Paper Citation Record · LEDGER

Topological Holography for Mixed-State Phases and Phase Transitions

As of 7 August 2026, this Paper Citation Record lists 100 of 123 outbound references and 10 inbound Pith citation observations for arXiv:2507.06218.

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

pith.paper-citation-record.v1
2507.06218 v1

Coverage vector

measured 100 of 123 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:16:59.691221Z

measured 110 of 110 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 10 of 10 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-01T16:24:07.943937Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T13:18:12.892390Z

Reference resolution

100 of 123 outbound references displayed

verified exact3
verified fuzzy0
unresolved97
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8d82a6b7-5731-43c9-8776-5157ebdc72af · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.651137Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22daf670-0e2e-42cc-afaf-ad91c9a4c61f · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.750322Z

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Observation 0187f180-4606-4a94-ae9a-a31fb052b1ab · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:55.148468Z

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Observation c9f60692-f99b-4e9b-9bf6-0d09e4b294c8 · outbound

This paper cites Appendix B: Modular Data In this section we present the modular data in the modular tensor categories we encountered in this paper.

Topological Holography for Mixed-State Phases and Phase Transitions Appendix B: Modular Data In this section we present the modular data in the modular tensor categories we encountered in this paper

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:55.635806Z

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Observation 41df2b52-8c66-495c-abf7-600eae1c8fba · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:07.177926Z

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Observation 6bdb2c7c-0b80-48ac-b297-1a0e2fdb96ed · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:06.961333Z

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Observation 63465887-6350-4507-ac30-107231f8a7c5 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:06.652705Z

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Observation c4571103-85c2-4d97-b8f6-d144d2d54366 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:06.398339Z

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Observation 950f20f8-da5f-4abc-a3c3-db3110d1318d · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:06.218417Z

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Observation ce74a646-90ec-4b1f-bc90-6c0d501a7662 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:06.072106Z

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Observation 46c0501f-8787-4223-b96e-3d8cde63ef9b · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:05.900931Z

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Observation 0035fdf7-8827-4938-8844-91e5e4cb7c15 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:05.729869Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 10fcb1e4-cbc9-4f79-b97b-c0ad803443b8 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:05.505027Z

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Observation 4edc752f-38fe-4df6-aab9-4bdf7115f0e9 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:05.310938Z

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Observation d58d8e6c-4300-480b-a834-0bee021fed09 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:05.106264Z

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Observation 723f0b75-0246-49a3-9c7f-b631337a3c09 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:04.922465Z

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Observation 1c0e3a1d-5daf-4f99-8335-43a9c69a442f · outbound

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Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:04.761305Z

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Observation 860f0a12-27c4-46c3-9470-99a0fe601ec3 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:04.612913Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5e7f58b6-ce76-4e46-83b5-9cd9c47bf30c · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:04.471317Z

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Observation 48af33de-15e1-4f33-9491-dfb0599b07c9 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:04.336119Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1846020e-5e56-4db2-b3d0-4574539e8c59 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:04.199579Z

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Observation 261fcbc0-17d4-47b9-8cb5-ab530ef25888 · outbound

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Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:04.020713Z

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Observation cdc7d155-36cf-4cab-b496-86655c62a2e1 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:03.869005Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d361848f-7511-4563-94a3-552ec3582f00 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:03.711478Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 34c24a5a-0051-4ede-b187-e1456760e686 · outbound

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Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:03.604154Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9faa4945-9f6d-494e-9a04-b2a47f60a735 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:03.397059Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ccff10d-0202-42a9-a070-5d8775158007 · outbound

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Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:03.202959Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8bdb0f77-3a2a-4ed5-9b1a-d27505bbfc39 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:02.932443Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f172e293-46df-4d1d-b567-9b8dde758ac0 · outbound

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Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:02.735394Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cadf97ef-5b69-44c7-8ea2-f4b632108872 · outbound

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Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:02.512369Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c2f581ef-33a6-435f-a391-51a25410369b · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:02.290360Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b1b00253-e275-41e0-a32e-bec7955b91da · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:02.102358Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f302d45b-2dea-42a5-8e68-e59548f34f82 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:01.809772Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 671f816e-00dc-48d7-864f-8c2fd0dea3bd · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:01.598102Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e88ff688-dac7-43be-a348-42208bf55116 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:01.424184Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0cf05831-0e02-4c21-9c33-3064190755ff · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:01.277112Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 80e94f97-e475-4490-acd8-f2bf12f24717 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:01.118569Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cc86c1b9-9412-4afc-8325-b52468913788 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:17:00.916818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 28211fcc-e3f2-44d0-aa51-47e526abc065 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.880928Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45cad5db-ce56-4975-a328-7e327eeafa88 · outbound

This paper cites an unresolved cited work.

Topological Holography for Mixed-State Phases and Phase Transitions Unresolved cited work

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:55.043454Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4dfc2ff1-aba1-49c4-bc9b-d205a32da615 · outbound

This paper cites Mixed-state phases from local reversibility.

Topological Holography for Mixed-State Phases and Phase Transitions Mixed-state phases from local reversibility

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.473629Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 066a8f8c-c543-499c-bfda-5f29f3d51db4 · outbound

This paper cites Stability of mixed-state quantum phases via finite markov length,.

Topological Holography for Mixed-State Phases and Phase Transitions Stability of mixed-state quantum phases via finite markov length,

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.562686Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00c59492-d1b7-402f-bb60-e40d357e7e52 · outbound

This paper cites Topological mixed states: Axiomatic approaches and phases of matter,.

Topological Holography for Mixed-State Phases and Phase Transitions Topological mixed states: Axiomatic approaches and phases of matter,

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.608957Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation caf42461-1ebd-4556-8cd7-a5084ff26f84 · outbound

This paper cites Strong-to-weak spontaneous breaking of 1-form symmetry and intrinsically mixed topological order,.

Topological Holography for Mixed-State Phases and Phase Transitions Strong-to-weak spontaneous breaking of 1-form symmetry and intrinsically mixed topological order,

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.662095Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e1d6afe-9101-447a-87ab-0232d88179ba · outbound

This paper cites Higher-form anomaly and long-range entanglement of mixed states.

Topological Holography for Mixed-State Phases and Phase Transitions Higher-form anomaly and long-range entanglement of mixed states

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.715717Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eab29950-5fef-4ce6-81cb-4bbccd2dc2b5 · outbound

This paper cites Intrin- sic mixed-state topological order,.

Topological Holography for Mixed-State Phases and Phase Transitions Intrin- sic mixed-state topological order,

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.749110Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87a3b9ad-3973-4355-a31f-655ee6b2f376 · outbound

This paper cites Anyon condensation in mixed-state topological order,.

Topological Holography for Mixed-State Phases and Phase Transitions Anyon condensation in mixed-state topological order,

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.815836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c5f812c-ca4b-4ff1-9dc5-e0a28be62a7a · outbound

This paper cites Symmetry Protected Topological Order in Open Quantum Systems.

Topological Holography for Mixed-State Phases and Phase Transitions Symmetry Protected Topological Order in Open Quantum Systems

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.852395Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58f68fd1-0231-4c61-9508-1c7ebfe10eb8 · outbound

This paper cites Average Symmetry-Protected Topological Phases.

Topological Holography for Mixed-State Phases and Phase Transitions Average Symmetry-Protected Topological Phases

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.882935Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ee8b36c-af15-4973-9376-39f2fc38f3c1 · outbound

This paper cites Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases,.

Topological Holography for Mixed-State Phases and Phase Transitions Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases,

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.918355Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad2d90e2-d0a3-4fda-9b58-bb0f9a990dd5 · outbound

This paper cites Symmetry protected topological phases under decoherence.

Topological Holography for Mixed-State Phases and Phase Transitions Symmetry protected topological phases under decoherence

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:50.991327Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b15a0ee9-6054-413d-91ae-d767f5e3ce8f · outbound

This paper cites Topological phases with average symmetries: The decohered, the disordered, and the in- trinsic,.

Topological Holography for Mixed-State Phases and Phase Transitions Topological phases with average symmetries: The decohered, the disordered, and the in- trinsic,

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.033755Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 558bd9a5-7e01-4889-858d-b79c19178c7a · outbound

This paper cites Fractonic higher-order topological phases in open quantum systems,.

Topological Holography for Mixed-State Phases and Phase Transitions Fractonic higher-order topological phases in open quantum systems,

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.078194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16b66d5b-5de5-4e1d-a5a3-50dfe71e5cf2 · outbound

This paper cites Symmetry Protected Topological Phases of Mixed States in the Doubled Space.

Topological Holography for Mixed-State Phases and Phase Transitions Symmetry Protected Topological Phases of Mixed States in the Doubled Space

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.166346Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24beda31-3f6b-4677-849a-267f6c1045a5 · outbound

This paper cites Tensor network formulation of symmetry protected topological phases in mixed states.

Topological Holography for Mixed-State Phases and Phase Transitions Tensor network formulation of symmetry protected topological phases in mixed states

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.192129Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35ddcb15-a717-4b36-8ad0-6fb40840aa87 · outbound

This paper cites Locally purified density opera- tors for symmetry-protected topological phases in mixed states,.

Topological Holography for Mixed-State Phases and Phase Transitions Locally purified density opera- tors for symmetry-protected topological phases in mixed states,

Reference 80

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.259078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa57ca50-994f-4d50-bdca-f38a5fc02972 · outbound

This paper cites Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems.

Topological Holography for Mixed-State Phases and Phase Transitions Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems

Reference 81

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:17:00.511207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e322eba4-fe35-4b78-a495-bf5861b02748 · outbound

This paper cites Mixed-state quantum anomaly and multipartite entan- glement,.

Topological Holography for Mixed-State Phases and Phase Transitions Mixed-state quantum anomaly and multipartite entan- glement,

Reference 82

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.352491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44ca360b-3dbb-4372-b320-269aedf94d82 · outbound

This paper cites Quantum criticality under decoherence or weak mea- surement,.

Topological Holography for Mixed-State Phases and Phase Transitions Quantum criticality under decoherence or weak mea- surement,

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.414354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7edd3fb1-dc9f-47f1-a7bd-9a64587a974d · outbound

This paper cites Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States.

Topological Holography for Mixed-State Phases and Phase Transitions Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States

Reference 84

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.473034Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48d9db53-65b9-441d-928f-c20fd072f7cb · outbound

This paper cites Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective.

Topological Holography for Mixed-State Phases and Phase Transitions Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective

Reference 85

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.547557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a9cf6e5-3aa9-4c41-82e9-8ba2b66e68c4 · outbound

This paper cites Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak.

Topological Holography for Mixed-State Phases and Phase Transitions Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.618879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14c86543-85b9-4b92-bbc8-9c2194ccc516 · outbound

This paper cites Instability of steady-state mixed-state symmetry- protected topological order to strong-to-weak sponta- neous symmetry breaking,.

Topological Holography for Mixed-State Phases and Phase Transitions Instability of steady-state mixed-state symmetry- protected topological order to strong-to-weak sponta- neous symmetry breaking,

Reference 87

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.675342Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 315f3572-6ec3-4143-9276-c81eeb45ab33 · outbound

This paper cites Fluctuation-Dissipation Theorem and Information Geometry in Open Quantum Systems.

Topological Holography for Mixed-State Phases and Phase Transitions Fluctuation-Dissipation Theorem and Information Geometry in Open Quantum Systems

Reference 88

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.730921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 471639ed-7805-4625-b8e2-7edfb0a524e2 · outbound

This paper cites Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order.

Topological Holography for Mixed-State Phases and Phase Transitions Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order

Reference 89

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:17:00.257857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8381fc10-2ead-4869-8bc3-b6d8b51fd021 · outbound

This paper cites Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking.

Topological Holography for Mixed-State Phases and Phase Transitions Error Threshold of SYK Codes from Strong-to-Weak Parity Symmetry Breaking

Reference 90

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:51.874504Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eae38b42-a90e-4774-88b4-4481ac0ea922 · outbound

This paper cites Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space.

Topological Holography for Mixed-State Phases and Phase Transitions Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space

Reference 91

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:17:00.056198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a4f19ed4-2c66-422f-a6c4-dc6223c7e258 · outbound

This paper cites Many-body quantum catalysts for transforming between phases of matter,.

Topological Holography for Mixed-State Phases and Phase Transitions Many-body quantum catalysts for transforming between phases of matter,

Reference 92

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.001540Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b89d7d8-5499-4963-b527-4fb014e89803 · outbound

This paper cites Hydrodynamics as the effective field the- ory of strong-to-weak spontaneous symmetry breaking,.

Topological Holography for Mixed-State Phases and Phase Transitions Hydrodynamics as the effective field the- ory of strong-to-weak spontaneous symmetry breaking,

Reference 93

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.055821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4abbad60-48f9-4afe-88ff-5ccce35c00e8 · outbound

This paper cites Diagnosing strong-to-weak sym- metry breaking via wightman correlators,.

Topological Holography for Mixed-State Phases and Phase Transitions Diagnosing strong-to-weak sym- metry breaking via wightman correlators,

Reference 94

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.122094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 801b658f-5136-48ee-8bf5-6ce2e02afe31 · outbound

This paper cites Efficient detection of strong-to-weak spontaneous symmetry breaking via the r´ enyi-1 correla- tor,.

Topological Holography for Mixed-State Phases and Phase Transitions Efficient detection of strong-to-weak spontaneous symmetry breaking via the r´ enyi-1 correla- tor,

Reference 95

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.180474Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e8f8a140-ac3b-4580-a07a-1f3a956f210d · outbound

This paper cites Bilayer construction for mixed state phenomena with strong, weak symmetries and symmetry breakings.

Topological Holography for Mixed-State Phases and Phase Transitions Bilayer construction for mixed state phenomena with strong, weak symmetries and symmetry breakings

Reference 96

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.203832Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98d620dc-aba5-4c3a-9fcd-ad274dfa1030 · outbound

This paper cites Entan- glement phases as holographic duals of anyon conden- sates,.

Topological Holography for Mixed-State Phases and Phase Transitions Entan- glement phases as holographic duals of anyon conden- sates,

Reference 97

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.270313Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0470301d-da60-4b2d-bdb1-6311476fb93e · outbound

This paper cites Fault-tolerant quantum computation by anyons,.

Topological Holography for Mixed-State Phases and Phase Transitions Fault-tolerant quantum computation by anyons,

Reference 98

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.356787Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cafce927-45de-41d4-9260-122bce655d04 · outbound

This paper cites Family of non- abelian kitaev models on a lattice: Topological con- densation and confinement,.

Topological Holography for Mixed-State Phases and Phase Transitions Family of non- abelian kitaev models on a lattice: Topological con- densation and confinement,

Reference 99

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.411712Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73af5a0f-8afa-4c56-946f-b8fe51b889ec · outbound

This paper cites Hamil- tonian and algebraic theories of gapped boundaries in topological phases of matter,.

Topological Holography for Mixed-State Phases and Phase Transitions Hamil- tonian and algebraic theories of gapped boundaries in topological phases of matter,

Reference 100

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.482028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5cfdc38a-e15c-4351-9903-ec631bb9c1d2 · outbound

This paper cites 205 (AMS Math- ematical Surveys and Monographs, 2015).

Topological Holography for Mixed-State Phases and Phase Transitions 205 (AMS Math- ematical Surveys and Monographs, 2015)

Reference 101

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.541638Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dca6b9fc-6b8f-4c80-b08e-1c9b50a9694e · outbound

This paper cites Finite group modular data,.

Topological Holography for Mixed-State Phases and Phase Transitions Finite group modular data,

Reference 102

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.578579Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3badb29-5b87-4c7e-bf3e-c56efa523c2c · outbound

This paper cites Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy.

Topological Holography for Mixed-State Phases and Phase Transitions Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

Reference 103

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.647904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3af80af7-b61b-49d8-970a-01864152a49c · outbound

This paper cites For canonical purification, this correspondence is less straightforward.

Topological Holography for Mixed-State Phases and Phase Transitions For canonical purification, this correspondence is less straightforward

Reference 104

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.725932Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ce63322-e76a-4f79-ae3a-7e1a1ef294e6 · outbound

This paper cites The finite group velocity of quantum spin systems,.

Topological Holography for Mixed-State Phases and Phase Transitions The finite group velocity of quantum spin systems,

Reference 105

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.766836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b182717c-980e-423b-ad17-615330fed363 · outbound

This paper cites Lieb-robinson bound and locality for general markovian quantum dynamics,.

Topological Holography for Mixed-State Phases and Phase Transitions Lieb-robinson bound and locality for general markovian quantum dynamics,

Reference 106

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.855281Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7908b530-d653-4671-9036-879f0bc06aed · outbound

This paper cites Speed limits and locality in many-body quantum dynamics,.

Topological Holography for Mixed-State Phases and Phase Transitions Speed limits and locality in many-body quantum dynamics,

Reference 107

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:52.903824Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acf4e13b-f96d-4ef1-9bbb-eb99664a49d5 · outbound

This paper cites The Perron–Frobenius theorem states that for a matrix with non-negative real components, the eigenvector with the largest eigenvalue also has non- negative real components.

Topological Holography for Mixed-State Phases and Phase Transitions The Perron–Frobenius theorem states that for a matrix with non-negative real components, the eigenvector with the largest eigenvalue also has non- negative real components

Reference 108

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.003294Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 912ef0a8-fa19-4c83-b107-50a015a73c4c · outbound

This paper cites Exploring critical systems under measurements and decoherence via Keldysh field theory.

Topological Holography for Mixed-State Phases and Phase Transitions Exploring critical systems under measurements and decoherence via Keldysh field theory

Reference 109

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.069360Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0089d274-1e98-4e9c-bca3-f2a07761d99b · outbound

This paper cites Intrinsically gapless topological phases,.

Topological Holography for Mixed-State Phases and Phase Transitions Intrinsically gapless topological phases,

Reference 110

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.146325Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7833c457-d0bb-45a9-83f7-9f3e49cef633 · outbound

This paper cites Anomalies and gauging of U(1) symmetries.

Topological Holography for Mixed-State Phases and Phase Transitions Anomalies and gauging of U(1) symmetries

Reference 111

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.234755Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df1faee7-637f-482c-b9a1-c06d64520cdf · outbound

This paper cites SymTh for non-finite symmetries,.

Topological Holography for Mixed-State Phases and Phase Transitions SymTh for non-finite symmetries,

Reference 112

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.303026Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01499fc3-b265-4fdd-bfbe-1f687bbcaca1 · outbound

This paper cites SymTFTs for Continuous non-Abelian Sym- metries,.

Topological Holography for Mixed-State Phases and Phase Transitions SymTFTs for Continuous non-Abelian Sym- metries,

Reference 113

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.417099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84f27529-1f09-4760-aa6a-9386e9f4782c · outbound

This paper cites Holographic duals of symmetry broken phases.

Topological Holography for Mixed-State Phases and Phase Transitions Holographic duals of symmetry broken phases

Reference 114

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.556502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51d13473-322f-4f93-a784-e250c685d406 · outbound

This paper cites SymTFTs for $U(1)$ symmetries from descent.

Topological Holography for Mixed-State Phases and Phase Transitions SymTFTs for $U(1)$ symmetries from descent

Reference 115

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.651435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7605f4f3-11a2-48fb-b997-451b97d8d798 · outbound

This paper cites Symmetry Topological Field Theory for Flavor Symmetry.

Topological Holography for Mixed-State Phases and Phase Transitions Symmetry Topological Field Theory for Flavor Symmetry

Reference 116

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.713713Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c8e7aee-6cca-4290-9e4c-5c2b2e5545c3 · outbound

This paper cites Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries.

Topological Holography for Mixed-State Phases and Phase Transitions Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries

Reference 117

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.816943Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cdf95314-6490-475e-acc5-bc4cfb0743e9 · outbound

This paper cites Lecture Notes on Generalized Symmetries and Applications.

Topological Holography for Mixed-State Phases and Phase Transitions Lecture Notes on Generalized Symmetries and Applications

Reference 118

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:53.898901Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 896d7355-a402-486f-86ce-d13f2ffb3d8f · outbound

This paper cites Drinfeld Centers and Morita Equivalence Classes of Fusion 2-Categories.

Topological Holography for Mixed-State Phases and Phase Transitions Drinfeld Centers and Morita Equivalence Classes of Fusion 2-Categories

Reference 119

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.012309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 611d77f9-51cc-4043-8c5f-59d656e4c9c4 · outbound

This paper cites Anomaly in open quantum systems and its implications on mixed-state quantum phases.

Topological Holography for Mixed-State Phases and Phase Transitions Anomaly in open quantum systems and its implications on mixed-state quantum phases

Reference 120

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.135486Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48804634-931c-4a3c-8a61-a7a1c409f367 · outbound

This paper cites SymSETs and self-dualities under gauging non-invertible symmetries.

Topological Holography for Mixed-State Phases and Phase Transitions SymSETs and self-dualities under gauging non-invertible symmetries

Reference 121

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.319732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14369f10-2489-43b3-adc0-ee2e1de57a3f · outbound

This paper cites The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed- State SPTs,.

Topological Holography for Mixed-State Phases and Phase Transitions The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed- State SPTs,

Reference 122

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.421292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08b02988-2d54-48ef-83e7-6986b5f0a821 · outbound

This paper cites SymTFT Approach for Mixed States with Non-Invertible Symmetries,.

Topological Holography for Mixed-State Phases and Phase Transitions SymTFT Approach for Mixed States with Non-Invertible Symmetries,

Reference 123

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.506348Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f8a88ba-8fa8-4b07-8538-ea79b9f4b6e5 · outbound

This paper cites Finite Group Modular Data.

Topological Holography for Mixed-State Phases and Phase Transitions Finite Group Modular Data

Reference 124

Resolution: unresolved; no resolver link, observed 2026-08-06T19:16:54.582272Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 3fa379e5-c3ac-42a5-958c-b387be4fdf74 · inbound

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Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model Topological Holography for Mixed-State Phases and Phase Transitions

Reference 56

Resolution: metadata mismatch; arxiv_id, observed 2026-05-18T13:41:25.835730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f34cc8af-8519-4f78-9fa6-b45e8592a315 · inbound

Krylov Complexity and Mixed-State Phase Transition cites this paper.

Krylov Complexity and Mixed-State Phase Transition Topological Holography for Mixed-State Phases and Phase Transitions

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-25T07:50:28.841657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 01d536f8-c619-4529-b33d-cf2f64bdd8cd · inbound

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On the SymTFTs of Finite Non-Abelian Symmetries Topological Holography for Mixed-State Phases and Phase Transitions

Reference 42

Resolution: metadata mismatch; arxiv_id, observed 2026-05-15T11:35:31.536808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6e00241a-d952-43ff-abd1-960e22820bfe · inbound

Generalized Complexity Distances and Non-Invertible Symmetries cites this paper.

Generalized Complexity Distances and Non-Invertible Symmetries Topological Holography for Mixed-State Phases and Phase Transitions

Reference 67

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T11:41:06.064529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 096c34aa-1332-4ebe-83a1-3d549b4230dc · inbound

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Categorical Symmetries via Operator Algebras Topological Holography for Mixed-State Phases and Phase Transitions

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:01:15.545830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ab1ac839-14f5-4afb-a78d-df9a38c4bf3b · inbound

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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs Topological Holography for Mixed-State Phases and Phase Transitions

Reference 45

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T20:56:12.115243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 49a78e21-25b8-4e19-bfbd-4387a3e53c53 · inbound

Algebras of order parameters in one-dimensional spin systems cites this paper.

Algebras of order parameters in one-dimensional spin systems Topological Holography for Mixed-State Phases and Phase Transitions

Reference 90

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:25:49.549288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e7769d65-1a45-4701-8125-891a036d3fe9 · inbound

Fracton Topological Holography cites this paper.

Fracton Topological Holography Topological Holography for Mixed-State Phases and Phase Transitions

Reference 68

Resolution: verified exact; arxiv_id, observed 2026-07-02T03:16:34.193894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 09db3454-1c3b-46a0-b2fa-c8da1e0c9bff · inbound

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From Topological Order to Mixed-State Phases: A Ground-State Probe of Fractionalized Excitations Topological Holography for Mixed-State Phases and Phase Transitions

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-03T13:18:12.893817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c8846a53-1823-4a62-89a6-e947145d4b7a · inbound

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From Topological Order to Mixed-State Phases: A Ground-State Probe of Fractionalized Excitations Topological Holography for Mixed-State Phases and Phase Transitions

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-06-30T10:44:37.372097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.