatility Models cites this paper.

On Quantum and Quantum-Inspired Maximum Likelihood Estimation and Filtering of Stochastic Volatility Models Statistical inference for quantum singular models

Reference 291

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:58:16.876733Z

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