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Paper Citation Record · LEDGER

Coupled-Layer Codes: Beyond Quantum Product Constructions

As of 14 August 2026, this Paper Citation Record lists 86 of 86 outbound references and 0 inbound Pith citation observations for arXiv:2608.10069.

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

pith.paper-citation-record.v1
2608.10069 v1

Coverage vector

measured 86 of 86 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-14T04:20:47.325707Z

measured 86 of 86 standing notices

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

measured 0 of 0 inbound itemization

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measured 0 of 1 external citation measurements

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Reference resolution

86 of 86 outbound references displayed

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  • verified fuzzy16
  • unresolved64
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  • malformed identifier0
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External citation measurements

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Outbound references

Observation d3c476a0-432d-44f7-afd3-6b525808ee0c · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 1

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Observation a615b56c-ecba-42c7-966a-58ea8158c8f3 · outbound

This paper cites IfU g “idso that˜s 1 is also anX-stabilizer, then we only need to relabel qubitsb 1b˜sa byb 1¨gb˜s1.

Coupled-Layer Codes: Beyond Quantum Product Constructions IfU g “idso that˜s 1 is also anX-stabilizer, then we only need to relabel qubitsb 1b˜sa byb 1¨gb˜s1

Reference 2

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Observation 53bba19a-39df-4bb5-a3d5-5a3f839c0ed1 · outbound

This paper cites V, the resulting code is independent of the representatives.

Coupled-Layer Codes: Beyond Quantum Product Constructions V, the resulting code is independent of the representatives

Reference 3

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Observation 2fbb76d9-3dad-4eae-9d84-c36b4d670f88 · outbound

This paper cites ABABto be the sign upon commuting a pair of operators, we have sgnpApe, ˜fq,Bph t,˜q2qq “sgn ´ Γp ˜fqpeq, ź gPC Γp ˜fqpUg´1phtqq ¯ sgn ´ź gPC Ugpep˜q2qq,h p˜q2q t ¯ “ ź gPC.

Coupled-Layer Codes: Beyond Quantum Product Constructions ABABto be the sign upon commuting a pair of operators, we have sgnpApe, ˜fq,Bph t,˜q2qq “sgn ´ Γp ˜fqpeq, ź gPC Γp ˜fqpUg´1phtqq ¯ sgn ´ź gPC Ugpep˜q2qq,h p˜q2q t ¯ “ ź gPC

Reference 4

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Observation fdc653b2-c4f0-4e18-a0e3-03e785e602ef · outbound

This paper cites This is captured by a few related concepts, namely the mapping cone, which in turn is related to partial gauging/partial lattice surgery between the lay- ers.

Coupled-Layer Codes: Beyond Quantum Product Constructions This is captured by a few related concepts, namely the mapping cone, which in turn is related to partial gauging/partial lattice surgery between the lay- ers

Reference 5

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Observation 986c4bc0-e7df-443f-b873-c755d3900ba0 · outbound

This paper cites As an ex- ample, we discussed thee´mbalanced product where the onsite unitary is Hadamard.

Coupled-Layer Codes: Beyond Quantum Product Constructions As an ex- ample, we discussed thee´mbalanced product where the onsite unitary is Hadamard

Reference 6

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Observation f500fac4-0267-44bc-abf5-23577d72be88 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 7

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source=pdf_text observed=2026-08-14T04:20:46.963155Z digest=sha256:d0ac3eea84a5104f20d5d3fcbdd6fcb45faa62d8b6418ffb2f22f6de55440b56

Observation 7ec970e9-3d05-4db4-b87c-28953e7ad48b · outbound

This paper cites Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}.

Coupled-Layer Codes: Beyond Quantum Product Constructions Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}

Reference 8

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Observation dc52fcfc-d7fe-4f20-9111-6a1e2ac8e6bc · outbound

This paper cites Bravyi and M.

Coupled-Layer Codes: Beyond Quantum Product Constructions Bravyi and M

Reference 9

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Observation dcbd04e1-020d-4ea8-8f9e-7f8490abb382 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 10

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Observation c5d222d4-8422-43ce-9405-c12d422a2f27 · outbound

This paper cites Panteleev and G.

Coupled-Layer Codes: Beyond Quantum Product Constructions Panteleev and G

Reference 11

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Observation 765f049c-21d4-456f-839b-48441d132969 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 12

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source=pdf_text observed=2026-08-14T04:20:46.983808Z digest=sha256:29d6eb77367d2ad8ed8a3910bfaa4917c29dffaca9d265d62006d05d12cc25b5

Observation 065f438c-53d4-42de-a41d-2432cd1d6fbe · outbound

This paper cites Panteleev and G.

Coupled-Layer Codes: Beyond Quantum Product Constructions Panteleev and G

Reference 13

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Observation 54783ee8-b13f-4126-9994-f47d96150e9a · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 14

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Observation 6c22b866-681c-4678-bd9d-b79a709f420a · outbound

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Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 15

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Observation 55b81369-49bb-42c0-a448-7d81de1c574f · outbound

This paper cites From Luttinger liquid to non-Abelian quantum Hall states.

Coupled-Layer Codes: Beyond Quantum Product Constructions From Luttinger liquid to non-Abelian quantum Hall states

Reference 16

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source=pdf_text observed=2026-08-14T04:20:46.999344Z digest=sha256:8f3ddf66e8c2e2db481f919d2980d1cd0a665cec66777b715e70e9b54ca6885e

Observation 5117ffd3-c468-4e2a-8b83-bc05e6ec9d7b · outbound

This paper cites Boson topological insulators: A window into highly entangled quantum phases.

Coupled-Layer Codes: Beyond Quantum Product Constructions Boson topological insulators: A window into highly entangled quantum phases

Reference 17

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

source=pdf_text observed=2026-08-14T04:20:47.003433Z digest=sha256:b39fe71415c26d8f7d6fcca6823c21cd220fa67fedd922827444ec9b1e3648ea

Observation 3e45735e-0108-434a-9da1-80cb09a60e6d · outbound

This paper cites Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model.

Coupled-Layer Codes: Beyond Quantum Product Constructions Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model

Reference 18

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Observation 3be77830-ce85-4e43-adeb-e42f3cdca7ce · outbound

This paper cites Jian and X.-L.

Coupled-Layer Codes: Beyond Quantum Product Constructions Jian and X.-L

Reference 19

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Observation 414047de-84b9-4c63-b5c0-9e22a3ff03bf · outbound

This paper cites Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases.

Coupled-Layer Codes: Beyond Quantum Product Constructions Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases

Reference 20

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Observation 06aa25cb-a5ff-4801-a6f4-3b9bcbb32177 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 21

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source=pdf_text observed=2026-08-14T04:20:47.021447Z digest=sha256:acbba148145d98c719bb52f26878a1feb8684cc0e3b12b1f8b5487607e8bf5e4

Observation e70d7401-02d3-485e-82ea-239e0e0661b3 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 22

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source=pdf_text observed=2026-08-14T04:20:47.025390Z digest=sha256:6539b69d0cc4e32211498877f21de55219e901bf6ba8e2cf66dd7633347dd426

Observation 4a2edbf6-ad4f-4c28-be4a-b00a518ff610 · outbound

This paper cites Prem, S.-J.

Coupled-Layer Codes: Beyond Quantum Product Constructions Prem, S.-J

Reference 23

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source=pdf_text observed=2026-08-14T04:20:47.029225Z digest=sha256:20198da1a45e0d8ee9d4bd5a7d30c04b3efee0f1491066134d3cb93f995d2268

Observation 8b1dc005-8fe2-4329-aadd-5720f275c61a · outbound

This paper cites Distilling Fractons from Layered Subsystem-Symmetry Protected Phases.

Coupled-Layer Codes: Beyond Quantum Product Constructions Distilling Fractons from Layered Subsystem-Symmetry Protected Phases

Reference 24

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source=pdf_text observed=2026-08-14T04:20:47.032820Z digest=sha256:e975eaae6ed5d73739b6f53baac3795b68ca3526cff15a973ea3fa6b20ecd3c9

Observation 693077cc-1113-4603-8928-f8074d3ac762 · outbound

This paper cites Designer non-Abelian fractons from topological layers.

Coupled-Layer Codes: Beyond Quantum Product Constructions Designer non-Abelian fractons from topological layers

Reference 25

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Observation 71fce6d6-f966-4df1-824a-9a538772132f · outbound

This paper cites Wen, Systematic construction of gapped nonliquid states, Phys.

Coupled-Layer Codes: Beyond Quantum Product Constructions Wen, Systematic construction of gapped nonliquid states, Phys

Reference 26

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Observation 2bfc262f-7138-4c20-b76d-6f447fd1f31d · outbound

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Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 27

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Observation ca9ee49d-e7d6-4021-a769-ceb7d75fe596 · outbound

This paper cites Sullivan, T.

Coupled-Layer Codes: Beyond Quantum Product Constructions Sullivan, T

Reference 28

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source=pdf_text observed=2026-08-14T04:20:47.049918Z digest=sha256:dbcf792115cd75f8dc860406965f3ef44d890e7b33df1663bfb578fc2097fb08

Observation c54ee59f-0ccd-4583-8803-3a76b7b0bf9b · outbound

This paper cites Wang, Nonliquid cellular states: Gluing gauge-higher- symmetry-breaking versus gauge-higher-symmetry-extension interfacial defects, Phys.

Coupled-Layer Codes: Beyond Quantum Product Constructions Wang, Nonliquid cellular states: Gluing gauge-higher- symmetry-breaking versus gauge-higher-symmetry-extension interfacial defects, Phys

Reference 29

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source=pdf_text observed=2026-08-14T04:20:47.053557Z digest=sha256:0219ba112d06107a8358b0c3d44b212487c68c229fc6bf6d83abc7a74f343d15

Observation 0367d98c-f3de-4cda-a484-17b9e4ac0ec4 · outbound

This paper cites Liu and W.

Coupled-Layer Codes: Beyond Quantum Product Constructions Liu and W

Reference 30

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source=pdf_text observed=2026-08-14T04:20:47.057254Z digest=sha256:64f3d3b8ffafcdac12f167a1b35b75ea563e178a4fd5a57c4c1c9818f7f750e2

Observation f3a544aa-fa7f-427e-b260-69211d19d53b · outbound

This paper cites Gapped boundaries of (3+1)d topological orders.

Coupled-Layer Codes: Beyond Quantum Product Constructions Gapped boundaries of (3+1)d topological orders

Reference 31

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source=pdf_text observed=2026-08-14T04:20:47.060925Z digest=sha256:9b23cea2459aed7fc3269852b0da772cf7985ef61eb61aa9d15598ff578dffb5

Observation 35731e73-9c7c-4aa5-a3bb-ac3bae849766 · outbound

This paper cites Garre-Rubio, Emergent (2+1)d topological orders from itera- tive (1+1)d gauging, Nature Communications15, 7986 (2024).

Coupled-Layer Codes: Beyond Quantum Product Constructions Garre-Rubio, Emergent (2+1)d topological orders from itera- tive (1+1)d gauging, Nature Communications15, 7986 (2024)

Reference 32

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source=pdf_text observed=2026-08-14T04:20:47.064690Z digest=sha256:be0a974b1e51c80f9566946b5b8099b13f0a772aea8a38559332d85c8a7afffc

Observation 9bb6deeb-c587-4f18-a39b-c694dc749f54 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 33

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source=pdf_text observed=2026-08-14T04:20:47.068032Z digest=sha256:a2c6f6b8e2f32fabbf0de6b642fb7c8fe3b3d848498245d227daceb73da50cd9

Observation b7779eec-2908-4ade-9b13-0b48ab9b737c · outbound

This paper cites String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation.

Coupled-Layer Codes: Beyond Quantum Product Constructions String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation

Reference 34

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source=pdf_text observed=2026-08-14T04:20:47.071972Z digest=sha256:ea1926131aeac5f5d715844227566d957a430f32de26f8e3c06a139a50de18b2

Observation 8aba0383-cdf9-4dd5-a38c-b81f21344dac · outbound

This paper cites There and Back Again: A Gauging Nexus between Topological and Fracton Phases.

Coupled-Layer Codes: Beyond Quantum Product Constructions There and Back Again: A Gauging Nexus between Topological and Fracton Phases

Reference 35

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source=pdf_text observed=2026-08-14T04:20:47.075732Z digest=sha256:9c5b9ce3a5a84f8273a582dc0e85cb790cf3312310ac159376f3dc878328df80

Observation 79d43b8b-54d0-4202-a676-d1141d6ee5e8 · outbound

This paper cites Constructing Bulk Topological Orders via Layered Gauging.

Coupled-Layer Codes: Beyond Quantum Product Constructions Constructing Bulk Topological Orders via Layered Gauging

Reference 36

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source=pdf_text observed=2026-08-14T04:20:47.079306Z digest=sha256:4a89747132ed7d31c2a0ec6a46ff8139292217d8078f58c1d7224d464e7d7f41

Observation dbd5b48f-847c-458e-a4b4-49a87871e47a · outbound

This paper cites Coupled-Layer Construction of Quantum Product Codes.

Coupled-Layer Codes: Beyond Quantum Product Constructions Coupled-Layer Construction of Quantum Product Codes

Reference 37

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source=pdf_text observed=2026-08-14T04:20:47.083181Z digest=sha256:c04ccb5d35f48a4787da82afbecc7df885bb407007f89c526dca8a5bad77a361

Observation 4bb09cf9-6cc6-4f6c-9ebc-c8bbcd66cc39 · outbound

This paper cites Vijay, J.

Coupled-Layer Codes: Beyond Quantum Product Constructions Vijay, J

Reference 38

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source=pdf_text observed=2026-08-14T04:20:47.087092Z digest=sha256:ab7ed6cc382f7a6958179239d0e807213e858a739b1262897bfd0268d2c2241d

Observation fb11505a-73f3-441c-9e1d-ce30fe68ffca · outbound

This paper cites Codimension-2 defects and higher symmetries in (3+1)D topological phases.

Coupled-Layer Codes: Beyond Quantum Product Constructions Codimension-2 defects and higher symmetries in (3+1)D topological phases

Reference 39

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no resolver link, observed 2026-08-14T04:20:47.090707Z

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source=pdf_text observed=2026-08-14T04:20:47.090707Z digest=sha256:21ce8bd008ee0f294290fbcdfd54c04aa97a2ddedaee0a5ea7bee68b6c115406

Observation 8a8f13b7-876f-4dad-b42d-c9cc59a96bc2 · outbound

This paper cites On Quantum Weight Reduction.

Coupled-Layer Codes: Beyond Quantum Product Constructions On Quantum Weight Reduction

Reference 40

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source=pdf_text observed=2026-08-14T04:20:47.094222Z digest=sha256:509f1d2846f75fa9f218c0be1f5d6294dd08280edd0a534fa04c1cc11d43d1be

Observation 227f54a7-4583-4ea8-be52-8cb42d3bd805 · outbound

This paper cites SSIP: automated surgery with quantum LDPC codes.

Coupled-Layer Codes: Beyond Quantum Product Constructions SSIP: automated surgery with quantum LDPC codes

Reference 41

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no resolver link, observed 2026-08-14T04:20:47.097744Z

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source=pdf_text observed=2026-08-14T04:20:47.097744Z digest=sha256:0273df8d5c2a4f0453d5198afd16d246d7b21fe6c06dd999586d465ccbe87cb9

Observation 8fd39f33-646a-4e45-b8fb-258ec6387bf3 · outbound

This paper cites Fault-tolerant logical measurements via homological measurement.

Coupled-Layer Codes: Beyond Quantum Product Constructions Fault-tolerant logical measurements via homological measurement

Reference 42

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no resolver link, observed 2026-08-14T04:20:47.101956Z

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source=pdf_text observed=2026-08-14T04:20:47.101956Z digest=sha256:21f5dd29f001abc0920984aeef0b53519f9d9ce1e3e125162d95730fae086613

Observation 2ca54584-bb61-4d80-a0f3-ae6be225d786 · outbound

This paper cites Parallel Logical Measurements via Quantum Code Surgery.

Coupled-Layer Codes: Beyond Quantum Product Constructions Parallel Logical Measurements via Quantum Code Surgery

Reference 43

Resolution
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no resolver link, observed 2026-08-14T04:20:47.106126Z

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source=pdf_text observed=2026-08-14T04:20:47.106126Z digest=sha256:0370b48cef63d2ac5dbd18cbb511d3b5df264644ff0f4f5bddaa90c1f1723686

Observation bb6b29c3-a58e-4c80-b8cd-27634b1b7c02 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 44

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verified exact
raw_fallback, observed 2026-08-14T04:20:47.817975Z

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.

source=pdf_text observed=2026-08-14T04:20:47.109958Z digest=sha256:85f9a070425c4a4a2bfea5f2de04d1f64bba9cb7bc989e4c681e783e2334437e

Observation 8f5655dd-d156-4292-b371-8e6df4e6d173 · outbound

This paper cites Cowtan, Z.

Coupled-Layer Codes: Beyond Quantum Product Constructions Cowtan, Z

Reference 45

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no resolver link, observed 2026-08-14T04:20:47.113404Z

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source=pdf_text observed=2026-08-14T04:20:47.113404Z digest=sha256:4799772e46a4754103997df15d30db9b4c499d92aa402fdb94449e446148efa6

Observation b36f7558-3777-4413-9672-c1d80f59d4bb · outbound

This paper cites Chang, Z.

Coupled-Layer Codes: Beyond Quantum Product Constructions Chang, Z

Reference 46

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no resolver link, observed 2026-08-14T04:20:47.117000Z

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source=pdf_text observed=2026-08-14T04:20:47.117000Z digest=sha256:4df8ff45340f0b355cc2a917eff702703727087b445b76c04f3463a84fc77d81

Observation f46dcd97-d573-4baa-a2c9-82d75262dc68 · outbound

This paper cites Logical computation with canonical lifted product codes.

Coupled-Layer Codes: Beyond Quantum Product Constructions Logical computation with canonical lifted product codes

Reference 47

Resolution
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source=pdf_text observed=2026-08-14T04:20:47.120423Z digest=sha256:53b742506749c4f708600e8aac6039e37a51ac33ea08d0ac1b8a15408afbbc94

Observation efdc70ba-8ace-4ee5-a4cd-1c69735761a0 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 48

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no resolver link, observed 2026-08-14T04:20:47.124265Z

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source=pdf_text observed=2026-08-14T04:20:47.124265Z digest=sha256:49498e334e0bfb1618ee4957bb0ccf95302507eccb5e6d6e79f9b1ad2e684281

Observation 4c6049c0-d2d2-4d81-b6c3-7293dce9e0f3 · outbound

This paper cites The Physics of (good) LDPC Codes II. Product constructions.

Coupled-Layer Codes: Beyond Quantum Product Constructions The Physics of (good) LDPC Codes II. Product constructions

Reference 49

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no resolver link, observed 2026-08-14T04:20:47.127888Z

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source=pdf_text observed=2026-08-14T04:20:47.127888Z digest=sha256:b97301580d00c9bcd2a2a0602a63b98a8448cb694d73517ab9d0927390e26322

Observation bf731e23-d296-45e2-91c8-701c7af59588 · outbound

This paper cites Quantum Glassiness.

Coupled-Layer Codes: Beyond Quantum Product Constructions Quantum Glassiness

Reference 50

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no resolver link, observed 2026-08-14T04:20:47.131846Z

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source=pdf_text observed=2026-08-14T04:20:47.131846Z digest=sha256:4b1ce3e0b89b1025028603b41302070e417915125fdfcb255c42d720c56f3b97

Observation 0dba0e6a-f976-4fdc-b259-dc294b09296b · outbound

This paper cites Quantum XYZ Product Codes.

Coupled-Layer Codes: Beyond Quantum Product Constructions Quantum XYZ Product Codes

Reference 51

Resolution
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no resolver link, observed 2026-08-14T04:20:47.135627Z

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source=pdf_text observed=2026-08-14T04:20:47.135627Z digest=sha256:f1f4364c52c7269e9d5efeabe96b6df99d4f2f34827a2e55affb07b20985e41e

Observation 47e0e6e5-4b44-4300-8811-0270defcb17c · outbound

This paper cites (3+1)-TQFTs and Topological Insulators.

Coupled-Layer Codes: Beyond Quantum Product Constructions (3+1)-TQFTs and Topological Insulators

Reference 52

Resolution
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source=pdf_text observed=2026-08-14T04:20:47.139254Z digest=sha256:31b5fa2d31f29d0601ec856039fb901a9efec96ef2efa779c80c66aa8fc8351e

Observation 935c4212-736f-4242-b6c9-59fe6d22422a · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 53

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unresolved
raw_fallback, observed 2026-08-14T04:20:48.390312Z

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.

source=pdf_text observed=2026-08-14T04:20:47.142719Z digest=sha256:68347b2f042512594ce9d3a1ccb51e67632dd6829588370a5bb68bab54862198

Observation 352247f6-56c9-4a7a-abef-03c087bc3270 · outbound

This paper cites Nontrivial Quantum Cellular Automata in Higher Dimensions.

Coupled-Layer Codes: Beyond Quantum Product Constructions Nontrivial Quantum Cellular Automata in Higher Dimensions

Reference 54

Resolution
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no resolver link, observed 2026-08-14T04:20:47.147009Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T04:20:47.147009Z digest=sha256:58d8d16af673975436d484026d2fca52ab089cbc271fb03fba42d197fa3adce0

Observation 0ddb66f0-f428-46cb-bee2-cb446ff38728 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 55

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unresolved
raw_fallback, observed 2026-08-14T04:20:48.376807Z

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.

source=pdf_text observed=2026-08-14T04:20:47.150790Z digest=sha256:19796cc1d195b12d35e4a5406f103770376ec5c88f568f287948acdac2c41912

Observation 99dee30d-44d6-406f-bf51-622ed0b86658 · outbound

This paper cites Yoshida, Topological phases with generalized global sym- metries, Phys.

Coupled-Layer Codes: Beyond Quantum Product Constructions Yoshida, Topological phases with generalized global sym- metries, Phys

Reference 56

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verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.365607Z

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.

source=pdf_text observed=2026-08-14T04:20:47.166688Z digest=sha256:1dbf213012408aa9a173f4449a439f2c558b61db7789fe0e1119d857e60e0224

Observation d047054f-94c3-4f00-991a-e4b0e5ac986d · outbound

This paper cites Yoshida, Gapped boundaries, group cohomology and fault- tolerant logical gates, Annals of Physics377, 387 (2017).

Coupled-Layer Codes: Beyond Quantum Product Constructions Yoshida, Gapped boundaries, group cohomology and fault- tolerant logical gates, Annals of Physics377, 387 (2017)

Reference 57

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raw_fallback, observed 2026-08-14T04:20:48.354226Z

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.

source=pdf_text observed=2026-08-14T04:20:47.170643Z digest=sha256:7831e29f6517d639c5af51ec6b46c39195773c79d0a4390bdb68da360ae2c986

Observation c6cd6702-3f88-47b1-a9f4-989d4be1787f · outbound

This paper cites Ungauging quantum error-correcting codes.

Coupled-Layer Codes: Beyond Quantum Product Constructions Ungauging quantum error-correcting codes

Reference 58

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no resolver link, observed 2026-08-14T04:20:47.174920Z

Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T04:20:47.174920Z digest=sha256:ecd2a028da830d6606904059ab08c3915754601a7a4009146afb5d5375df9bd1

Observation df747bb3-3dcc-4ad8-ade0-97090979796f · outbound

This paper cites Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order.

Coupled-Layer Codes: Beyond Quantum Product Constructions Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order

Reference 59

Resolution
unresolved
no resolver link, observed 2026-08-14T04:20:47.179171Z

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source=pdf_text observed=2026-08-14T04:20:47.179171Z digest=sha256:9c38dc7c7fb7fd3ed4d75661f1ca01d7d27eab83cbe6fd0e1e254cbab955a21d

Observation 4a45e462-37ff-41fa-a347-2467c8d644c1 · outbound

This paper cites The Physics of (good) LDPC Codes I. Gauging and dualities.

Coupled-Layer Codes: Beyond Quantum Product Constructions The Physics of (good) LDPC Codes I. Gauging and dualities

Reference 60

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no resolver link, observed 2026-08-14T04:20:47.187681Z

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source=pdf_text observed=2026-08-14T04:20:47.187681Z digest=sha256:3d25387dfa088cc4a44acdccdee327fa9461e25e522c0e267e11df9861cef56c

Observation d3b1df4e-2fa9-4df0-b7cd-3cbd1780024a · outbound

This paper cites Hatcher,Algebraic topology(Cambridge Univ.

Coupled-Layer Codes: Beyond Quantum Product Constructions Hatcher,Algebraic topology(Cambridge Univ

Reference 61

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source=pdf_text observed=2026-08-14T04:20:47.191920Z digest=sha256:3c021a8d08a31d213ab85558148a3dff63acb20bb8aefe540ba17804861c85ed

Observation 3a96bc3e-b92e-4261-8b60-ca3f0c783040 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 62

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raw_fallback, observed 2026-08-14T04:20:48.331016Z

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.

source=pdf_text observed=2026-08-14T04:20:47.196380Z digest=sha256:43f901daa50dc3eaa6e26a996ae5b648811044b3061d451e4019a949ed6b2283

Observation 3f0cfdf6-3fcd-450c-b4a6-f377fc2bcf2c · outbound

This paper cites Nussinov and G.

Coupled-Layer Codes: Beyond Quantum Product Constructions Nussinov and G

Reference 63

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verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.319606Z

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

source=pdf_text observed=2026-08-14T04:20:47.206916Z digest=sha256:e7cc7aa22502eeab7fa8ac7e432d101794afd8d7df8549a0507aa801350de1f7

Observation 93ceb2db-4f8e-4dc6-b045-a3eca2709a81 · outbound

This paper cites Cobanera, G.

Coupled-Layer Codes: Beyond Quantum Product Constructions Cobanera, G

Reference 64

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verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.307856Z

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

source=pdf_text observed=2026-08-14T04:20:47.210483Z digest=sha256:1afd9a6e1119cfad0492d90c858ab86b4edf50818efe597ff2f05d449c008057

Observation 8482d8ec-f5cd-42fb-a70b-3e6261220a59 · outbound

This paper cites The Bond-Algebraic Approach to Dualities.

Coupled-Layer Codes: Beyond Quantum Product Constructions The Bond-Algebraic Approach to Dualities

Reference 65

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source=pdf_text observed=2026-08-14T04:20:47.214110Z digest=sha256:8df9180efe5b8e3d52c1dd01d828325bdd79cef463f6100ad585d9a3993a1518

Observation 0a51948f-e9f4-4755-9352-7007b94057c8 · outbound

This paper cites Ji and X.-G.

Coupled-Layer Codes: Beyond Quantum Product Constructions Ji and X.-G

Reference 66

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verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.293358Z

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.

source=pdf_text observed=2026-08-14T04:20:47.223173Z digest=sha256:c167dd2d40719a8fc6bc748eaf2fedef647d003fda3bf20991f7ceee3285b00b

Observation 497f37ca-a5cf-4d73-9d1f-1a5dfeff2dd3 · outbound

This paper cites Poulin, Stabilizer formalism for operator quantum error cor- rection, Phys.

Coupled-Layer Codes: Beyond Quantum Product Constructions Poulin, Stabilizer formalism for operator quantum error cor- rection, Phys

Reference 67

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no resolver link, observed 2026-08-14T04:20:47.231697Z

Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T04:20:47.231697Z digest=sha256:150d32c4c5c36301cacf1deeb380d0bcf29775d1bb5c0acfc8c788010db6a1de

Observation efa363b6-f07a-4e0e-86d6-4ec4f581410e · outbound

This paper cites A holographic view of topological stabilizer codes.

Coupled-Layer Codes: Beyond Quantum Product Constructions A holographic view of topological stabilizer codes

Reference 68

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no resolver link, observed 2026-08-14T04:20:47.236027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T04:20:47.236027Z digest=sha256:ec864c23bf7678151f18af1255572c6ffd39af651efaa7bdcb514231df6cd7b2

Observation 5701473b-fb62-488e-9178-759919f8cf7c · outbound

This paper cites Commuting Pauli Hamiltonians as maps between free modules.

Coupled-Layer Codes: Beyond Quantum Product Constructions Commuting Pauli Hamiltonians as maps between free modules

Reference 69

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no resolver link, observed 2026-08-14T04:20:47.242576Z

Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T04:20:47.242576Z digest=sha256:39587b823eb1a5d149d40887c94f20d1475418109b9f51541589e92483af6c64

Observation f5f1f200-e139-4cf6-95f5-da2195f84bbd · outbound

This paper cites Wen, Quantum orders in an exact soluble model, Phys.

Coupled-Layer Codes: Beyond Quantum Product Constructions Wen, Quantum orders in an exact soluble model, Phys

Reference 70

Resolution
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raw_fallback, observed 2026-08-14T04:20:48.272307Z

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.

source=pdf_text observed=2026-08-14T04:20:47.246130Z digest=sha256:77dddeb01b37e9aedab459df47ea49250c6c28c5c87ab27bd70c0ef8c023bca5

Observation aded7c4d-cff5-4a84-ad67-1f11079938e5 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 71

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unresolved
raw_fallback, observed 2026-08-14T04:20:48.259450Z

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.

source=pdf_text observed=2026-08-14T04:20:47.249839Z digest=sha256:03656ef311bbfe5f630c9268534d78435a4ef975df3c512aa17dca10c8fdfaf8

Observation a35367ce-5fc7-4a79-82fd-1f4ca9e6f669 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 72

Resolution
unresolved
raw_fallback, observed 2026-08-14T04:20:48.247295Z

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.

source=pdf_text observed=2026-08-14T04:20:47.253489Z digest=sha256:4083c6ebfef796c9df7277c7ee12748bf6bf53a6cc362e0385fc2637da17e0cf

Observation 50e22958-3f0f-4f1a-89a7-52608d4aadb1 · outbound

This paper cites Gorantla, S.-H.

Coupled-Layer Codes: Beyond Quantum Product Constructions Gorantla, S.-H

Reference 73

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.235443Z

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

source=pdf_text observed=2026-08-14T04:20:47.257271Z digest=sha256:7d661cc84da875d15452ac0517bdd13e9e8060a7440f54d164e66aec237016d8

Observation 4cb268de-4131-48ae-a25c-131eea811904 · outbound

This paper cites Higher cup products on hypercubic lattices: application to lattice models of topological phases.

Coupled-Layer Codes: Beyond Quantum Product Constructions Higher cup products on hypercubic lattices: application to lattice models of topological phases

Reference 74

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unresolved
no resolver link, observed 2026-08-14T04:20:47.262071Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T04:20:47.262071Z digest=sha256:f24833e883d53975f691e6950a0a1e3211d575880bf0040fbe52166b1fea52e6

Observation c0d3983a-d471-4e84-b23e-7fdd622942dd · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 75

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unresolved
raw_fallback, observed 2026-08-14T04:20:48.214751Z

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.

source=pdf_text observed=2026-08-14T04:20:47.266174Z digest=sha256:a0651e4a10383a86366c16c9e7ab5862c82b6491fffc7b685024d908dbbbde32

Observation 134c98a5-db30-4b51-95f7-a748a013c3e7 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 76

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unresolved
raw_fallback, observed 2026-08-14T04:20:48.179154Z

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.

source=pdf_text observed=2026-08-14T04:20:47.270283Z digest=sha256:2acbb64f291cbbe16a187eebc9f9ac1d5e77147d4e506a2410f665c6fb5a2663

Observation 82ef718e-1c8f-463e-9d5e-22e6390aa690 · outbound

This paper cites Maximally Extendable Sheaf Codes.

Coupled-Layer Codes: Beyond Quantum Product Constructions Maximally Extendable Sheaf Codes

Reference 77

Resolution
unresolved
no resolver link, observed 2026-08-14T04:20:47.274040Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T04:20:47.274040Z digest=sha256:e53fae3616c458935dad6dab660c457493a2f933a5b8dc29a778cab76660a0d6

Observation fb6e4360-86b9-445a-ba68-09fc86376554 · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 78

Resolution
unresolved
raw_fallback, observed 2026-08-14T04:20:48.165943Z

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.

source=pdf_text observed=2026-08-14T04:20:47.278964Z digest=sha256:ab45e23149446c70745a721658602fe7d07ac99bf8fc8bb8f744594d947f1da1

Observation 90e8a81b-f2ed-4f26-ae23-5cf07d59c4f1 · outbound

This paper cites The stabilizer group isS“ xαpe x, a2q,βpe z, b2q,ξpa 1, q2q,ζpb 1, q2qy, and the chain complex is given in Figure 7.

Coupled-Layer Codes: Beyond Quantum Product Constructions The stabilizer group isS“ xαpe x, a2q,βpe z, b2q,ξpa 1, q2q,ζpb 1, q2qy, and the chain complex is given in Figure 7

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.154407Z

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.

source=pdf_text observed=2026-08-14T04:20:47.283660Z digest=sha256:e6e25025a527dce0679c65289fa2f27da180f9c27d43608f2220289bb85fa0ab

Observation 39743e48-8fc1-4e8c-8f5d-38a16b6c8e69 · outbound

This paper cites Sincerq 2s “ rq1 2s, there existsgPGsuch thatq 2 “g¨q 1 2, therefore Suppp ˜fqXSupppU gp ˜fqq ‰ H.

Coupled-Layer Codes: Beyond Quantum Product Constructions Sincerq 2s “ rq1 2s, there existsgPGsuch thatq 2 “g¨q 1 2, therefore Suppp ˜fqXSupppU gp ˜fqq ‰ H

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.142166Z

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.

source=pdf_text observed=2026-08-14T04:20:47.295576Z digest=sha256:4aa9d19ce32493519e12e0b5f510cfe1372af579d75a0ea819ace5a013592f6c

Observation 5cd9ba21-c116-4de5-bf37-a8e6f51112b0 · outbound

This paper cites 38 pðùqdirection: if Suppp ˜fqXSupppU gp ˜fqq‰H, then there existsq 2,q1 2P ˜fsuch thatq 2“g¨q 1 2, so thatg q2“gg q1.

Coupled-Layer Codes: Beyond Quantum Product Constructions 38 pðùqdirection: if Suppp ˜fqXSupppU gp ˜fqq‰H, then there existsq 2,q1 2P ˜fsuch thatq 2“g¨q 1 2, so thatg q2“gg q1

Reference 81

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.130519Z

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.

source=pdf_text observed=2026-08-14T04:20:47.303336Z digest=sha256:96763bbeb854f4d27d8bf6b8bbdb42ab5b67f1473d9f568e4d79e132d533a7aa

Observation 09895282-9b71-456b-a49c-a475b0dc2448 · outbound

This paper cites Finally, the group element satisfyingq1 1“q 1¨gis unique because the group action is free.

Coupled-Layer Codes: Beyond Quantum Product Constructions Finally, the group element satisfyingq1 1“q 1¨gis unique because the group action is free

Reference 82

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.114762Z

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.

source=pdf_text observed=2026-08-14T04:20:47.307565Z digest=sha256:5bbe09687ec38928fc9ffba2587b0950ead944170e3eb44d28021bbcf782c7e9

Observation 48e6ad7a-b50a-4cfb-978d-8b1b0791b20d · outbound

This paper cites Sinceg¨q 1 2PSupppU gp ˜f1qqXSuppp ˜fq, we see the intersection is not empty.

Coupled-Layer Codes: Beyond Quantum Product Constructions Sinceg¨q 1 2PSupppU gp ˜f1qqXSuppp ˜fq, we see the intersection is not empty

Reference 83

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.096231Z

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.

source=pdf_text observed=2026-08-14T04:20:47.311779Z digest=sha256:be38ce2a5465ae26d069010b127bb61eb52ab59b4aff87d656eab6525ad65a22

Observation b2f5f296-4542-4543-8706-e82c66c1acfd · outbound

This paper cites an unresolved cited work.

Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work

Reference 84

Resolution
parse uncertain
raw_fallback, observed 2026-08-14T04:20:48.081821Z

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.

source=pdf_text observed=2026-08-14T04:20:47.315767Z digest=sha256:c9f231936d66796ee6e942a1b9b0b65136d8dc68b164555067a7d05b0ac9a6ae

Observation 2c4dad12-4009-470f-92ef-6ea6b4f0318c · outbound

This paper cites 40 Now we consider the commutation relation betweenApq1, ˜fqandApq 1 1, ˜f1q.

Coupled-Layer Codes: Beyond Quantum Product Constructions 40 Now we consider the commutation relation betweenApq1, ˜fqandApq 1 1, ˜f1q

Reference 85

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.069804Z

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.

source=pdf_text observed=2026-08-14T04:20:47.320273Z digest=sha256:5a942accf6f8ab24305bfa94738e46d6ed2376a92e82449c33408425e6c4891d

Observation fccac6ba-69f2-4d16-bece-e486f0fe0c56 · outbound

This paper cites Therefore we havepq 1 2, g¨q1 2qPK.

Coupled-Layer Codes: Beyond Quantum Product Constructions Therefore we havepq 1 2, g¨q1 2qPK

Reference 86

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T04:20:48.057234Z

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.

source=pdf_text observed=2026-08-14T04:20:47.325707Z digest=sha256:1cca5de919c9220b82324b8b71eefe74fbc2f9b4cc7c958107d7459f7f196a9b

Pith citing papers

No inbound Pith citation observations are available.