Paper Citation Record · LEDGER

Structure of matrix product locally purifiable density operators

As of 21 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2608.02724.

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

pith.paper-citation-record.v1
2608.02724 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:11:46.170683Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

47 of 47 outbound references displayed

verified exact2
verified fuzzy20
unresolved25
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation eb8814f4-91a9-4f1a-a6cd-8581e5a31632 · outbound

This paper cites A proof is provided in appendix A.

Structure of matrix product locally purifiable density operators A proof is provided in appendix A

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.217288Z

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 32ca0a39-e807-4e72-9034-b8e4a80fe107 · outbound

This paper cites The condition on theN th tensor A[N] is that the overall state is normalized, trP i,aAia [N]Λ[N](Aia [N])† = 1.

Structure of matrix product locally purifiable density operators The condition on theN th tensor A[N] is that the overall state is normalized, trP i,aAia [N]Λ[N](Aia [N])† = 1

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.151055Z

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 5706cf56-d16c-4ed5-adf1-9ef46acdbb40 · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:11:47.170338Z

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 1f068259-a679-49c2-af70-ccf73d350989 · outbound

This paper cites Schuch, D.

Structure of matrix product locally purifiable density operators Schuch, D

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.042929Z

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 65bb1772-bb6e-4014-8fe1-9a4345146a97 · outbound

This paper cites Take the canonical regular elementω∈A∗ and define a matrix b(ω)such thattr[b(ω)ϕ(x)] =ω(x)for anyx∈A.

Structure of matrix product locally purifiable density operators Take the canonical regular elementω∈A∗ and define a matrix b(ω)such thattr[b(ω)ϕ(x)] =ω(x)for anyx∈A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.129367Z

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 60e147a8-ddfd-43ad-8c09-0fcb797b1274 · outbound

This paper cites We denote byC[G]the group algebra which is the vector space formally spanned by elements of the groupG.

Structure of matrix product locally purifiable density operators We denote byC[G]the group algebra which is the vector space formally spanned by elements of the groupG

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.109655Z

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 dee35ee2-bb9a-46d1-b000-267ccc53a763 · outbound

This paper cites Fork= 1,...,N, we define the generators Gk =Z ik−1XcXik,satisfying[Z ⊗N+2,Gk] = 0.

Structure of matrix product locally purifiable density operators Fork= 1,...,N, we define the generators Gk =Z ik−1XcXik,satisfying[Z ⊗N+2,Gk] = 0

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.091836Z

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 7cbcabc0-cc85-49cf-b1b2-3c809e507aa6 · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:45.986265Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7516cc61-3ac6-48ed-9a5a-ac6ab3093e4d · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:45.990684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c9b3351-c1c1-46c4-b012-158b63c86ccb · outbound

This paper cites Chen, Z.-C.

Structure of matrix product locally purifiable density operators Chen, Z.-C

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:45.995508Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f3ac407-f7d3-4609-9ae2-cf3363820bee · outbound

This paper cites Schuch, D.

Structure of matrix product locally purifiable density operators Schuch, D

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.961559Z

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 ca18834f-96b1-4987-8ba3-a6f2eb0699b5 · outbound

This paper cites Verstraete, J.

Structure of matrix product locally purifiable density operators Verstraete, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.027641Z

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 418ce5ae-f5f7-40f2-8f2f-f4e4cf66be1d · outbound

This paper cites Zwolak and G.

Structure of matrix product locally purifiable density operators Zwolak and G

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.010065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6845ad4b-95a6-48f3-a9e3-08f27b04b47f · outbound

This paper cites Let Aia [n]∈M Dn+1,Dn be a purification tensor.

Structure of matrix product locally purifiable density operators Let Aia [n]∈M Dn+1,Dn be a purification tensor

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:47.189740Z

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 825d2051-0535-4c2b-aeb8-1e85b77a7c9e · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:11:46.999071Z

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 5d02cf85-c848-4a57-916b-9720a563a41d · outbound

This paper cites Molnar, N.

Structure of matrix product locally purifiable density operators Molnar, N

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.019323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2630c796-0201-4019-929f-2211f34d4e90 · outbound

This paper cites Matrix Product Density Operators: when do they have a local parent Hamiltonian?.

Structure of matrix product locally purifiable density operators Matrix Product Density Operators: when do they have a local parent Hamiltonian?

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:11:46.580749Z

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 bbf049a3-2546-46e6-ab1b-5e034f8828c0 · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.027612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 19f9fef8-58ab-43df-a131-6d9f0f124711 · outbound

This paper cites Matrix product operator algebras I: representations of weak Hopf algebras and projected entangled pair states.

Structure of matrix product locally purifiable density operators Matrix product operator algebras I: representations of weak Hopf algebras and projected entangled pair states

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.035731Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a03c367-e8dc-45ba-8ecd-2f3a01fd1f6b · outbound

This paper cites Guo, J.-H.

Structure of matrix product locally purifiable density operators Guo, J.-H

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.040263Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1b28cad-1cde-4b77-b15a-0727513626d6 · outbound

This paper cites Perez-Garcia, F.

Structure of matrix product locally purifiable density operators Perez-Garcia, F

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.044302Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15e474e3-9d47-4056-8e68-ad3cf52a6885 · outbound

This paper cites Ignacio Cirac, D.

Structure of matrix product locally purifiable density operators Ignacio Cirac, D

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.922194Z

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 fbf65224-f41a-4a70-9262-77cef8c8589c · outbound

This paper cites Styliaris, R.

Structure of matrix product locally purifiable density operators Styliaris, R

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.906441Z

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 f253bd80-b677-4582-a1cd-cc7c3ef02c65 · outbound

This paper cites Kliesch, D.

Structure of matrix product locally purifiable density operators Kliesch, D

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.889366Z

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 2d2a0cbc-6188-498a-bc7a-9aa2c287153e · outbound

This paper cites De las Cuevas, T.

Structure of matrix product locally purifiable density operators De las Cuevas, T

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.870741Z

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 6d5e2618-3edd-4a7a-b49d-f966b4d68129 · outbound

This paper cites Cirac, D.

Structure of matrix product locally purifiable density operators Cirac, D

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.855037Z

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 6ca2914b-2b02-47de-8b5d-3706f75a3549 · outbound

This paper cites Fannes, B.

Structure of matrix product locally purifiable density operators Fannes, B

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.074159Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c136374-b8c7-45d6-8157-6ef664d83f69 · outbound

This paper cites Schön, E.

Structure of matrix product locally purifiable density operators Schön, E

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.828212Z

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 ba47d85e-dbd3-4524-bfb1-eea9cd5d86e3 · outbound

This paper cites De las Cuevas, J.

Structure of matrix product locally purifiable density operators De las Cuevas, J

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.808545Z

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 c56ae17b-4735-4979-8f58-d177e9d1ec39 · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.089022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09368e3e-e2ac-4e01-abca-f36c70adf8ed · outbound

This paper cites Molnar, Y.

Structure of matrix product locally purifiable density operators Molnar, Y

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.784999Z

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 87a314a3-c2e7-493e-9c18-3ed99bfa0320 · outbound

This paper cites Molnar, J.

Structure of matrix product locally purifiable density operators Molnar, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.765001Z

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 157f16aa-423d-421b-9f25-63ce9fb1a5a0 · outbound

This paper cites PEPS as unique ground states of local Hamiltonians.

Structure of matrix product locally purifiable density operators PEPS as unique ground states of local Hamiltonians

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.104621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cbb70624-7ffd-4671-b424-21869cb1b858 · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.109669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e3e27d8-3055-4c98-910c-7bd76ccc3e6b · outbound

This paper cites Schuch, I.

Structure of matrix product locally purifiable density operators Schuch, I

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.736892Z

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 4bdb77b9-6087-4288-8468-7f3a5715eb53 · outbound

This paper cites de Groot, A.

Structure of matrix product locally purifiable density operators de Groot, A

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.119788Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f5930ca-4f75-44f7-b0a8-c27ce4af261d · outbound

This paper cites Ma and C.

Structure of matrix product locally purifiable density operators Ma and C

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.124867Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ad40215-05fc-4b24-b5b7-98907c7f699d · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:11:46.699706Z

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 e64e81a9-2d37-4741-bd08-92b971772efd · outbound

This paper cites Garre-Rubio, L.

Structure of matrix product locally purifiable density operators Garre-Rubio, L

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:11:46.680144Z

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 305535ec-8c28-4bfe-9ae4-871cd73a7a52 · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.137283Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3b1084f-33b5-40e5-a858-cfb48ef9e6c6 · outbound

This paper cites Sun, Anomalous matrix product operator sym- metries and 1d mixed-state phases, arXiv preprint arXiv:2504.16985 (2025).

Structure of matrix product locally purifiable density operators Sun, Anomalous matrix product operator sym- metries and 1d mixed-state phases, arXiv preprint arXiv:2504.16985 (2025)

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.141368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 282849e1-d0aa-4329-954c-72163bec3063 · outbound

This paper cites Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries.

Structure of matrix product locally purifiable density operators Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.145404Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb5f1371-133c-487b-9d2f-bd8ebee4d325 · outbound

This paper cites McGinley and S.

Structure of matrix product locally purifiable density operators McGinley and S

Reference 43

Resolution: verified exact; raw_fallback, observed 2026-08-15T15:11:46.338653Z

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 387e889f-ab4b-46b1-8438-33f661d2f921 · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:11:46.645927Z

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 5369a0bd-8243-4a90-aed5-34342d0e8725 · outbound

This paper cites Chen and T.

Structure of matrix product locally purifiable density operators Chen and T

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.160123Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c1867de-456a-4194-9a5f-4886d27b3e1d · outbound

This paper cites Chen and T.

Structure of matrix product locally purifiable density operators Chen and T

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.165512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0cb5510a-c23b-4e9c-a048-36490833dbcc · outbound

This paper cites an unresolved cited work.

Structure of matrix product locally purifiable density operators Unresolved cited work

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-15T15:11:46.170683Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.