Paper Citation Record · LEDGER

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code

As of 14 August 2026, this Paper Citation Record lists 71 of 71 outbound references and 3 inbound Pith citation observations for arXiv:2510.20489.

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

pith.paper-citation-record.v1
2510.20489 v3

Coverage vector

measured 71 of 71 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T08:32:12.364749Z

measured 74 of 74 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T07:11:27.964028Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T21:43:58.673881Z

Reference resolution

71 of 71 outbound references displayed

verified exact9
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External citation measurements

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Outbound references

Observation 4de318de-debe-44ba-b4cb-41e511dd3b1b · outbound

This paper cites Journal of Mathematical Physics43(9), 4452–4505 (2002) https://doi.org/10.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Journal of Mathematical Physics43(9), 4452–4505 (2002) https://doi.org/10

Reference 1

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 2

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 3

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 4

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This paper cites Annals of Physics 303(1), 2–30 (2003) https://doi.org/10.1016/S0003-4916(02)00018-0.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Annals of Physics 303(1), 2–30 (2003) https://doi.org/10.1016/S0003-4916(02)00018-0

Reference 5

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Observation 0282d4b6-2189-4cee-be76-7c65b92c0fc5 · outbound

This paper cites Quantum codes on a lattice with boundary.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Quantum codes on a lattice with boundary

Reference 6

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Observation 35c93c21-c26c-46e3-9b80-76703fdc116b · outbound

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 7

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This paper cites Science374(6572), 1237–1241 (2021) https://doi.org/10.1126/science.abi8378 17.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Science374(6572), 1237–1241 (2021) https://doi.org/10.1126/science.abi8378 17

Reference 8

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This paper cites Nature605(7911), 669–674 (2022) https://doi.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature605(7911), 669–674 (2022) https://doi

Reference 9

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Reference 10

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 11

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This paper cites Nature638(8052), 920–926 (2025) https://doi.org/10.1038/s41586-024-08449-y.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature638(8052), 920–926 (2025) https://doi.org/10.1038/s41586-024-08449-y

Reference 12

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This paper cites Nature (2025) https://doi.org/10.1038/s41586-025-09061-4.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature (2025) https://doi.org/10.1038/s41586-025-09061-4

Reference 13

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Science385(6715), 1327–1331 (2024) https://doi.org/10.1126/science

Reference 14

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature626(7997), 58–65 (2024) https://doi.org/10

Reference 15

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature645(8081), 620–625 (2025) https://doi.org/10.1038/s41586-025-09367-3

Reference 16

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature589(7841), 220–224 (2021) https://doi.org/10.1038/s41586-020-03079-6 20

Reference 17

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Science345(6194), 302–305 (2014) https://doi.org/10.1126/ science.1253742

Reference 18

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Reference 19

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Reference 20

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature627(8005), 778–782 (2024) https://doi.org/10.1038/s41586-024-07107-7

Reference 21

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This paper cites IEEE Transactions on Information Theory60(2), 1193–1202 (2014) https://doi.org/10.1109/TIT.2013.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code IEEE Transactions on Information Theory60(2), 1193–1202 (2014) https://doi.org/10.1109/TIT.2013

Reference 22

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Reference 23

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Observation fa70fae5-93c2-4d6a-82a8-197f51476540 · outbound

This paper cites Tour de gross: A modular quantum computer based on bivariate bicycle codes.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Tour de gross: A modular quantum computer based on bivariate bicycle codes

Reference 24

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Reference 25

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 26

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code SciPost Phys.16, 122 (2024) https://doi.org/10.21468/SciPostPhys.16.5.122

Reference 27

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Quantum5, 585 (2021) https://doi.org/10.22331/ q-2021-11-22-585 21

Reference 28

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum2, 020340 (2021) https://doi.org/10.1103/PRXQuantum.2.020340

Reference 29

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature Communications7(1), 12302 (2016) https://doi

Reference 30

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Reference 31

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Annales de l’Institut Henri Poincar´ e D8(2), 269–321 (2021)

Reference 32

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum5, 020343 (2024) https://doi.org/10.1103/PRXQuantum.5.020343

Reference 33

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Reference 34

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code https://arxiv.org/abs/ 2412.16727

Reference 35

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum6, 040305 (2025) https://doi.org/10.1103/gskb-t5ql

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Annals of Physics303(1), 31–58 (2003) https://doi.org/10.1016/S0003-4916(02)00019-2

Reference 37

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Reference 38

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Observation 31b647ed-fd00-4052-87c1-0681a6339e8d · outbound

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum2, 020341 (2021) https://doi.org/10.1103/PRXQuantum

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code npj Quantum Information10(1), 136 (2024) https://doi.org/10.1038/s41534-024-00945-3

Reference 41

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Journal of Statistical Physics126(4), 977–986 (2007) https://doi.org/10.1007/s10955-006-9156-1

Reference 43

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Quantum2, 68 (2018) https://doi.org/10.22331/ q-2018-05-24-68

Reference 44

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Observation 069d11ba-2850-44d9-b87a-04e4113559cc · outbound

This paper cites [29] compared to our convention, thus their correponding thresholds.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code [29] compared to our convention, thus their correponding thresholds

Reference 45

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Reference 46

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum5, 020349 (2024) https://doi.org/10.1103/PRXQuantum.5.020349

Reference 47

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Observation b3a2eec1-0bb5-4ed2-9174-f15e4751be97 · outbound

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Reference 48

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Journal of High Energy Physics2015(2), 172 (2015) https://doi.org/10.1007/ JHEP02(2015)172

Reference 49

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Reference 50

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Observation ba89e9c3-577e-471e-b98b-eac37f292f51 · outbound

This paper cites Annual Review of Condensed Matter Physics14(Volume 14, 2023), 57–82 (2023) https://doi.org/ 10.1146/annurev-conmatphys-040721-021029.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Annual Review of Condensed Matter Physics14(Volume 14, 2023), 57–82 (2023) https://doi.org/ 10.1146/annurev-conmatphys-040721-021029

Reference 51

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Observation 1c1aaa12-8259-4a01-864a-fc3596d0eb1f · outbound

This paper cites Journal of Mathematical Physics12(10), 2259–2272 (1971) https://doi.org/10.1063/1.1665530 23.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Journal of Mathematical Physics12(10), 2259–2272 (1971) https://doi.org/10.1063/1.1665530 23

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:10.752961Z

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Observation dc414963-25ed-43e3-a47b-dda8ad5cb7ca · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 53

Resolution: verified exact; doi, observed 2026-08-04T08:33:24.198304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d57797e9-3d4b-4262-9eec-b8229ed0e4d7 · outbound

This paper cites [69–71], Fig S1 for error channels, and Fig S2 for error worldlines.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code [69–71], Fig S1 for error channels, and Fig S2 for error worldlines

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:10.876034Z

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Observation 5d69b57f-4f5b-442d-831e-7a0e3a3be04f · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:10.940026Z

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Observation d2741742-43ea-43c0-bb76-1aeccd96eda1 · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 56

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Observation 1849eb97-79b1-4763-b98c-519f4eb2691f · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 57

Resolution: verified exact; doi, observed 2026-08-04T08:33:24.045340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e28c9185-22e9-45ba-8bd8-490a4b629780 · outbound

This paper cites Nature Communications12(1), 2172 (2021) https://doi.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Nature Communications12(1), 2172 (2021) https://doi

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:11.072673Z

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Observation 967f7bfa-a69b-466c-988e-c0b2eda8b175 · outbound

This paper cites PRX Quantum4, 030338 (2023) https://doi.org/10.1103/PRXQuantum.4.030338.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum4, 030338 (2023) https://doi.org/10.1103/PRXQuantum.4.030338

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:11.114739Z

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Observation 0da80c00-1a04-481e-9c2a-aa862e63c41a · outbound

This paper cites npj Quantum Information11(1), 149 (2025) https://doi.org/ 10.1038/s41534-025-01074-1.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code npj Quantum Information11(1), 149 (2025) https://doi.org/ 10.1038/s41534-025-01074-1

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:11.204827Z

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Observation 152d3a7a-d904-4159-8e00-904367d32869 · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:11.320003Z

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Observation 04a0b577-4d8e-452a-9d5b-387654360012 · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:11.384819Z

Source-reported events for the cited work

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Observation c6b4f77b-f1d3-4fd6-9b1f-a80f688d105b · outbound

This paper cites https://arxiv.org/abs/2403.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code https://arxiv.org/abs/2403

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:11.514750Z

Source-reported events for the cited work

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Observation 8c61356f-91b3-411e-b047-2d441aad9b3a · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 64

Resolution: malformed identifier; no resolver link, observed 2026-08-04T08:32:11.606718Z

Source-reported events for the cited work

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Observation 7c68de9e-485b-44f3-b904-ddcf9ef703b7 · outbound

This paper cites an unresolved cited work.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Unresolved cited work

Reference 65

Resolution: malformed identifier; no resolver link, observed 2026-08-04T08:32:11.724828Z

Source-reported events for the cited work

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Observation 524a9bb2-07b5-4486-afff-5ddae114b44d · outbound

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum6, 020357 (2025) https://doi.org/ 10.1103/rmy6-9n89

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:11.846038Z

Source-reported events for the cited work

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Observation 6a82c4ab-03d4-467f-89a0-1bc32248de5a · outbound

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code PRX Quantum6, 030330 (2025) https://doi.org/10.1103/ 7x71-8j7k

Reference 67

Resolution: malformed identifier; no resolver link, observed 2026-08-04T08:32:11.924749Z

Source-reported events for the cited work

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Observation e973abbb-3ba3-4b24-8ea0-2a7b5b915c55 · outbound

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Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Com- munications in Mathematical Physics324(2), 351–399 (2013) https://doi.org/10

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:12.073622Z

Source-reported events for the cited work

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Observation 1cebcb15-7f40-4d5c-9499-3b7b8d32b76d · outbound

This paper cites Oxford University Press, Oxford; New York (2001).

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Oxford University Press, Oxford; New York (2001)

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-04T08:32:12.165849Z

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Observation 9919c64a-a948-4732-8a35-5db2984281de · outbound

This paper cites Physica68(3), 570–578 (1973) https://doi.org/10.1016/ 0031-8914(73)90381-9.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code Physica68(3), 570–578 (1973) https://doi.org/10.1016/ 0031-8914(73)90381-9

Reference 70

Resolution: malformed identifier; no resolver link, observed 2026-08-04T08:32:12.239849Z

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Observation caeafb22-09f6-4356-9e49-bccddbe6df7b · outbound

This paper cites +” and the differential “∂.

Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code +” and the differential “∂

Reference 71

Resolution: verified exact; doi, observed 2026-08-04T08:33:23.802680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation 175f84d0-7236-4ccc-aa75-a23a96d4e078 · inbound

Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions cites this paper.

Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-07-01T02:17:17.369259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d7ab3835-4592-4653-a922-c64503d450af · inbound

Homomorphic Quantum Error Correction cites this paper.

Homomorphic Quantum Error Correction Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code

Reference 50

Resolution: verified exact; arxiv_id, observed 2026-07-01T02:17:17.369259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cad1f3c9-b660-4eaf-8d0d-e7e231818ac2 · inbound

Confinement as Decoding: Higher Form Codes and Lattice Yang-Mills Theory cites this paper.

Confinement as Decoding: Higher Form Codes and Lattice Yang-Mills Theory Phenomenological Noise Models and Optimal Thresholds of the 3D Toric Code

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T07:11:27.964028Z

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Unavailable: canonical work link unavailable.