Paper Citation Record · LEDGER

Causal Decompositions of 1D Quantum Cellular Automata

As of 7 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 2026-08-06T06:34:29.942622+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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:18.556856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:11.325284Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:21:23.593385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:11.393277Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:11.431610Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:18.439817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:21:23.474124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:18.344149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:21:23.299993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:11.748401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:11.862816Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:12.003128Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:21:23.099823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:18.203771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:18.073787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:17.972398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:17.822955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:17.617408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:17.428153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:12.805981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:21:22.874127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:17.262286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.106383Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:17.163272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:21:22.663483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:16.887195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:16.764840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:16.677963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.579848Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:21:16.429981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.694863Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.768218Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.825118Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.893452Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.941307Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:13.988780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T22:21:14.073614Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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 2026-08-06T06:34:29.942622+00:00.

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.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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 2026-08-06T06:34:29.942622+00:00.

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.

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.

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 2026-08-06T06:34:29.942622+00:00.