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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

Pith citing papers itemized under the disclosed page cap.

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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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source=pdf_text observed=2026-08-14T04:20:46.941262Z digest=sha256:a9459e43ba03f0b311dc0a8c454c16a06478199dfdab754d3828127ac7dc9ee5

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=sha256:1bde6833cbe6bc2024790731ed4d6cd40a95b29763bb15a94fb9bc0c5814763b

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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source=pdf_text observed=2026-08-14T04:20:46.975608Z digest=sha256:71b57c1a7702ab9e97d9307b5f205686f5aa024e8fad3b2d319041e07d28b687

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=sha256:970095f4de2a5b8e80e09f39afc252ae39840dca22b962cf9c1ecb2292f75faf

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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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=sha256:1b8053c2676720385e6c2bc65dcffcf949d291695fe21c89b30461db2d734940

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=sha256:1c1e2ec64324547e29467380fb9375dd2434f03d38c3c938a8189cebd6f3c819

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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source=pdf_text observed=2026-08-14T04:20:47.021447Z digest=sha256:98989f239e91885c59e450b24fe4cdfa022e877f6747e56e17725dc1e5630a89

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:fad16da67631b14a19460966310f0352d8298d028c1cc1c7d841e51c3b6b77a6

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:f6147db74d9291964952c79fdf658dc249c0acd2ccc4ef7b4ac8a2f0ef4ec21e

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=sha256:1c0f12fa0253519faaa55ee2f2c4ed031edf21f021bc83f6da38d94349d6dade

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=sha256:3bf36a66d8ed40e9a6942ab8da6034972f54fea446a3b79f4a4620aa0c5416c7

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:a3d82ca4506c73c3523145f33f351c740074b1fba6d0c53ad2524669a5a895d4

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=sha256:52d0d96b3bfd13e401104c702334b14d9b33fc3832ec1d07718dfcc3063d7447

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=sha256:211fea3027d653a6a27ebe6885f994cbf727ef83809f408875aa4739b7ca46e9

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=sha256:8f7af587c502704840e7bebdf2a5afc730e4c6383564fb0568cef48d1447e8e7

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=sha256:13b8c32957611d404bb496d12d6517460fec1841d707bc9ec7585d8f4a12e81e

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=sha256:2f13a1b819704873a1b48f05082581936e966fb3bf35d358534ac2e5ce1ebf68

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:cd28e52e9501c7608893f2cf17273b87407f0fb93c1c69e72293cdcbb1d40e5e

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=sha256:5831b242a8fb31cedb4055a7e329638a5cd7d9c9df08b5b50c89dbeb8adef68e

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:f2cee26586af594597860789e00c7ef0e9193cf2d4965de89b307523ed7d6830

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

This paper cites Vijay, J.

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

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source=pdf_text observed=2026-08-14T04:20:47.087092Z digest=sha256:107cb947fc3e5ac0274b32b62eaa0077979a96b8f14e46d3cc5c2e381b8931f1

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

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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:f8afc467a9e1d5ab7791c7eb5c6e08fba54ca98308ed94f46bb56fdcdc115467

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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no resolver link, observed 2026-08-14T04:20:47.094222Z

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source=pdf_text observed=2026-08-14T04:20:47.094222Z digest=sha256:6668f7303eca3b11e9259b03625bb37ed52faa782180ebcf7b6a40bc73f31a2f

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=sha256:366de36e84651d6f8a556df08d60bf9bd2f46d828255f8d183a855916bb05cbd

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=sha256:4d4449ada7264b53d71246b6cea567655bb0de6ceeb10ff598dd60982787cd71

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=sha256:6b3eb02f0bd91b1d764dce411dda6d7b9b1386d874d1dac84f06af387eece8d3

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=sha256:9bf9ed47ef2df6f4565db9a132b68c7b0f0678756219b808908d80db76182602

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:e6e3ddc6d020003e9a36030a5d5dfb68356b75d261a8b3437f2dbea92b366ed1

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=sha256:9802dd4afde38ab54dfb360d8fc098fc02121f88735da59a7cdfa58676d8f858

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=sha256:74773276505aa7fb4578c05b4ab5cd7678898d28d7a106af3c3105f8a835cb99

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=sha256:4ca6105254c76a60e65a4d10b515eff04244728ea1941d57d7c52cf88564300b

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=sha256:5f62d8ce2ebd052d2a69bc04e6812a54c842a12f337fb4ad6793a9eb64d5c92a

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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unresolved
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=sha256:9bc1cd382f294f62bdf080fcb413387f276238b6a8a604d62cc6b484f1034263

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
unresolved
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=sha256:91bdb4041dc4a789a0813aef7ddeb8e033541301e5bf7245d22fc434f486aeb3

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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no resolver link, observed 2026-08-14T04:20:47.139254Z

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source=pdf_text observed=2026-08-14T04:20:47.139254Z digest=sha256:705adf917043c6d60d3bc5d56c5d94c58e7e200e9d3d597a662bb502b5003414

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=sha256:27313f8e9b26f7bc1fbe3dd0458ea4fa04b4d7b9949fe1002dde8742a70d5147

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:ae9ab4d24e5fd291572ee3fbf267898d2b6ee3f4c11735704ffdf1a1a8d15da1

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=sha256:1e0752c87a6162bdbb029ae158fec9a8554d7f2227ee1d5807ac2d924688edf8

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=sha256:7b10f4e5b05679e8f270c94f69be730ac32bf17583c06607facf2b874698720c

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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verified fuzzy
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:f21f91b1dffc35e383cf37454e178c1e34cc39f2e14a146cc1c1549c9e43adb5

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:c5455ecf5e6791c26d5c691707d12e7ba6d9395a07e2f04d28ca84e131d1f024

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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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:dc73e1e5e95f08038fb3465fc23c470692b338947912c8a7ec4c9174b3d4f890

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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source=pdf_text observed=2026-08-14T04:20:47.187681Z digest=sha256:f2710723b24e4986f13a1baf04dd28bf9993fbdc00d8eb05755a520f292eda1d

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=sha256:96f39bf68aed332f098213ea4712992231012201af73fd2e698f75c3d2324b2e

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:ce038eb0cbee88f6a4de2fa549e5950db050d27feca02c0128bd66790b36902d

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:b7262e4d87f19ddabd9466c9999d82e129c715acaa72806d9ad9d2496033c86f

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=sha256:5fea99e7dd9fcf7f536aa34b4234fe1e9a6993ceb1180cf268804df139678f9b

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

Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T04:20:47.214110Z digest=sha256:a50c9147278e21b72784573e219cf2ee194f042038b4633236ab3fd014cab46c

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:a9295d14ac89b5e67d2ff0d6d6b3daf79899e94c83335719d3bbfadcef674bb6

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=sha256:6c2c9e54311bc983bf88f29bd5ecf4faf0b912c48300d6dc697d1188ec0d131f

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=sha256:14d1becab94b74a005c3eead5649f531caee9a0abc1ae6e89a89366171aae1a1

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=sha256:59e46c366e974f524036e91ab9930190611ccff1d93b2dcbf5637f0973d42ad3

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=sha256:93a0cd729ffc6c6e89ba6251cb82896f86a26fe77cf74324070d365037b1c0bc

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=sha256:21c08813bdcb39670673f9d420574ec8622ce8b6d7226055ea3a5d7a3d87f641

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=sha256:8db6ebe00aff6c89442c58b5558ec35ba51593043d04ec33ebb617567b4cdf17

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:a7b024f2b284f02fe7c3e044ca651c38002ecbc30ad9656547a46d5e5598186a

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

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source=pdf_text observed=2026-08-14T04:20:47.262071Z digest=sha256:fd90fe330181952284f4342a07bd6955a11b37c1b886efb08946800bad8dbbd9

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=sha256:6d724402f23f9d21fd0fdf154677dd8a0ad49b744d2a60debfa5bc9a7780a150

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:e8fc2a8a866d57c49d7f426ec4ec7598cf3affaea86dc239a883a8408c1b30eb

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=sha256:9f25ecad35cb95a7deaa3b9a87de757876076a74c6be25601c842d0d32683d58

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=sha256:4cbc7cc19ce98121de5c501c61a2c2c3521315cb951c066132db7b98e31a66a8

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=sha256:932094ef9894328f08ae4b239b4b60fc7024a1a4d108f8ee9fdb6a9ba7ceddb9

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=sha256:3a5f93992ab3bd13f45db376d896399f10415276fd8a9ba2fdbb17a8eaaf110b

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:cbed9fbaf6eeb69996c5084cb3d46db7f5cf2a1d6df6e345ec055c09b99d3574

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=sha256:7cdff497890635eb7c8e213b2066fb048046025b351afb896d72dc0de38adf53

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:c87209085531e124d3595106141ecb3954be7fe4e3d5503422bb54d3ffe3bd5b

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=sha256:050f5621292cef18f27673a6e587230202ab27777db443b92082043e84006b48

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=sha256:22d558acca499664a0d9364d38feda6b7d089d2147985646ba41b900a77cbabd

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=sha256:36e9dbb37763b5a90715def63e70c5ddf3b1067a3fa5f6851b38ab773acd92b2

Pith citing papers

No inbound Pith citation observations are available.