Paper Citation Record · LEDGER

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection

As of 6 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 4 inbound Pith citation observations for arXiv:2606.27105.

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

pith.paper-citation-record.v1
2606.27105 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T04:47:49.271684Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T02:17:59.137302Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-03T12:28:07.157476Z

Reference resolution

16 of 16 outbound references displayed

verified exact0
verified fuzzy0
unresolved15
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 76af8061-4a01-4339-a56d-996e40b8b1ef · outbound

This paper cites We reformulate Theorem 3 as the theorem below.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection We reformulate Theorem 3 as the theorem below

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b548187-5d99-4c91-b6e0-065c0b25c047 · outbound

This paper cites an unresolved cited work.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

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Observation 7e5fd49f-4b7d-4066-8341-b51dbf83e667 · outbound

This paper cites Dimensions of Specht and irreducible components, which appear in the fourth-order Clifford twirling formula.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Dimensions of Specht and irreducible components, which appear in the fourth-order Clifford twirling formula

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f2d84bf-23c7-4673-a379-748fde34602b · outbound

This paper cites Character table of the symmetric groupS4.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Character table of the symmetric groupS4

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae00d65c-db9e-470c-9c49-b105669b8f94 · outbound

This paper cites For the witness induced by the triangle criterion [89] W=T= I+X−Y+Z 1+ √ 3 ⊗∣0n−1⟩⟨0n−1∣, ̃W= ̃T=I−T,(E52) its spectrum is spec(̃T)={0,3− √ 3,1,.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection For the witness induced by the triangle criterion [89] W=T= I+X−Y+Z 1+ √ 3 ⊗∣0n−1⟩⟨0n−1∣, ̃W= ̃T=I−T,(E52) its spectrum is spec(̃T)={0,3− √ 3,1,

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 969d2c02-33b0-423f-90b3-6a93cb05a942 · outbound

This paper cites an unresolved cited work.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 454a5745-cd21-4462-a530-40dbc7649b1f · outbound

This paper cites Step 4: Evaluation of the fiveQ-sector invariants.We now substitute the above traces into Eq.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Step 4: Evaluation of the fiveQ-sector invariants.We now substitute the above traces into Eq

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fd8b62f-8444-4e64-af13-5aba8b9dfee2 · outbound

This paper cites We first prove the existence of such a state and then calculate the coefficients introduced in Theorem 6 and Theorem 13.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection We first prove the existence of such a state and then calculate the coefficients introduced in Theorem 6 and Theorem 13

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90716b23-4d81-4666-b4f3-0e95af81a6a5 · outbound

This paper cites They become products of Pauli operators under Jordan-Wigner transformation.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection They become products of Pauli operators under Jordan-Wigner transformation

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ceb7de39-4278-40e2-9a0d-96eb9a0eccbe · outbound

This paper cites an unresolved cited work.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e03a82ae-7b9e-4eac-b102-91d7dc570958 · outbound

This paper cites an unresolved cited work.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4bb8661-40b2-4848-b205-6e1721c5077c · outbound

This paper cites Then the set of free states is the convex hull ofG n,F=Conv(G n)⊆DF, also known as the convex Gaussian states [20].

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Then the set of free states is the convex hull ofG n,F=Conv(G n)⊆DF, also known as the convex Gaussian states [20]

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 825d394e-2ae2-405b-96ac-5be43a001808 · outbound

This paper cites an unresolved cited work.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1d4de92-ef96-468a-bd49-729b6cd0aadd · outbound

This paper cites an unresolved cited work.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7745487b-702b-4172-9e5f-42d694795936 · outbound

This paper cites In this caseν(A 1,A 2)≡∑a∈A1 a(mod 2),ν(A 2,A 3)=ν(A 3,A 1)=0.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection In this caseν(A 1,A 2)≡∑a∈A1 a(mod 2),ν(A 2,A 3)=ν(A 3,A 1)=0

Reference 15

Resolution: malformed identifier; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e80f708a-a573-412f-abac-e7fba6c65de0 · outbound

This paper cites an unresolved cited work.

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-26T04:47:49.271684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation db97048f-09b4-4d8b-9f48-90a2eacf4019 · inbound

Computable fermionic non-Gaussianity from the covariance matrix cites this paper.

Computable fermionic non-Gaussianity from the covariance matrix Witness expansion: A unified framework for analytical and measurable mixed-state resource detection

Reference 185

Resolution: verified exact; local_arxiv, observed 2026-07-03T12:28:07.159564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 53f9ce0f-237d-4717-addd-ed5b8c5c6dd9 · inbound

Parametrized-circuit-free quantum regression with variance regularization cites this paper.

Parametrized-circuit-free quantum regression with variance regularization Witness expansion: A unified framework for analytical and measurable mixed-state resource detection

Reference 71

Resolution: unresolved; no resolver link, observed 2026-07-12T07:39:35.969979Z

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Observation 95e8f438-8525-4dcd-9b15-a7bcf3fa8e7c · inbound

Rigorous characterization of continuous-variable quantum states via optical parametric amplifiers cites this paper.

Rigorous characterization of continuous-variable quantum states via optical parametric amplifiers Witness expansion: A unified framework for analytical and measurable mixed-state resource detection

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-01T19:22:15.099525Z

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Unavailable: canonical work link unavailable.

Observation 8b4b21ac-ba0a-4a65-b1a7-9959cd07c688 · inbound

Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity cites this paper.

Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity Witness expansion: A unified framework for analytical and measurable mixed-state resource detection

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-03T02:17:59.137302Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.