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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

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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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  • unresolved64
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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=sha256:6f7fa4cb88b6c0e2e06fa4c7d6e63861bd4cb7e9856980170f7f30501500ab0d

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

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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:a6da779387c45645cf70852d95e0aac9cb946b3ba7f8facd47f0eba4678cd141

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

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

Reference 14

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source=pdf_text observed=2026-08-14T04:20:46.991872Z digest=sha256:ed9e6893a31d8a8b2ad8a1c65fefb85689cd143c42f50e4b1673f9419a2fdd0f

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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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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source=pdf_text observed=2026-08-14T04:20:47.003433Z digest=sha256:a46e6476592d2858504607513afa282bda06974df515692bd9746446e7df0b04

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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source=pdf_text observed=2026-08-14T04:20:47.012171Z digest=sha256:5284f433afd13c369fd6f98aa59f820469e03a1e70568b5751215da0a5ca54aa

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

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

Reference 21

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

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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:ce78cf0708925be0ad07ec7f4af9d84fc2c92736a3964fc1f9eecef4bf95a634

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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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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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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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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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=sha256:092f5a7f534dbe56d02762b4532ff67c15aad90f97a35015757bf8f7be69debe

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:e65f251c3140eb2f519b237aa2c448230fad3f839964f4361686c98cf3015915

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=sha256:86904a04afd079d038c7b132d04f99f8379719ed80e8275d98d045cb7c8b044a

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

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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=sha256:3f1df7313aa3a87ca42abce9babf5b2a5702d1226644fc30d6baabfa8f44d8e4

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:c78134d04e8659528f94ab7fda294c8a3fb339f5fb9e0c3668e941c5154c07a0

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=sha256:07156d6f22ee391061059c70b2d1a5029fb2ad8b489f7dab0c4e12c9d1f20bd0

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=sha256:206f6d3cf42e5bf5e36edfeb0eba7cd5bbe97a2ad53f4a51fb1b92dfd6f89c76

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=sha256:5c77c10e8fb2bb3527c611fc04bf943092b0c01ff134fa5a25773fe28efe8a3e

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=sha256:8429d3aee7790d4754756638428240d959a4eef5e6497aee5bde5f4e21588165

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=sha256:3c4a04bd8d41c0f0028ba86fb68f9396bd148243685767a4344f6f266c48eae8

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:d33746b605320ff862d7c3f9e751200f1dbd29a91ac43872a9916ce6dcd09904

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

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

Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T04:20:47.097744Z digest=sha256:3e898f0d0d26b9e78851793358fe00e30ae239b5ab6386423e5f3d9a579fcf17

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

Resolution
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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:e4f94b975ece94978617eca255b2af62b36ef283c8006e150fd1e585bdba5d23

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:d37e83a5d58d15d29321b28b50bc5ffe7cc04a10f134e1e5354c88a1e22299ad

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:e6d3f7e36a51ec2d7a30a008d268d1115290f9a9f68e2bb78dd93728b8aa36c9

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:bca8caa27af5145f610bec2a8fb14cc6a731ccb26e769d980afb0782e6fc115e

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=sha256:4ca1ca87cb7cf385b6d8901dcb3ad16e6ac54d3f7477569200954f0e7e3b232c

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

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no resolver link, observed 2026-08-14T04:20:47.120423Z

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source=pdf_text observed=2026-08-14T04:20:47.120423Z digest=sha256:b031bc719170f8617e57c4dbaad715336c28adddcffda9ed2f50749e8d8edbcb

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=sha256:2c3d996eb4709c0c1243972a937ddc1b6076c00e8f4fbfc41d25ed87992ed99c

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:dd0ebd54acb34f9e4c919a67e691f4f7046ad62775ac858be1d413c363954bed

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

This paper cites Quantum Glassiness.

Coupled-Layer Codes: Beyond Quantum Product Constructions Quantum Glassiness

Reference 50

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

Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T04:20:47.131846Z digest=sha256:2347c70484dcec4e5c89db1b184bd22c3691c775e625e143ded43d3dfccaac18

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:b5509d90e4915634270ee3eb61eaeff8ee4ce07cdbb80b18345e0046f4a184e5

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:ca4382911eadc36453e72c61a73891af5fac031118e364de27ba309a9dc747ce

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=sha256:7f47a1e9d3f6c8d61ae5db6760cb0a94813642797c35cf5f2071e54d1a6d6a7a

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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source=pdf_text observed=2026-08-14T04:20:47.147009Z digest=sha256:ab2db7220e82cf3eeb8e54a315a6429f0278c27b1e3eeaad625957729c2af34a

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

Resolution
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:b58492dcf857917955e57d2b0632840fc1735e25ae88fce8153f16ddfdaa19c3

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

Resolution
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:b89f3e5a4856ea16c8454870b828b71d6d6086b48f3bf00fbed2e0b6e6ec7ad1

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:a08e71f156160f93ac37c7ef1d2d26bfb2a860f991a8233ac6e9dfe7a2c862dc

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

Resolution
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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:ef89a9ce9b8e0f3a6a34d118ed2aa3b237405af20dc34e847b914c3848104e15

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

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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=sha256:8e1e8b527f5cd949092303155298bc4cb91de072ae5ec230651df3cdaed33703

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=sha256:20ddd242bab7bbd8ff81ace981275cfd9b480713eb024ac6fce45dfbaa22d304

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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raw_fallback, observed 2026-08-14T04:20:48.342061Z

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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=2026-08-14T04:20:47.191920Z digest=sha256:c9d6f4b6913dffc6695f703215d7b0013b3374b805d6f54c7cbf2110d7e26a3a

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=sha256:44c25b84a095fbad3835761e7feaf14f0c9d3d250482162c4dbec8e85a40aa36

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:c77243d66bed188bb647e8ca06340619eb5e1dc3c527347c1471836d062d8e6a

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

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=2026-08-14T04:20:47.210483Z digest=sha256:34add8398348178a1f0cccebb55400849bdfd57b26a402166992ef685d848217

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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no resolver link, observed 2026-08-14T04:20:47.214110Z

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source=pdf_text observed=2026-08-14T04:20:47.214110Z digest=sha256:129708922dac7e8e94aed1efc18a080e01ad4673dd733092fe676c5e8d080891

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=sha256:455db9e0c62577b7671594dae04c6ae6f75395a0e5b3d8addc70c403a6fb7867

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

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

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source=pdf_text observed=2026-08-14T04:20:47.231697Z digest=sha256:bdb0bc4216b4b12a377ac9accf8a1e35b833621f7ac17f2250dfff144138bfbf

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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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T04:20:47.236027Z digest=sha256:a0d65f81de3c1e3db92a2f09c5926196f03c9fffaa6e324764270e0bab220d05

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

Resolution
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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:ca5cb37e9aa228cdb45322fd3be5f3afa2ef66be3cade388227e9ce8ba863694

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
verified fuzzy
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=sha256:66158153e40bb45b26a1e8a144619d9197b8b45cfe1808bd95c9c1c342f69a1a

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:acbb9b87b6350c66e5e89fab934733a02133d5598696afa038d8a8c91e81a8b5

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

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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=sha256:153a2254f350384806a512efda9dde948f26a767db8d06cc083e208be45616ac

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

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=2026-08-14T04:20:47.257271Z digest=sha256:84a18b82fba672b5ed461cccec3067c3f58fcc248cf694e536ca614573baf807

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

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

Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T04:20:47.262071Z digest=sha256:c20961cf6e701ce73e2c9fce5e2dde0d1a4de6516a8e1213290da67beefe9050

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=sha256:53d0b5844197d74130248e957ad6db11e5db451b21c77245ce9cd337a9cab09e

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:e68ca5c05998b098f57b10b282e5dc63f38454f35c3304f9a98197234fd43785

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=sha256:32d913839fdba5495b26a68494e1efa806a648de691b37cfd37b713cf4055097

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=sha256:9cd7fb17670ff91e9382273aafa786af920bf6b15f3b4ae5b0cb22742598ce02

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:ea28e991ee7a104b5c8cb01f3512286269af7412feab25dcc581334394aee418

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:ea3a136cfa4b11eae7733cd114d7e50515a0e12e9685ec7972a5ae4fd03fd640

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=sha256:391caa06c00d1ba9e3563303893726684b1ec8f90ea2c033511a8e88c264f45c

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:ea5719e0ef5ed6e1658854339fe28007832b939bc3b37181df938972f4f796af

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:af02b3a6b72c7418491aaeaee349256b65a334c69fce9302e8ff62878cd803a0

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=sha256:12d7f72b88f823067ced8e0b08930a95fb91f24068ed671970f40e863406609b

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=sha256:4017070a01344956296611e9ed4fe815cdb5a3d6308361bc23112fc0335b250e

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=sha256:8c9353df634f96fe3b56aee982009d247759e78446a4f3e2245ad4d175ec295c

Pith citing papers

No inbound Pith citation observations are available.