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Paper Citation Record · LEDGER

Causal Decompositions of 1D Quantum Cellular Automata

As of 20 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 3 inbound Pith citation observations for arXiv:2506.22219.

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

pith.paper-citation-record.v1
2506.22219 v1

Coverage vector

measured 62 of 62 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:21:15.807362Z

measured 65 of 65 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:24:10.305958Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-06T18:26:25.447451Z

Reference resolution

62 of 62 outbound references displayed

  • verified exact18
  • verified fuzzy15
  • unresolved29
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c567233d-2484-4d9c-81f9-128e7318de4f · outbound

This paper cites Quantum common causes and quantum causal models.

Causal Decompositions of 1D Quantum Cellular Automata Quantum common causes and quantum causal models

Reference 1

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source=pdf_text observed=2026-08-06T22:21:11.279766Z digest=sha256:339fd75b21a00c32153683a43f908031acdad0dc73b2c82e7e793f09a6e394cd

Observation d8028cc9-3c2e-437e-8dd0-08681faeda56 · outbound

This paper cites Quantum Causal Models.

Causal Decompositions of 1D Quantum Cellular Automata Quantum Causal Models

Reference 2

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source=pdf_text observed=2026-08-06T22:21:11.325284Z digest=sha256:7baceae23c52b20f8bed272a9c65de0134fd106dfdeac780e32dabd289112676

Observation 23aacdbe-dbe8-4fd8-85df-a1d99412a10d · outbound

This paper cites Causal structure in the presence of sectorial constraints, with application to the quantum switch,.

Causal Decompositions of 1D Quantum Cellular Automata Causal structure in the presence of sectorial constraints, with application to the quantum switch,

Reference 3

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source=pdf_text observed=2026-08-06T22:21:11.363250Z digest=sha256:29f9fc68bb013e4d150d8c9806b299df8873174107fe48fb6136a9199735d783

Observation a6c68872-a717-42fd-aacb-650916cc0e98 · outbound

This paper cites Semicausal operations are semilocalizable.

Causal Decompositions of 1D Quantum Cellular Automata Semicausal operations are semilocalizable

Reference 4

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source=pdf_text observed=2026-08-06T22:21:11.393277Z digest=sha256:0da85823d9395e1c1fe01e35f3f5b4e88ede01cb2cfd3eec1d09e037f6c3945f

Observation 0deb5b26-208a-4abe-8ed0-aabdc44895a5 · outbound

This paper cites Causal and compositional structure of unitary transformations.

Causal Decompositions of 1D Quantum Cellular Automata Causal and compositional structure of unitary transformations

Reference 5

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source=pdf_text observed=2026-08-06T22:21:11.431610Z digest=sha256:78c13906fbb8ba7458d536b9d9e06d07d2215f8bdcd486f81edb737d9e79b99d

Observation 23fd66cb-a8c9-4df2-aae3-ddd843a5a8f2 · outbound

This paper cites Routed quantum circuits.

Causal Decompositions of 1D Quantum Cellular Automata Routed quantum circuits

Reference 6

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local_arxiv, observed 2026-08-06T22:21:18.439817Z

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source=pdf_text observed=2026-08-06T22:21:11.517962Z digest=sha256:98dd0893bbb1ad79b520a716f16da1bc5684e770e999895bb24dc6ff8f5f1a06

Observation 034d4135-2618-47f8-bdac-7114f7397eb0 · outbound

This paper cites Vanrietvelde, Routed quantum circuits: an extended framework for coherent control and indefinite causal order.

Causal Decompositions of 1D Quantum Cellular Automata Vanrietvelde, Routed quantum circuits: an extended framework for coherent control and indefinite causal order

Reference 7

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source=pdf_text observed=2026-08-06T22:21:11.583636Z digest=sha256:90ae0a7d07e199f1c28920087a9fcb20c6c6bf46e30661c8b0d81bfc197f010f

Observation 7ebc7e34-7124-4314-b274-552681e55f14 · outbound

This paper cites Commuting operations factorise.

Causal Decompositions of 1D Quantum Cellular Automata Commuting operations factorise

Reference 8

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source=pdf_text observed=2026-08-06T22:21:11.650407Z digest=sha256:eff9546685ad8b23b92d43edb836ae249c3a84e66abb4a6db208405b930cbfb3

Observation a6d8f123-049e-4a84-ae01-9e1ee3011f21 · outbound

This paper cites Quantum mechanical computers,.

Causal Decompositions of 1D Quantum Cellular Automata Quantum mechanical computers,

Reference 9

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source=pdf_text observed=2026-08-06T22:21:11.726128Z digest=sha256:d87bf4976005ed471f7db5ead09b264e6589e6735839bd49e06ba426a04622cc

Observation cc33e413-36c7-4b62-b29f-f30693672d9b · outbound

This paper cites Reversible quantum cellular automata.

Causal Decompositions of 1D Quantum Cellular Automata Reversible quantum cellular automata

Reference 10

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source=pdf_text observed=2026-08-06T22:21:11.748401Z digest=sha256:28c1b1dbe258cb2f0c09b686d855de4a606b5630459c88ab7d3085bf0d024921

Observation aa8d557d-5248-431a-ba99-c0ec65e33765 · outbound

This paper cites An overview of Quantum Cellular Automata.

Causal Decompositions of 1D Quantum Cellular Automata An overview of Quantum Cellular Automata

Reference 11

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source=pdf_text observed=2026-08-06T22:21:11.862816Z digest=sha256:fc84bf79aa24a3ce4e4739021a159d1426a1cbcbf42aaa1451315756ab2e56d6

Observation 91150fb8-e597-4d72-89c2-73da80ff308e · outbound

This paper cites A review of Quantum Cellular Automata.

Causal Decompositions of 1D Quantum Cellular Automata A review of Quantum Cellular Automata

Reference 12

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source=pdf_text observed=2026-08-06T22:21:12.003128Z digest=sha256:d9b1ec96b2ef6602168bfc08651767803ab48f7fb1bb88a5be8921b53557c475

Observation 685f4d1c-2e9a-4485-8e3c-c506967a53d6 · outbound

This paper cites On one-dimensional quantum cellular automata,.

Causal Decompositions of 1D Quantum Cellular Automata On one-dimensional quantum cellular automata,

Reference 13

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source=pdf_text observed=2026-08-06T22:21:12.098596Z digest=sha256:c4431e2ee8d9623ec95d575518f656fe707a4a89217ee81ffbb0f4d4bc79c680

Observation 45396163-7b69-4c45-bd1c-c56f9d0f4e2b · outbound

This paper cites Intrinsically universal n-dimensional quantum cellular automata.

Causal Decompositions of 1D Quantum Cellular Automata Intrinsically universal n-dimensional quantum cellular automata

Reference 14

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source=pdf_text observed=2026-08-06T22:21:12.197911Z digest=sha256:c84fe6cf77a319923a39ea627fd0bc747a58d7a6cfd132e20204bdd08a54f128

Observation 4ff45401-c6f5-461e-acac-a03308beed11 · outbound

This paper cites Derivation of the Dirac Equation from Principles of Information Processing.

Causal Decompositions of 1D Quantum Cellular Automata Derivation of the Dirac Equation from Principles of Information Processing

Reference 15

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source=pdf_text observed=2026-08-06T22:21:12.301126Z digest=sha256:2cd14a501a33c9794c82ae9957065281deb75b9e7c28c2ec0bb392ced5eab2ae

Observation 16423869-9143-4343-9bec-3e349f6d399b · outbound

This paper cites Weyl, Dirac and Maxwell Quantum Cellular Automata: analitical solutions and phenomenological predictions of the Quantum Cellular Automata Theory of Free Fields.

Causal Decompositions of 1D Quantum Cellular Automata Weyl, Dirac and Maxwell Quantum Cellular Automata: analitical solutions and phenomenological predictions of the Quantum Cellular Automata Theory of Free Fields

Reference 16

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source=pdf_text observed=2026-08-06T22:21:12.435695Z digest=sha256:141639180b807a3d30c9d58068f303f8c6b60b98a7e7d19c6ea8ae3b391e547f

Observation f7a78410-23a5-42ad-8e13-24691590d5d7 · outbound

This paper cites A quantum cellular automaton for one-dimensional QED.

Causal Decompositions of 1D Quantum Cellular Automata A quantum cellular automaton for one-dimensional QED

Reference 17

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local_arxiv, observed 2026-08-06T22:21:17.822955Z

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source=pdf_text observed=2026-08-06T22:21:12.549931Z digest=sha256:a6ca5dfa2b15b371de6b1cb473c078b1abee1a408b3873f52b9ba792ab0a26b0

Observation e5254d1a-9e69-4a2d-9fe3-a46cba61a682 · outbound

This paper cites A relativistic discrete spacetime formulation of 3+1 QED.

Causal Decompositions of 1D Quantum Cellular Automata A relativistic discrete spacetime formulation of 3+1 QED

Reference 18

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source=pdf_text observed=2026-08-06T22:21:12.643848Z digest=sha256:7d05da68dc46cc8f1a715d014e35bceebafc5caf7ecca98e12d4a072cb1b2410

Observation d3d11c99-d9c0-4ee3-8cd6-379d6ee1f0bb · outbound

This paper cites One-dimensional quantum cellular automata over finite, unbounded configurations.

Causal Decompositions of 1D Quantum Cellular Automata One-dimensional quantum cellular automata over finite, unbounded configurations

Reference 19

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source=pdf_text observed=2026-08-06T22:21:12.742828Z digest=sha256:a8ad92c75e75ef2d31bd940da4b57ed27ff5849e3d79b4f35982f37761cb9e5e

Observation ab15625d-4773-4085-a888-8ef105e03c9d · outbound

This paper cites Index theory of one dimensional quantum walks and cellular automata.

Causal Decompositions of 1D Quantum Cellular Automata Index theory of one dimensional quantum walks and cellular automata

Reference 20

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source=pdf_text observed=2026-08-06T22:21:12.805981Z digest=sha256:b6f7070ebb17444e5ce8d8cfe938358373383361a32b72c1e0ed26ed08a0fc64

Observation 8e104c45-77fa-4d8b-b605-09cc8deca15b · outbound

This paper cites Partitions in quantum theory,.

Causal Decompositions of 1D Quantum Cellular Automata Partitions in quantum theory,

Reference 21

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source=pdf_text observed=2026-08-06T22:21:12.863211Z digest=sha256:d4312cb5a7c09fdcac7817ed7fbd19716b252273350fe7f030c806040a6c4363

Observation d232803b-24ab-4c4d-8c06-62036410d9ef · outbound

This paper cites Unitarity plus causality implies localizability.

Causal Decompositions of 1D Quantum Cellular Automata Unitarity plus causality implies localizability

Reference 22

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source=pdf_text observed=2026-08-06T22:21:12.976180Z digest=sha256:99c56c44ba2c48acaf77a58774ef5b1c36d87d358994fb9e46a2299535020bb5

Observation 7b248ae6-c0cc-460c-a7e2-1b5607adea88 · outbound

This paper cites Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants.

Causal Decompositions of 1D Quantum Cellular Automata Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants

Reference 23

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source=pdf_text observed=2026-08-06T22:21:13.106383Z digest=sha256:26a53dacb2fdc88682538d1a6eee1bb1da0b37c016f8dbd628cc635a0da63c29

Observation c632cde6-cc9c-4187-b808-a4edf2b9952e · outbound

This paper cites Matrix Product Representation of Locality Preserving Unitaries.

Causal Decompositions of 1D Quantum Cellular Automata Matrix Product Representation of Locality Preserving Unitaries

Reference 24

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source=pdf_text observed=2026-08-06T22:21:13.172153Z digest=sha256:a7a500b41067f2809d556f2fd5847dc68763b7b478ed5e547e9eb6bfb6e21d54

Observation 6fd277ae-8693-4aaa-a38e-baf5dafbb029 · outbound

This paper cites Fermionic quantum cellular automata and generalized matrix-product unitaries,.

Causal Decompositions of 1D Quantum Cellular Automata Fermionic quantum cellular automata and generalized matrix-product unitaries,

Reference 25

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source=pdf_text observed=2026-08-06T22:21:13.211089Z digest=sha256:d8d9b69d28e1d6df5eda389136329c84d3970a5b1265c7ac3dde03136ffb86fc

Observation bcfaac3a-0ac8-43cb-85bf-e21985215b85 · outbound

This paper cites Matrix-product unitaries: Beyond quantum cellular automata.

Causal Decompositions of 1D Quantum Cellular Automata Matrix-product unitaries: Beyond quantum cellular automata

Reference 26

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source=pdf_text observed=2026-08-06T22:21:13.394084Z digest=sha256:19637beaa4ef636cf63b28e2b41d57b63ea2bf86ea8b706fb3630d9f230c55f4

Observation 58781ee4-e3b3-4597-a95a-6eb653a867ea · outbound

This paper cites Shaded tangles for the design and verification of quantum circuits.

Causal Decompositions of 1D Quantum Cellular Automata Shaded tangles for the design and verification of quantum circuits

Reference 27

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source=pdf_text observed=2026-08-06T22:21:13.489205Z digest=sha256:078d03ed8f501e89a7ff2bdcf6d099766bfdfc8940c9c8f8539fc3111eb820c0

Observation 495c9523-518d-454e-8206-86358b4cd493 · outbound

This paper cites Causal Fermions in Discrete Spacetime.

Causal Decompositions of 1D Quantum Cellular Automata Causal Fermions in Discrete Spacetime

Reference 28

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local_arxiv, observed 2026-08-06T22:21:16.677963Z

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source=pdf_text observed=2026-08-06T22:21:13.534101Z digest=sha256:82c9983d9057ae84bfe84f0d45aaaf7d52043d1720ab16c07eed48d9c86c3dee

Observation 483025be-15e8-40c8-9cf3-af40b5671397 · outbound

This paper cites Interacting invariants for Floquet phases of fermions in two dimensions.

Causal Decompositions of 1D Quantum Cellular Automata Interacting invariants for Floquet phases of fermions in two dimensions

Reference 29

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source=pdf_text observed=2026-08-06T22:21:13.579848Z digest=sha256:19bd8db871cef8bc5bbe969a921a1031a6199f42820ed8d4ad347fc63cc1f326

Observation a7ac699b-ad49-4fc8-bbac-9304c99ecc1c · outbound

This paper cites Fermionic cellular automata in one dimension.

Causal Decompositions of 1D Quantum Cellular Automata Fermionic cellular automata in one dimension

Reference 30

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source=pdf_text observed=2026-08-06T22:21:13.628713Z digest=sha256:f9da3c5f2432c2fba9948a1ab56de4663b072bcfb1ddf3414ea24490313eeddf

Observation 62717002-dff5-44c4-8539-89dc94ce0118 · outbound

This paper cites An index for quantum cellular automata on fusion spin chains.

Causal Decompositions of 1D Quantum Cellular Automata An index for quantum cellular automata on fusion spin chains

Reference 31

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source=pdf_text observed=2026-08-06T22:21:13.694863Z digest=sha256:669ca72d4b9f5e49140f2c77130b96dd106ecd07bd05059fcf94d4c7d40b0c46

Observation 5ace730b-f077-4a87-90e2-d401ef62bdae · outbound

This paper cites DHR bimodules of quasi-local algebras and symmetric quantum cellular automata.

Causal Decompositions of 1D Quantum Cellular Automata DHR bimodules of quasi-local algebras and symmetric quantum cellular automata

Reference 32

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source=pdf_text observed=2026-08-06T22:21:13.768218Z digest=sha256:92444f4facb77e68b52424d13d26c51d02e80be55b75d48587ce729f7df684c5

Observation 5170d8b1-f0be-40ae-954a-da77856ca696 · outbound

This paper cites Quantum cellular automata and categorical dualities of spin chains,.

Causal Decompositions of 1D Quantum Cellular Automata Quantum cellular automata and categorical dualities of spin chains,

Reference 33

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source=pdf_text observed=2026-08-06T22:21:13.825118Z digest=sha256:bfc931f4e5b7db52f2863ab76b4bdf2b83cf9908208f27c2898703ca11fa00f0

Observation 89fecda1-c1b2-44ab-8425-b4843729d90a · outbound

This paper cites Quantum Cellular Automata on Symmetric Subalgebras.

Causal Decompositions of 1D Quantum Cellular Automata Quantum Cellular Automata on Symmetric Subalgebras

Reference 34

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source=pdf_text observed=2026-08-06T22:21:13.893452Z digest=sha256:0bfcb8262185a7c42c09ea45c538c91cb039e5905698e821e793e8f010974ca1

Observation 05659013-bd23-44bb-b9cb-84da31d9dd88 · outbound

This paper cites Classification of Quantum Cellular Automata.

Causal Decompositions of 1D Quantum Cellular Automata Classification of Quantum Cellular Automata

Reference 35

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source=pdf_text observed=2026-08-06T22:21:13.941307Z digest=sha256:c29975467be8fc2cfe55dd5d05f50c294ac607c2ced5fa693d26285f7fe16dcb

Observation eff3621d-efbe-4cfc-bda3-ea83986ce44d · outbound

This paper cites Nontrivial Quantum Cellular Automata in Higher Dimensions.

Causal Decompositions of 1D Quantum Cellular Automata Nontrivial Quantum Cellular Automata in Higher Dimensions

Reference 36

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source=pdf_text observed=2026-08-06T22:21:13.988780Z digest=sha256:595ead6f4c4373a6d5fd92489dd7fb2dfe748351b49860e70419b2bab62ae2fb

Observation dbf1d292-7c0a-4ea1-b44e-c803f15778e0 · outbound

This paper cites Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D.

Causal Decompositions of 1D Quantum Cellular Automata Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D

Reference 37

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:21:14.073614Z digest=sha256:05ff5aabbb16c8b1a273b2c7cba619bcc5413332888d2cdf2d500b53c7e5332c

Observation 19e2173b-ec3d-40d8-bb4d-07361ce0b89c · outbound

This paper cites Invertible subalgebras.

Causal Decompositions of 1D Quantum Cellular Automata Invertible subalgebras

Reference 38

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:21:16.165867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.103210Z digest=sha256:5f5005204349c5218308bfcb2c4bb3a16e3bc3baa72f5f29d3a5b3aa85fe6f98

Observation 7a697a37-2cce-4c69-9a43-42def33f2263 · outbound

This paper cites Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond.

Causal Decompositions of 1D Quantum Cellular Automata Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond

Reference 39

Resolution
unresolved
no resolver link, observed 2026-08-06T22:21:14.153031Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:21:14.153031Z digest=sha256:f025d1bed4ae5ff1c8eb6ca692ea3c3a6a5d87f2629f84cca4e7f228c42e4497

Observation 6a95ad28-cbc6-4570-bf79-a53f1a636fc4 · outbound

This paper cites Classification of qubit cellular automata on hypercubic lattices.

Causal Decompositions of 1D Quantum Cellular Automata Classification of qubit cellular automata on hypercubic lattices

Reference 40

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:21:16.004264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.201097Z digest=sha256:ca556cecc58ea0f9ad9bb604593f41caf4637225fbb60a653f18d9a356a99200

Observation f9255ccd-bb4e-4bb2-b7bf-daeaf80d3edd · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:22.448044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.258822Z digest=sha256:bb069be30f26277fc4077aa7c083ccb27cf6be20e049e20a94cbdf0c08fe72b2

Observation 623b7809-1424-4341-a3cc-e648f140d9c4 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:22.245906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.318636Z digest=sha256:cbaa9314938ce7fbf037ab6791e848863f2761c855c64cf5a6d74d3a9665b4a4

Observation 107acc30-4d35-4f39-bf24-338ef3bc1874 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:22.019358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.351681Z digest=sha256:8d18de1e2692b934b5f57e61795230fd64738add78a28b5dddac263f66197b74

Observation 3ec08b4b-9b96-4a89-ba42-fa92e4410b28 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:21.808352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.407869Z digest=sha256:2b8baa97903ad700644a3cdb4fddfe1ca1f73678d0a6e0aa621a3ffa8b7eaf72

Observation 5423ec7e-eccf-47b6-a946-89008e55ad1d · outbound

This paper cites Lemma B.3 shows thatZ(ω)∨A 2 is equal to the latter’s RHS, so A′ 1 =Z(ω)∨A 2.

Causal Decompositions of 1D Quantum Cellular Automata Lemma B.3 shows thatZ(ω)∨A 2 is equal to the latter’s RHS, so A′ 1 =Z(ω)∨A 2

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:21.616351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.524424Z digest=sha256:bf95396d7439beb2aa8c6b5a431808edc73f4af1e701b3fdb63ed554c3af71ce

Observation e1143eb4-7849-4264-90c7-2715e4f365c5 · outbound

This paper cites Therefore the previous reasoning applies to it, soZJn+l+2,−1K = (Zn+l+1∩Zn+l+2)∨(Z−1∩Z0).

Causal Decompositions of 1D Quantum Cellular Automata Therefore the previous reasoning applies to it, soZJn+l+2,−1K = (Zn+l+1∩Zn+l+2)∨(Z−1∩Z0)

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:21.422024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.588002Z digest=sha256:4a8bf5e0c0440cc5b8343877425115f7d769fdc8c73e06a98e46670002163ea6

Observation 19c20146-9188-46c9-989d-958643d91cc0 · outbound

This paper cites (78) Proof.

Causal Decompositions of 1D Quantum Cellular Automata (78) Proof

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:21.208226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.651707Z digest=sha256:2bc833a93e7f527109b66ee01a44f8dc841b6a89bc7e6a60b0025d648ed2e79d

Observation 64ef622c-74e4-49b5-a257-046c3472e949 · outbound

This paper cites (81) Proof.

Causal Decompositions of 1D Quantum Cellular Automata (81) Proof

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:21.031445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.725982Z digest=sha256:8675ecd6a28c9302ade4c5a725f1a45c75c133393eee62b7d2c6b542e77377a1

Observation ee334341-dc46-4eb3-8224-406604d5e726 · outbound

This paper cites The reverse inclusion is obtained through π(F′ 1∩µF2)⊆F ′ 1∩πµF2 =F′ 1∩πF2, where we used Lemma D.4 then πµ =π.

Causal Decompositions of 1D Quantum Cellular Automata The reverse inclusion is obtained through π(F′ 1∩µF2)⊆F ′ 1∩πµF2 =F′ 1∩πF2, where we used Lemma D.4 then πµ =π

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:20.858218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.807517Z digest=sha256:a333305afde6e7f8bead18d45d603d67fdccec2179ac9ada94f9bb21fe8e19c9

Observation ea492fd3-45ef-4651-b02a-6ae9c88d06f5 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:20.672899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.895211Z digest=sha256:868ce93b7522e98e52c5d3d7ad8156bc89bebbc0f4749f1e82522b17a4f09c13

Observation 3d34e7df-7be5-425b-8840-88cd1d27ab1b · outbound

This paper cites D.2 Vertex-splitting The crucial tool in the proof of Theorem 3.1 is the following refinement lemma.

Causal Decompositions of 1D Quantum Cellular Automata D.2 Vertex-splitting The crucial tool in the proof of Theorem 3.1 is the following refinement lemma

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:20.475060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:14.988335Z digest=sha256:fd2354f50b94032cd017b98b1e34075ae7a6a90953fa8f82c8beae2c98accf1a

Observation d0bf8e3d-58f7-4411-b9b7-a8ec778e7037 · outbound

This paper cites We also write q9 :=p9 +l and q+:=p+−l.

Causal Decompositions of 1D Quantum Cellular Automata We also write q9 :=p9 +l and q+:=p+−l

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:20.299351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.067928Z digest=sha256:4ce68931a8d3d51de7511a1c49d89e2b121197568eac21443a0537a00913d511

Observation 77ac497f-0f62-4af7-aeb1-5dec0f97dcd0 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:20.106466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.163402Z digest=sha256:8428be679e3e242c17323f480b45506399378e0466a0e3d42a04cdd9098e14f6

Observation ea737d1f-b242-425e-a398-8ff39ff604cb · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:19.903549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.228729Z digest=sha256:8cbc00829e9ca1257c4e0fc483b7e1ea53327251a02568428c1671f253de437e

Observation aba23cab-1f15-49b1-824e-6a98f43763cd · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:19.725862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.294403Z digest=sha256:80eac72fec828b7774359b017a4ccb1df2ca8d353c4686907e871d22b9bdc797

Observation 94fafe44-780c-4363-9715-d3bfe7f8b481 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:19.484858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.388079Z digest=sha256:c673b66027d5c731246dbc330d00db898d27060478e2eb6c00ad7d96f898a98d

Observation f93391f3-6cf3-4cd5-883d-48c2cfff7f2e · outbound

This paper cites Before we turn to the proof, let us make a few comments.

Causal Decompositions of 1D Quantum Cellular Automata Before we turn to the proof, let us make a few comments

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:19.269787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.545073Z digest=sha256:b6299dfbdc008f9f867384bc42e19cd987bcb773e1997759eab5e7a123270c73

Observation 241721cf-7efb-4b12-8692-ea3a67f99909 · outbound

This paper cites First, (91a) and (91b) tell us that for any m, AJm,− 1 4 K ⊆ AJm,0K andAJ 1 4,mK ⊆ AJ0,mK; after splitting every vertex, this yields (109a).

Causal Decompositions of 1D Quantum Cellular Automata First, (91a) and (91b) tell us that for any m, AJm,− 1 4 K ⊆ AJm,0K andAJ 1 4,mK ⊆ AJ0,mK; after splitting every vertex, this yields (109a)

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:21:19.083718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.630207Z digest=sha256:1d91497684125402ee269489fdd6ad1abca848a4015cc208a40024523dc11641

Observation f130ba7b-aa2b-440e-9e7a-8bc1d1821762 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:18.931660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.698309Z digest=sha256:9dbf5a398e08e602231554f227fc7100c9210b8e7788957bfef11c5a165d779b

Observation 6e80d792-98fb-4175-a8e2-484db577c281 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:18.767347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.742769Z digest=sha256:a9d12ea625178d339df5aba0b849e0b195321512f36bc70e5a200e5decee8f1b

Observation 871d1e16-f244-49e3-8311-6a615cebb9b3 · outbound

This paper cites an unresolved cited work.

Causal Decompositions of 1D Quantum Cellular Automata Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:21:18.654869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:15.807362Z digest=sha256:c69a5ea80793ea3d57eeb3368eebe66f239b54e934ddc519946eb28957e809f6

Observation 6d3d8fbc-5213-40ce-b85c-13f6bcc0e0ac · outbound

This paper cites Fermionic quantum cellular automata and generalized matrix product unitaries.

Causal Decompositions of 1D Quantum Cellular Automata Fermionic quantum cellular automata and generalized matrix product unitaries

Reference 2021

Resolution
verified exact
local_arxiv, observed 2026-08-06T22:21:17.022859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T22:21:13.312522Z digest=sha256:43c1c4c13d2e674265f24c731af7d132bd2da1fff3303f13f73c430d251a7580

Pith citing papers

Observation 2d926e80-5fbb-419f-afdd-aa81ee70b5f7 · inbound

Partitions in quantum theory cites this paper.

Partitions in quantum theory Causal Decompositions of 1D Quantum Cellular Automata

Reference 38

Resolution
unresolved
no resolver link, observed 2026-08-06T22:24:10.305958Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:10.305958Z digest=sha256:e27593cefb5225f0d4e7d8a9da4f01ec94af9b8ce8588ffe37e21e5d7128f965

Observation b625b6d0-5d8d-441c-a8f9-342fafa3c487 · inbound

An order-theoretic circuit syntax and characterisation of the concept lattice cites this paper.

An order-theoretic circuit syntax and characterisation of the concept lattice Causal Decompositions of 1D Quantum Cellular Automata

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-06T19:40:00.924332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T19:40:00.924332Z digest=sha256:e721efbf3a0204a0e4960a25f573d418cb6a6110c758c38e1f89caf3bb521e28

Observation 29328cdc-c9fc-45ae-a957-5e442b495d41 · inbound

Routing Quantum Control of Causal Order cites this paper.

Routing Quantum Control of Causal Order Causal Decompositions of 1D Quantum Cellular Automata

Reference 60

Resolution
verified exact
local_arxiv, observed 2026-08-06T18:26:25.452277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T18:26:25.397457Z digest=sha256:9d65898e0e7a0d4902cb66e825bc32a0eb1df930fbe3f500205efcea0adc430f