Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T01:57:31.919136Z
Paper Citation Record · LEDGER
As of 15 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 0 inbound Pith citation observations for arXiv:2607.21698.
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 2026-08-03T01:57:31.919136Z
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
68 of 68 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 5bcafbb5-b8ea-4fdc-bbd2-20b3d34577a2 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Hence H 2(SL(2,Z p); Wittpt) = 0: the central extension splits, and since the kernel is central the split extension is the direct product (A.21)
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 91d0428f-1def-4607-b433-43e4ddc49b58 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata (D.34) Indeed, any element of Kerϕ, such asyabove, is a linear combination of terms which also satisfyc 2 =c ′ 2 (so in particular∂c 2 =∂c ′ 2 is trivially true)
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f73a17d9-87f2-4871-8b76-9cec73d2d1b8 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata (D.35) Clearly,∂(c 2 +c ′
Reference 3
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Unavailable: canonical work link unavailable.
Observation 406d2d45-60f3-449a-a418-38b879f6ec53 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata In the case of an infinite cu- bical lattice, the homology is trivial, so every cycle is a boundary
Reference 4
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Unavailable: canonical work link unavailable.
Observation b118ebea-ac75-4f35-bf3d-810930f9ce1b · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata expanded region
Reference 5
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Unavailable: canonical work link unavailable.
Observation 610dee79-a127-45de-b6bf-3ad1e65771db · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata ICTP Lectures on (Non-)Invertible Generalized Symmetries
Reference 6
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Unavailable: canonical work link unavailable.
Observation c963c3e6-bd80-4d2b-96ec-92d4a0592196 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Lectures on Generalized Symmetries
Reference 7
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Unavailable: canonical work link unavailable.
Observation 8e7fcffa-ec70-48b6-9373-4bd18af62c13 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
Reference 8
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Unavailable: canonical work link unavailable.
Observation cb67ef9a-11d9-40a0-ab69-cc25ed7bbb41 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Lecture Notes on Generalized Symmetries and Applications
Reference 9
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Unavailable: canonical work link unavailable.
Observation 5b9bb64e-428e-4263-a771-9cd96393461e · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Dhr bimodules of quasi-local algebras and symmetric quantum cellular automata,
Reference 10
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Unavailable: canonical work link unavailable.
Observation 9fef8ed3-1bd7-494d-b212-c31bd86fd1b3 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Quantum Cellular Automata on Symmetric Subalgebras,
Reference 11
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Unavailable: canonical work link unavailable.
Observation 21067f90-e10e-4607-a344-bbe12c37cc0d · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Quantum cellular automata and categorical dualities of spin chains,
Reference 12
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Unavailable: canonical work link unavailable.
Observation 1b178525-e072-4264-9a98-0d75acdb2053 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Index theory of one dimensional quantum walks and cellular automata,
Reference 13
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Unavailable: canonical work link unavailable.
Observation ae077a20-e90b-4105-9bb7-bfdf978005fb · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
Reference 14
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Unavailable: canonical work link unavailable.
Observation 6b8cb146-a16b-4143-9ded-a950380f01b1 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a5ec35c4-f5b4-4399-9a56-69f6201b532d · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
Reference 16
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Unavailable: canonical work link unavailable.
Observation 15ac7a31-1c9b-4625-8f75-bc82449d8cbc · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Cluster state as a non-invertible symmetry protected topological phase,
Reference 17
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Unavailable: canonical work link unavailable.
Observation fa67e187-7db5-4d3e-b909-bd615464ae57 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata An operator algebraic approach to fusion category symmetry on the lattice
Reference 18
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Unavailable: canonical work link unavailable.
Observation 8a8fb6f8-ec86-44d3-83fb-08c9ac509bc0 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Generalized Kramers-Wannier Self-Duality in Hopf-Ising Models,
Reference 19
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Unavailable: canonical work link unavailable.
Observation 34ff2a1f-2db3-4981-9185-220327b5f826 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Remarks on non-invertible symmetries on a tensor product Hilbert space in 1+1 dimensions,
Reference 20
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Unavailable: canonical work link unavailable.
Observation 9beb91c2-76a9-4bff-8c3b-3d5fa3a1a07d · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata On the structure of categorical duality operators,
Reference 21
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Unavailable: canonical work link unavailable.
Observation 1b6d5b6f-171a-48f9-add8-a374a2f2fede · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata
Reference 22
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Unavailable: canonical work link unavailable.
Observation 646b0c38-62c6-4643-a180-0f989e24d8e8 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Kramers-Wannier-like duality defects in (3+1)d gauge theories
Reference 23
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Unavailable: canonical work link unavailable.
Observation d6bd2c10-c7a9-4843-a7ae-71324a13f83f · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-Invertible Duality Defects in 3+1 Dimensions
Reference 24
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Unavailable: canonical work link unavailable.
Observation d6dd9539-172c-48a3-bd45-25def7224148 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-Invertible Higher-Categorical Symmetries
Reference 25
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Unavailable: canonical work link unavailable.
Observation 739f5d1e-2811-4337-b45e-42dade757019 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
Reference 26
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Unavailable: canonical work link unavailable.
Observation d7374aa9-e9c8-4db9-81eb-62826e96a585 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata $SL(2,\mathbb{Z})$ action on QFTs with $\mathbb{Z}_2$ symmetry and the Brown-Kervaire invariants
Reference 27
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Unavailable: canonical work link unavailable.
Observation b8eb1d1e-b626-44e8-b35f-0ae60b35c1db · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
Reference 28
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Unavailable: canonical work link unavailable.
Observation 5054cd5c-4b6e-4b29-9bbd-25937156e604 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Tensor Networks for Noninvertible Symmetries in 3+1D and Beyond,
Reference 29
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Unavailable: canonical work link unavailable.
Observation 2d075327-c3bc-4d19-96c3-498b599fc3c0 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory
Reference 30
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Unavailable: canonical work link unavailable.
Observation ed23af3c-734d-4ad6-87bd-9a59d7880e7e · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
Reference 31
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Unavailable: canonical work link unavailable.
Observation 9b90a60f-76fe-4ae9-bdc5-85a2d1e813bf · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Symmetry TFTs from String Theory
Reference 32
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Unavailable: canonical work link unavailable.
Observation 64bcf3da-c6a8-4588-afee-8e1d7bb262af · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Symmetry TFTs for Non-Invertible Defects
Reference 33
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Unavailable: canonical work link unavailable.
Observation af798262-2ead-45c7-b4be-0a66099121a8 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata The holography of non-invertible self-duality symmetries,
Reference 34
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Unavailable: canonical work link unavailable.
Observation ec24c580-176c-4ce1-b9b1-27ba2648ea39 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Fusion 3-Categories for Duality Defects
Reference 35
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Unavailable: canonical work link unavailable.
Observation 380daff2-6295-4062-b4a5-5afd5eaf5d9e · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
Reference 36
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Unavailable: canonical work link unavailable.
Observation d64f6a00-fdf3-473f-b29e-0ccf2e7eaaaf · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Nontrivial Quantum Cellular Automata in Higher Dimensions
Reference 37
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Unavailable: canonical work link unavailable.
Observation db4ffe57-1a0a-4d6f-a4f5-4a7ce7a5de99 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D
Reference 38
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Unavailable: canonical work link unavailable.
Observation f1f95ec0-6fe4-4161-b73a-e9a49c2b05e4 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Clifford quantum cellular automata from topological quantum field theories and invertible subalgebras
Reference 39
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Unavailable: canonical work link unavailable.
Observation 7521b921-5b7b-43ac-8b52-ebbca1e63b08 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Pumping Chirality in Three Dimensions
Reference 40
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Unavailable: canonical work link unavailable.
Observation db6bc424-19ed-4db4-ae3d-bfd9890486c6 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Generalized Global Symmetries
Reference 41
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Unavailable: canonical work link unavailable.
Observation 60da76e9-6175-43aa-9e64-f01b418ac0f1 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata A categorical construction of 4D TQFTs
Reference 42
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Unavailable: canonical work link unavailable.
Observation 507ddd16-b89b-454e-a506-0d09b4f005ed · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata State-Sum Invariants of 4-Manifolds I
Reference 43
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Unavailable: canonical work link unavailable.
Observation 2bfa5687-741c-4ba5-9a9f-3bce2dc9bc2e · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata (3+1)-TQFTs and Topological Insulators
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0c9f2e58-a37f-483a-b90e-b0e1f52faf54 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Higher Gauging and Non-invertible Condensation Defects
Reference 46
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Unavailable: canonical work link unavailable.
Observation a135c494-1dd2-4c29-819a-844726d339aa · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Topological phases of unitary dynamics: Classification in Clifford category
Reference 47
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Unavailable: canonical work link unavailable.
Observation 40d0b760-2440-4fcc-be36-6ffd21c2a05a · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Categorifying Clifford QCA,
Reference 48
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Unavailable: canonical work link unavailable.
Observation 9d5da2ec-b01b-42f7-8cd3-397a9da0272c · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States,
Reference 49
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Unavailable: canonical work link unavailable.
Observation 5a3dee4d-0b87-4a27-8e39-0d2840979c2d · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Quantum Cellular Automata: The Group, the Space, and the Spectrum
Reference 50
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Unavailable: canonical work link unavailable.
Observation 8a21d3bd-4ef6-45d2-866f-f41533a8efb5 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise
Reference 51
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Unavailable: canonical work link unavailable.
Observation aaefc1f9-4f36-4505-91ab-a8a5ae3985c3 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Loops in 4+1d topological phases,
Reference 52
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Unavailable: canonical work link unavailable.
Observation c2aeca27-bd8f-486e-aec4-195bc56c04d7 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata The Witt group of non-degenerate braided fusion categories
Reference 53
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Unavailable: canonical work link unavailable.
Observation f9274ce4-6da2-4b40-8fc2-84c979aeb635 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata On braided fusion categories. I,
Reference 54
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Unavailable: canonical work link unavailable.
Observation 49169e22-6d55-4ad1-9b23-0d0ff5abe8cd · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata An Ideal Characterization of the Clifford Operators
Reference 55
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Unavailable: canonical work link unavailable.
Observation 147be398-e939-43c1-a0a9-870683667b8e · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$
Reference 56
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Unavailable: canonical work link unavailable.
Observation 8bb1bcd1-eb84-4626-a2d9-fe85875e0187 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Work in Progress,
Reference 57
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Unavailable: canonical work link unavailable.
Observation b8f9b3df-8628-4d7f-aa4f-9f1d9e0c2ee9 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Higher symmetry and gapped phases of gauge theories
Reference 58
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Unavailable: canonical work link unavailable.
Observation b551ab73-9fde-42ba-aacc-4a4a17114660 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions
Reference 59
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Unavailable: canonical work link unavailable.
Observation 0b086bd5-19f5-431a-ac9a-dc8f42095e4c · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Bosonization in three spatial dimensions and a 2-form gauge theory
Reference 60
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Unavailable: canonical work link unavailable.
Observation 3963a8b5-af36-4d9c-b699-ab174fc2c809 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Higher cup products on hypercubic lattices: application to lattice models of topological phases
Reference 61
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Unavailable: canonical work link unavailable.
Observation 3f40b39f-074f-4321-8a88-9c34ca11f583 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase
Reference 62
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Unavailable: canonical work link unavailable.
Observation 52659bed-c011-426a-8c7c-e0004ea916ca · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata The Group Structure of Quantum Cellular Automata
Reference 63
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Unavailable: canonical work link unavailable.
Observation b813e55b-7204-47e7-bebd-650be314ff1c · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations
Reference 64
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Unavailable: canonical work link unavailable.
Observation f6a93b41-4360-4a12-97b3-faf51984df45 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Non-Clifford quantum cellular automata from invertible topological quantum field theories
Reference 65
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Unavailable: canonical work link unavailable.
Observation 62f1a344-088d-4a74-b407-fd42859a5e95 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Topological phases with generalized global symmetries
Reference 66
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Unavailable: canonical work link unavailable.
Observation fbafebdb-34dc-4b19-8e09-2e06ffce9f93 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Long-range entanglement from measuring symmetry-protected topological phases
Reference 67
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Unavailable: canonical work link unavailable.
Observation 048742e5-ef1a-4a5b-81db-4756e1ec2931 · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models
Reference 68
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Unavailable: canonical work link unavailable.
Observation 04355c48-7300-4720-b744-edf6a370a5eb · outbound
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata 3-Fermion topological quantum computation
Reference 69
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Unavailable: canonical work link unavailable.
No inbound Pith citation observations are available.