Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T04:20:47.325707Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T04:20:47.325707Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
86 of 86 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation d3c476a0-432d-44f7-afd3-6b525808ee0c · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a615b56c-ecba-42c7-966a-58ea8158c8f3 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 53bba19a-39df-4bb5-a3d5-5a3f839c0ed1 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions V, the resulting code is independent of the representatives
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2fbb76d9-3dad-4eae-9d84-c36b4d670f88 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fdc653b2-c4f0-4e18-a0e3-03e785e602ef · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 986c4bc0-e7df-443f-b873-c755d3900ba0 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions As an ex- ample, we discussed thee´mbalanced product where the onsite unitary is Hadamard
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f500fac4-0267-44bc-abf5-23577d72be88 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 7ec970e9-3d05-4db4-b87c-28953e7ad48b · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation dc52fcfc-d7fe-4f20-9111-6a1e2ac8e6bc · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Bravyi and M
Reference 9
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Unavailable: canonical work link unavailable.
Observation dcbd04e1-020d-4ea8-8f9e-7f8490abb382 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c5d222d4-8422-43ce-9405-c12d422a2f27 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Panteleev and G
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 765f049c-21d4-456f-839b-48441d132969 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 065f438c-53d4-42de-a41d-2432cd1d6fbe · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Panteleev and G
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 54783ee8-b13f-4126-9994-f47d96150e9a · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 6c22b866-681c-4678-bd9d-b79a709f420a · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 55b81369-49bb-42c0-a448-7d81de1c574f · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions From Luttinger liquid to non-Abelian quantum Hall states
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5117ffd3-c468-4e2a-8b83-bc05e6ec9d7b · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Boson topological insulators: A window into highly entangled quantum phases
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3e45735e-0108-434a-9da1-80cb09a60e6d · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3be77830-ce85-4e43-adeb-e42f3cdca7ce · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Jian and X.-L
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 414047de-84b9-4c63-b5c0-9e22a3ff03bf · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 06aa25cb-a5ff-4801-a6f4-3b9bcbb32177 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e70d7401-02d3-485e-82ea-239e0e0661b3 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4a2edbf6-ad4f-4c28-be4a-b00a518ff610 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Prem, S.-J
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8b1dc005-8fe2-4329-aadd-5720f275c61a · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Distilling Fractons from Layered Subsystem-Symmetry Protected Phases
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 693077cc-1113-4603-8928-f8074d3ac762 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Designer non-Abelian fractons from topological layers
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 71fce6d6-f966-4df1-824a-9a538772132f · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Wen, Systematic construction of gapped nonliquid states, Phys
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2bfc262f-7138-4c20-b76d-6f447fd1f31d · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ca9ee49d-e7d6-4021-a769-ceb7d75fe596 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Sullivan, T
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c54ee59f-0ccd-4583-8803-3a76b7b0bf9b · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0367d98c-f3de-4cda-a484-17b9e4ac0ec4 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Liu and W
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f3a544aa-fa7f-427e-b260-69211d19d53b · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Gapped boundaries of (3+1)d topological orders
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 35731e73-9c7c-4aa5-a3bb-ac3bae849766 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9bb6deeb-c587-4f18-a39b-c694dc749f54 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b7779eec-2908-4ade-9b13-0b48ab9b737c · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 8aba0383-cdf9-4dd5-a38c-b81f21344dac · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions There and Back Again: A Gauging Nexus between Topological and Fracton Phases
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 79d43b8b-54d0-4202-a676-d1141d6ee5e8 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Constructing Bulk Topological Orders via Layered Gauging
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation dbd5b48f-847c-458e-a4b4-49a87871e47a · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Coupled-Layer Construction of Quantum Product Codes
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4bb09cf9-6cc6-4f6c-9ebc-c8bbcd66cc39 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Vijay, J
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fb11505a-73f3-441c-9e1d-ce30fe68ffca · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Codimension-2 defects and higher symmetries in (3+1)D topological phases
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8a8f13b7-876f-4dad-b42d-c9cc59a96bc2 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions On Quantum Weight Reduction
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 227f54a7-4583-4ea8-be52-8cb42d3bd805 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions SSIP: automated surgery with quantum LDPC codes
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8fd39f33-646a-4e45-b8fb-258ec6387bf3 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Fault-tolerant logical measurements via homological measurement
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2ca54584-bb61-4d80-a0f3-ae6be225d786 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Parallel Logical Measurements via Quantum Code Surgery
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bb6b29c3-a58e-4c80-b8cd-27634b1b7c02 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 8f5655dd-d156-4292-b371-8e6df4e6d173 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Cowtan, Z
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b36f7558-3777-4413-9672-c1d80f59d4bb · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Chang, Z
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f46dcd97-d573-4baa-a2c9-82d75262dc68 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Logical computation with canonical lifted product codes
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation efdc70ba-8ace-4ee5-a4cd-1c69735761a0 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4c6049c0-d2d2-4d81-b6c3-7293dce9e0f3 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions The Physics of (good) LDPC Codes II. Product constructions
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bf731e23-d296-45e2-91c8-701c7af59588 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Quantum Glassiness
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0dba0e6a-f976-4fdc-b259-dc294b09296b · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Quantum XYZ Product Codes
Reference 51
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 47e0e6e5-4b44-4300-8811-0270defcb17c · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions (3+1)-TQFTs and Topological Insulators
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 935c4212-736f-4242-b6c9-59fe6d22422a · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 352247f6-56c9-4a7a-abef-03c087bc3270 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Nontrivial Quantum Cellular Automata in Higher Dimensions
Reference 54
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0ddb66f0-f428-46cb-bee2-cb446ff38728 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 99dee30d-44d6-406f-bf51-622ed0b86658 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Yoshida, Topological phases with generalized global sym- metries, Phys
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d047054f-94c3-4f00-991a-e4b0e5ac986d · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Yoshida, Gapped boundaries, group cohomology and fault- tolerant logical gates, Annals of Physics377, 387 (2017)
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c6cd6702-3f88-47b1-a9f4-989d4be1787f · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Ungauging quantum error-correcting codes
Reference 58
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation df747bb3-3dcc-4ad8-ade0-97090979796f · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4a45e462-37ff-41fa-a347-2467c8d644c1 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions The Physics of (good) LDPC Codes I. Gauging and dualities
Reference 60
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d3b1df4e-2fa9-4df0-b7cd-3cbd1780024a · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Hatcher,Algebraic topology(Cambridge Univ
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3a96bc3e-b92e-4261-8b60-ca3f0c783040 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3f0cfdf6-3fcd-450c-b4a6-f377fc2bcf2c · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Nussinov and G
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 93ceb2db-4f8e-4dc6-b045-a3eca2709a81 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Cobanera, G
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 8482d8ec-f5cd-42fb-a70b-3e6261220a59 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions The Bond-Algebraic Approach to Dualities
Reference 65
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0a51948f-e9f4-4755-9352-7007b94057c8 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Ji and X.-G
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 497f37ca-a5cf-4d73-9d1f-1a5dfeff2dd3 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Poulin, Stabilizer formalism for operator quantum error cor- rection, Phys
Reference 67
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation efa363b6-f07a-4e0e-86d6-4ec4f581410e · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions A holographic view of topological stabilizer codes
Reference 68
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5701473b-fb62-488e-9178-759919f8cf7c · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Commuting Pauli Hamiltonians as maps between free modules
Reference 69
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f5f1f200-e139-4cf6-95f5-da2195f84bbd · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Wen, Quantum orders in an exact soluble model, Phys
Reference 70
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation aded7c4d-cff5-4a84-ad67-1f11079938e5 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 71
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a35367ce-5fc7-4a79-82fd-1f4ca9e6f669 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 72
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 50e22958-3f0f-4f1a-89a7-52608d4aadb1 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Gorantla, S.-H
Reference 73
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4cb268de-4131-48ae-a25c-131eea811904 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Higher cup products on hypercubic lattices: application to lattice models of topological phases
Reference 74
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c0d3983a-d471-4e84-b23e-7fdd622942dd · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 75
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 134c98a5-db30-4b51-95f7-a748a013c3e7 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 76
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 82ef718e-1c8f-463e-9d5e-22e6390aa690 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Maximally Extendable Sheaf Codes
Reference 77
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fb6e4360-86b9-445a-ba68-09fc86376554 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 78
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 90e8a81b-f2ed-4f26-ae23-5cf07d59c4f1 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 39743e48-8fc1-4e8c-8f5d-38a16b6c8e69 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5cd9ba21-c116-4de5-bf37-a8e6f51112b0 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 09895282-9b71-456b-a49c-a475b0dc2448 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 48e6ad7a-b50a-4cfb-978d-8b1b0791b20d · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Sinceg¨q 1 2PSupppU gp ˜f1qqXSuppp ˜fq, we see the intersection is not empty
Reference 83
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b2f5f296-4542-4543-8706-e82c66c1acfd · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Unresolved cited work
Reference 84
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2c4dad12-4009-470f-92ef-6ea6b4f0318c · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions 40 Now we consider the commutation relation betweenApq1, ˜fqandApq 1 1, ˜f1q
Reference 85
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation fccac6ba-69f2-4d16-bece-e486f0fe0c56 · outbound
Coupled-Layer Codes: Beyond Quantum Product Constructions Therefore we havepq 1 2, g¨q1 2qPK
Reference 86
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.
No inbound Pith citation observations are available.