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Paper Citation Record · LEDGER

Reasoning about Continuous-Variable Quantum Systems

As of 4 August 2026, this Paper Citation Record lists 100 of 112 outbound references and 0 inbound Pith citation observations for arXiv:2607.23137.

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

pith.paper-citation-record.v1
2607.23137 v1

Coverage vector

measured 100 of 112 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T03:36:05.051623Z

measured 100 of 100 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

100 of 112 outbound references displayed

  • verified exact10
  • verified fuzzy0
  • unresolved87
  • parse uncertain0
  • malformed identifier3
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f7846035-677c-467e-b86c-d0fc4f125aed · outbound

This paper cites 2006.Infinite dimensional analysis: a hitchhiker’s guide.

Reasoning about Continuous-Variable Quantum Systems 2006.Infinite dimensional analysis: a hitchhiker’s guide

Reference 1

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source=pdf_text observed=2026-08-01T03:36:01.550175Z digest=sha256:c5f38f94dbd3fc65efe49ee2a10554a365ee1b12dd136b67376cab14be4de364

Observation 16d31ce0-4f06-4cf1-bc22-3bff87058d2b · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 2

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source=pdf_text observed=2026-08-01T03:36:01.611360Z digest=sha256:bd4fb2b60aa454a3ae6d823ed6ffec39ba2720dd56d32d81cc674a72c69552ce

Observation 224c443e-1492-4f90-9d3e-493f6f19eed1 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 3

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source=pdf_text observed=2026-08-01T03:36:01.653694Z digest=sha256:32f44f93ef66e6e49cf6178b88a6ec76cb2f2497e03fe7e12097848367817030

Observation 20502da6-9a19-4fd8-acf4-8640c17d50a8 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 4

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source=pdf_text observed=2026-08-01T03:36:01.759668Z digest=sha256:82c3886aead0a0df139bf512e6bcfe15e09155c90ac2247095ea183960cd92f1

Observation d2a07dc3-018d-4077-9571-c4c4f16cbbcc · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 5

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source=pdf_text observed=2026-08-01T03:36:01.855253Z digest=sha256:2d420badbfbba63505a9f199cfa67c4e642102b562dc2a3a4da925f136444a03

Observation 4251d8ea-c26d-473b-ad65-353e9e9ec481 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 6

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source=pdf_text observed=2026-08-01T03:36:01.966377Z digest=sha256:772a722123b77749850fed05389e3fecafe98195b4cc05eb67cca50565a9885d

Observation 6e89f817-57f5-49fb-857d-d1b72089f340 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 7

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source=pdf_text observed=2026-08-01T03:36:02.042839Z digest=sha256:e408967a767f9f7c56261969bf2f405bce9bd45be8e24f76c331385937adc09d

Observation c1b63db1-b61f-4d3e-a0a4-d7207766e4f9 · outbound

This paper cites 2020.Boundary value problems, Weyl functions, and differential operators.

Reasoning about Continuous-Variable Quantum Systems 2020.Boundary value problems, Weyl functions, and differential operators

Reference 8

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source=pdf_text observed=2026-08-01T03:36:02.138621Z digest=sha256:f7dad3c995027f1ddf50c5562e606adebab08772d7b072d4192377c27908c298

Observation 12e15ef3-17ea-41eb-9396-33704fcd1e2f · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 9

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doi, observed 2026-08-01T03:38:24.324632Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-08-01T03:36:02.251275Z digest=sha256:0acc436b84c184616e2d715f69158487dda8a56b10e5a300c6534f6bfebc3b82

Observation f2fbaa25-9b0c-4ab1-b2f0-7c36b0fad3e8 · outbound

This paper cites Eli Bourassa, Rafael N.

Reasoning about Continuous-Variable Quantum Systems Eli Bourassa, Rafael N

Reference 10

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source=pdf_text observed=2026-08-01T03:36:02.342046Z digest=sha256:e247f40f08126f17bacfd356e75fe7ce331d1f0eda9af7756215216c8eba4eb2

Observation ea25792a-0ae1-4c3a-860f-409b336e04f1 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 11

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source=pdf_text observed=2026-08-01T03:36:02.447739Z digest=sha256:f0b37db9ee1face5e368453587c47a45016e9026bcf4287e173df89d3651556b

Observation a21808f1-5b80-46cb-ae05-f49e07ab68a6 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 12

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source=pdf_text observed=2026-08-01T03:36:02.524642Z digest=sha256:23f6ddcc8bb0a36abc8040acfed359f06b1e77309baaf46b3a5e661527051389

Observation a1446ae3-f976-4392-9976-3250b9180a04 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 13

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source=pdf_text observed=2026-08-01T03:36:02.604921Z digest=sha256:8fc74d469fc3b6c545d5b5159a6b89c7c48cbf44b457d39bb5b0409ba6658f23

Observation 18901baa-48ae-4a99-b8b7-224dcc819777 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 14

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source=pdf_text observed=2026-08-01T03:36:02.750796Z digest=sha256:60fa42bd52878ba9bef3a8160d2f81b5962a203fa19d1bc795894f688d1ad07c

Observation ebf241ec-53ba-49a6-88a3-2892f351dd1b · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 15

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source=pdf_text observed=2026-08-01T03:36:02.824887Z digest=sha256:2dbed5e877f6c05aabf02e5f044db165516724f87371e2365709b6c30aec036c

Observation c5558333-a7c1-4633-bf42-459cb83cda7d · outbound

This paper cites 1998.Multivalued linear operators.

Reasoning about Continuous-Variable Quantum Systems 1998.Multivalued linear operators

Reference 16

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source=pdf_text observed=2026-08-01T03:36:02.903578Z digest=sha256:59ff2b7fc2e230326071bc1510db51ee005b4db1250fcbe184eeb57a605a8122

Observation 8a79af37-9742-40d7-88c6-27102eaac2a6 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 17

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source=pdf_text observed=2026-08-01T03:36:02.964553Z digest=sha256:4abd76aedebce8367509c509240ca7c8890c2928bea49d1fd1df2e4b6de6a0d2

Observation 1c28fcf8-617f-4546-bb9f-d74aacdcaf30 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 18

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source=pdf_text observed=2026-08-01T03:36:03.062651Z digest=sha256:ffad43d6aaf163c07e1b35b7ba939e464df430ed0710e14abd7cc96099d43f3b

Observation 732bd928-5726-4dd4-9b3f-bd3f64381f56 · outbound

This paper cites Diestel and J.

Reasoning about Continuous-Variable Quantum Systems Diestel and J

Reference 19

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source=pdf_text observed=2026-08-01T03:36:03.172772Z digest=sha256:22b87f62734628b83341ed58578bf7418edf29ca6ed81f53da9ecadab987734b

Observation 1b84bffb-03ef-4c61-8d87-3158826b7c29 · outbound

This paper cites Dunford and J.T.

Reasoning about Continuous-Variable Quantum Systems Dunford and J.T

Reference 20

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source=pdf_text observed=2026-08-01T03:36:03.285061Z digest=sha256:b52d919764b6c3983badb7af6c3ccc2936b9dd1b851021d4c4658023a8820111

Observation 343c0698-eec5-4359-aed3-d13fd3309b8c · outbound

This paper cites End-to-End Formalization of Quantum Error Correction.

Reasoning about Continuous-Variable Quantum Systems End-to-End Formalization of Quantum Error Correction

Reference 21

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source=pdf_text observed=2026-08-01T03:36:03.367982Z digest=sha256:cdeb10137b313ba8c206bb77ff6f6f74acdfcc817108e07b1f00854a40a352b7

Observation 8135d9ab-edcd-467c-8aca-0da58e18b644 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 22

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source=pdf_text observed=2026-08-01T03:36:03.448773Z digest=sha256:459bef3c2968e3b5d53790e98b7d344015882bcbc34b978b1657c14dd07b847a

Observation b9ae6162-7e4c-4e6b-84d9-82a169ecfc0b · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 23

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source=pdf_text observed=2026-08-01T03:36:03.562336Z digest=sha256:6a4dfe8812152662a0ba6815fc4a5e7f356cd40869a2a710b6cd100a61fb6b24

Observation 5aaedffb-e594-4091-a3c0-b683859c758a · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 24

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source=pdf_text observed=2026-08-01T03:36:03.620800Z digest=sha256:b67cf75a21d079185880b87817a1f71ae6c39de3ca044040a36a39cd590f77bd

Observation 43e0bed2-6254-4b77-bbbb-572e48f63c74 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 25

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source=pdf_text observed=2026-08-01T03:36:03.727726Z digest=sha256:4bd6021fd73c66efdf370f04656e05326c2ded2fa76e21dedb114ee5d2b20bf6

Observation 99e9d9da-571c-49c8-9a4d-d53cfd4f9890 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 26

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source=pdf_text observed=2026-08-01T03:36:03.784058Z digest=sha256:f025fb3d59d3a25effad03449da42473dd9b3120f16952a0d912f5b1e697f5de

Observation 520573f8-4a8d-4257-bb11-af5831406d0c · outbound

This paper cites 2001.Statistical structure of quantum theory.

Reasoning about Continuous-Variable Quantum Systems 2001.Statistical structure of quantum theory

Reference 27

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source=pdf_text observed=2026-08-01T03:36:03.834773Z digest=sha256:80dc9e8d86b358427194664e1a635120e14e550f70597b0ead2a2d5485823723

Observation 8e26ff52-f3d4-413e-a23b-e4978a8f0229 · outbound

This paper cites 2011.Probabilistic and statistical aspects of quantum theory.

Reasoning about Continuous-Variable Quantum Systems 2011.Probabilistic and statistical aspects of quantum theory

Reference 28

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source=pdf_text observed=2026-08-01T03:36:03.947857Z digest=sha256:47d4a8339cb7bbb3b26e7be0b49771341d29ad892e9bc7aedeb6f23bc9b07e02

Observation 32d7704a-fcc0-47ad-8389-a0d1e928b024 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 29

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source=pdf_text observed=2026-08-01T03:36:04.003139Z digest=sha256:f4c7dc5258ed7004f677c8791f25bf2ff5aeb223acf9d7b2535d5d4409d1484f

Observation a4680456-8c9f-468a-b886-9ace9a7d0f3a · outbound

This paper cites 2016.Analysis in Banach spaces.

Reasoning about Continuous-Variable Quantum Systems 2016.Analysis in Banach spaces

Reference 30

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source=pdf_text observed=2026-08-01T03:36:04.113243Z digest=sha256:328da8378acd3527c6e833bfae3fbdc59ceeec62490348235a9fc57eceadbec6

Observation b3e21ff5-401e-4e79-b1c7-410754ed15b1 · outbound

This paper cites 1997.Fundamentals of the Theory of Operator Algebras.

Reasoning about Continuous-Variable Quantum Systems 1997.Fundamentals of the Theory of Operator Algebras

Reference 31

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source=pdf_text observed=2026-08-01T03:36:04.172889Z digest=sha256:70491541f012bb2e32691c964835d45b2224151ee012f8e0536f679f47e45726

Observation 79a93f56-62f6-4945-adbf-5d06145953b7 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 32

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source=pdf_text observed=2026-08-01T03:36:04.277805Z digest=sha256:f26335b8eace76aa6cc097345a54dc62f82c3b9c54963bd8051655be24d9dd3b

Observation 2909be7b-8f24-421a-acad-74308bf9f2ed · outbound

This paper cites 2013.Perturbation theory for linear operators.

Reasoning about Continuous-Variable Quantum Systems 2013.Perturbation theory for linear operators

Reference 33

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source=pdf_text observed=2026-08-01T03:36:04.337832Z digest=sha256:422b54d16155c8cfcd79b37bb518898d3f0f7f5106664e9735dd2771cdfcdb31

Observation 267a0502-4c6a-4caf-8d0d-986a015a4a55 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 34

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source=pdf_text observed=2026-08-01T03:36:04.446142Z digest=sha256:def5cef8120bfcff15a704dc7f26a1a8e4ca834bff93dbd8de702c2b4c4eb520

Observation 4f63f7c5-d50d-4c1b-a35a-829c0b4fefb0 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 35

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source=pdf_text observed=2026-08-01T03:36:04.552045Z digest=sha256:abad9aa2005bf921ad69f0472edc0c37d74651ee03f093a8a942b6b384aa8c01

Observation 69c4ba7d-618d-42bf-b6ea-8707d9e4e6aa · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 36

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source=pdf_text observed=2026-08-01T03:36:04.663742Z digest=sha256:048511208973def65cace91a6467b127c53221ac781e8d86aaac44e90edf56e1

Observation b6cf3e8e-ee88-445b-b4d8-a57e65c180a6 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 37

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source=pdf_text observed=2026-08-01T03:36:04.723704Z digest=sha256:7279ab8f327b6479754bb9bbad7ac2e3ce3c8a0091b84c8ff8ee6f3f666a34fb

Observation b53ce3af-a533-491b-a9a7-8e9b920cc88d · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 38

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doi, observed 2026-08-01T03:38:24.210009Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-08-01T03:36:04.780302Z digest=sha256:56ca608dc1db650d3dae81a6b7903ddcc6e8b634a53e5d8e920e25d77d84f038

Observation 93870229-6eb3-4d62-8dd9-1218b217c922 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 39

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doi, observed 2026-08-01T03:38:24.033375Z

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source=pdf_text observed=2026-08-01T03:36:04.784548Z digest=sha256:4605128a1d3239525d41c55fd480ceb1d85c732ecd4313f1ae5e915eb00b1a11

Observation 4d09749b-2812-4f79-93cd-ffd96eecf186 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 40

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source=pdf_text observed=2026-08-01T03:36:04.789010Z digest=sha256:7cbbbbcb9556a2b5a478d0227b7dd1cbfca436cb5006a0545c46fbc8e9e8ce0a

Observation 6f26266c-a6d0-48f0-9dd2-d714e0f21625 · outbound

This paper cites Braunstein.

Reasoning about Continuous-Variable Quantum Systems Braunstein

Reference 41

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source=pdf_text observed=2026-08-01T03:36:04.793492Z digest=sha256:10aad358b682255739f24cc9c37ff2e505ed7d64223cc8ccef0d485c8c48e91a

Observation eac11128-8e7b-4256-8902-2c165063cb94 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 42

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Observation 2d7b27d2-30cd-4f0c-872d-067bd03a91e5 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 43

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Observation 9defc0aa-2762-40da-9aae-21c2a2bb1e74 · outbound

This paper cites 2005.Abstraction, Refinement and Proof for Probabilistic Systems.

Reasoning about Continuous-Variable Quantum Systems 2005.Abstraction, Refinement and Proof for Probabilistic Systems

Reference 44

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Observation f22d6969-7b67-4cdf-b983-c7248ca5dfa1 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 45

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Observation 8293bc3c-a9a3-475f-86da-ad9abc86b33b · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 46

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Observation f09a972c-2ab3-44a4-a64a-c5ff18a49f08 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 47

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Observation 5a1ef2ef-77d8-42fc-96a9-c868f09558ee · outbound

This paper cites 1980.Methods of modern mathematical physics: Functional analysis.

Reasoning about Continuous-Variable Quantum Systems 1980.Methods of modern mathematical physics: Functional analysis

Reference 48

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Observation 1f8e5e70-e4a3-49d1-b93c-e8cdefd68fda · outbound

This paper cites 1987.Real and complex analysis.

Reasoning about Continuous-Variable Quantum Systems 1987.Real and complex analysis

Reference 49

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Observation 4b935485-54fc-4e76-b01f-1c86197cad34 · outbound

This paper cites 2012.Unbounded self-adjoint operators on Hilbert space.

Reasoning about Continuous-Variable Quantum Systems 2012.Unbounded self-adjoint operators on Hilbert space

Reference 50

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Observation e441d4bd-419f-4862-a03c-bc92ffb0c881 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 51

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Observation 9cab4f38-82d3-49fc-8aec-8f98e8b9e896 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 52

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Observation 44adf98e-8eb7-4db1-afcd-ff1f018bbd40 · outbound

This paper cites Hoare meets Heisenberg: A Lightweight Logic for Quantum Programs.

Reasoning about Continuous-Variable Quantum Systems Hoare meets Heisenberg: A Lightweight Logic for Quantum Programs

Reference 53

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Observation c45ad392-b6ab-4e3e-a942-3dc936273084 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 54

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Observation 6e228854-783a-4d36-a6e4-df7a48f7e766 · outbound

This paper cites Tse, Haocun Yu, N.

Reasoning about Continuous-Variable Quantum Systems Tse, Haocun Yu, N

Reference 55

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Observation 576501c9-397f-4b68-8d3d-cc16cca5b7e0 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 56

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Observation cf378017-2e60-4d5c-9b01-0ad7a5d0e258 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 57

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Observation 598d1591-5601-4023-9a57-21d612ee2fe8 · outbound

This paper cites Quantum references.

Reasoning about Continuous-Variable Quantum Systems Quantum references

Reference 58

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Observation 1a329be6-c29b-442a-9511-2653fafaea0c · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 59

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Observation 2eb4f01d-58c4-4673-b173-56eaae11a58f · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 60

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Observation e61204b9-6fe7-44fe-a04d-54a8dd71c0d0 · outbound

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Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 61

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Observation b41cc290-2aca-41f0-a802-23120cc530ee · outbound

This paper cites QECV: Quantum Error Correction Verification.

Reasoning about Continuous-Variable Quantum Systems QECV: Quantum Error Correction Verification

Reference 62

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Observation bde80235-a8c1-48e5-b48d-68b6eac70a8c · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 63

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Observation 23ad30d3-b1d4-456b-b8f3-4d7c32f7d91c · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 64

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Observation 87d345ad-85bc-4160-af1b-bfd0c55a2c75 · outbound

This paper cites Birkhoff-von Neumann Quantum Logic as an Assertion Language for Quantum Programs.

Reasoning about Continuous-Variable Quantum Systems Birkhoff-von Neumann Quantum Logic as an Assertion Language for Quantum Programs

Reference 65

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Observation 310a8191-281d-400e-8a3c-ceb8d985c1b0 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 66

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Observation e1bdcdf4-5117-4738-ace2-c93059798bb6 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 67

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Observation 147321c7-30c5-4ecd-9bfa-33c99445aa1d · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 68

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Observation 4761f284-f4f0-4038-a56c-58b5d04281b6 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 69

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Observation 81acf81d-dcf2-4bbc-bb85-c36850a37e5b · outbound

This paper cites Reasoning about Parallel Quantum Programs.

Reasoning about Continuous-Variable Quantum Systems Reasoning about Parallel Quantum Programs

Reference 70

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Observation f808191b-8c40-43b0-8163-c84f26cfbe7a · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 71

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Observation 224e5319-5746-4281-b783-6a182537a3b9 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 72

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Observation bdb14ada-54cf-4b17-b938-df7664a2b906 · outbound

This paper cites By the definition of closure, the domain Dom(𝑇) is dense inDom(𝔱 𝑇)with respect to the form norm.

Reasoning about Continuous-Variable Quantum Systems By the definition of closure, the domain Dom(𝑇) is dense inDom(𝔱 𝑇)with respect to the form norm

Reference 75

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Observation 8650cc3e-5ad6-4f87-959f-e89c9ec49966 · outbound

This paper cites continue.

Reasoning about Continuous-Variable Quantum Systems continue

Reference 76

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Observation a7626f2b-1285-4716-9641-839b35c54c5d · outbound

This paper cites We show that Í 𝑖 𝔱𝑄[𝐾𝑖 u]= Í 𝑗 𝔱𝑄[𝐿𝑗 u]for any𝑢∈H.

Reasoning about Continuous-Variable Quantum Systems We show that Í 𝑖 𝔱𝑄[𝐾𝑖 u]= Í 𝑗 𝔱𝑄[𝐿𝑗 u]for any𝑢∈H

Reference 77

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Observation 4b7d3960-c7bc-4295-9b26-ff4fbe05784b · outbound

This paper cites By the spectral approximation𝑄= Ã 𝑛𝑄𝑛 used above, and the continuity of the trace over positive forms, we have: Tr(𝑄J𝑆K(𝜌))=sup 𝑛 Tr 𝑄𝑛J𝑆K(𝜌).

Reasoning about Continuous-Variable Quantum Systems By the spectral approximation𝑄= Ã 𝑛𝑄𝑛 used above, and the continuity of the trace over positive forms, we have: Tr(𝑄J𝑆K(𝜌))=sup 𝑛 Tr 𝑄𝑛J𝑆K(𝜌)

Reference 78

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Observation 84c17044-770a-4f2a-b9d7-ee5042928afd · outbound

This paper cites • Validity:By the Exact Duality established above,Tr(wlp(𝑆,𝑄)𝜌)=Tr(𝑄J𝑆K(𝜌))≥Tr(𝑄J𝑆K(𝜌)).

Reasoning about Continuous-Variable Quantum Systems • Validity:By the Exact Duality established above,Tr(wlp(𝑆,𝑄)𝜌)=Tr(𝑄J𝑆K(𝜌))≥Tr(𝑄J𝑆K(𝜌))

Reference 79

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Observation 31cca163-a3cf-401d-aa49-0c3a09090579 · outbound

This paper cites By definition, Dom(𝔱𝑄)⊆Dom(𝔱 𝑃) and 𝔱𝑃[v]≤𝔱 𝑄[v] for all v∈Dom(𝔱 𝑄).

Reasoning about Continuous-Variable Quantum Systems By definition, Dom(𝔱𝑄)⊆Dom(𝔱 𝑃) and 𝔱𝑃[v]≤𝔱 𝑄[v] for all v∈Dom(𝔱 𝑄)

Reference 80

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Observation 8b3ac64e-1a4d-4d6b-bbef-311db79da02c · outbound

This paper cites By Theorem A.3, the form 𝔱𝑃 is defined by 𝔱𝑃[v]=Í 𝑗𝑐𝑗 𝔱𝑃 𝑗[v]and is a closed form.

Reasoning about Continuous-Variable Quantum Systems By Theorem A.3, the form 𝔱𝑃 is defined by 𝔱𝑃[v]=Í 𝑗𝑐𝑗 𝔱𝑃 𝑗[v]and is a closed form

Reference 81

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Observation 53d9ca98-6360-4ae8-b3f2-f328d8f3efec · outbound

This paper cites By Theo- rem A.3,𝔱𝑃(v)=sup 𝑛 𝔱𝑃𝑛(v).

Reasoning about Continuous-Variable Quantum Systems By Theo- rem A.3,𝔱𝑃(v)=sup 𝑛 𝔱𝑃𝑛(v)

Reference 82

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Observation 3f347249-b6b3-4ece-a329-f83f10e7dcb7 · outbound

This paper cites Hence Tr(𝑃𝑠𝑦𝑛𝜌)=Tr(𝑄𝜌)=Tr(𝑄JskipK(𝜌)).

Reasoning about Continuous-Variable Quantum Systems Hence Tr(𝑃𝑠𝑦𝑛𝜌)=Tr(𝑄𝜌)=Tr(𝑄JskipK(𝜌))

Reference 83

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Observation 4bf704c4-cf11-46d7-9926-7666cdb4a3ee · outbound

This paper cites By the induction hypothesis for 𝑆2,𝑅∈P.

Reasoning about Continuous-Variable Quantum Systems By the induction hypothesis for 𝑆2,𝑅∈P

Reference 84

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Observation 2fa1a916-e7b7-478d-8aed-f935da378a43 · outbound

This paper cites The measurement outcome space is denoted by(Ω𝑀,Σ𝑀,𝜇) , the Kraus-density operator at outcome𝜈 by𝑀𝜈, and the continuation with𝑥=𝜈 by𝑆 𝜈.

Reasoning about Continuous-Variable Quantum Systems The measurement outcome space is denoted by(Ω𝑀,Σ𝑀,𝜇) , the Kraus-density operator at outcome𝜈 by𝑀𝜈, and the continuation with𝑥=𝜈 by𝑆 𝜈

Reference 85

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Observation 58ba0a12-c02a-41da-b741-4bdb3382d612 · outbound

This paper cites Define𝑋 0 =0, and 𝔱𝑋𝑛+1[u]= 𝔱 𝑄[𝑀0u]+𝔱 wlpsyn(𝑆𝑏𝑜𝑑 𝑦,𝑋𝑛)[𝑀1u].

Reasoning about Continuous-Variable Quantum Systems Define𝑋 0 =0, and 𝔱𝑋𝑛+1[u]= 𝔱 𝑄[𝑀0u]+𝔱 wlpsyn(𝑆𝑏𝑜𝑑 𝑦,𝑋𝑛)[𝑀1u]

Reference 86

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Observation e39d43ac-66af-4679-8cb8-4afee480074a · outbound

This paper cites The total cost is C(𝑆,𝜌)= ∞∑︁ 𝑘=0 𝜀Tr(𝜌 𝑘)+C(𝑆 𝑏𝑜𝑑𝑦,𝑀 1𝜌𝑘𝑀† 1) <∞.

Reasoning about Continuous-Variable Quantum Systems The total cost is C(𝑆,𝜌)= ∞∑︁ 𝑘=0 𝜀Tr(𝜌 𝑘)+C(𝑆 𝑏𝑜𝑑𝑦,𝑀 1𝜌𝑘𝑀† 1) <∞

Reference 87

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Observation e5373e07-c39e-4645-aac2-bbfda9091f3d · outbound

This paper cites Their sum is 𝔱𝑄[u]+𝜀∥ u∥2, which exactly matches the syntactic rule 𝔱wp(skip,𝑄)[u].

Reasoning about Continuous-Variable Quantum Systems Their sum is 𝔱𝑄[u]+𝜀∥ u∥2, which exactly matches the syntactic rule 𝔱wp(skip,𝑄)[u]

Reference 88

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Observation d1daeaaf-4333-481b-8d58-9d1dcad2b09d · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 89

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Observation 84341996-d23a-49af-ab37-313baf6e6aa3 · outbound

This paper cites an unresolved cited work.

Reasoning about Continuous-Variable Quantum Systems Unresolved cited work

Reference 90

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Observation f2158779-dd17-458d-ad68-3eaed26e0e28 · outbound

This paper cites Both components are defined as infinite limits of their 𝑁 -step truncations.

Reasoning about Continuous-Variable Quantum Systems Both components are defined as infinite limits of their 𝑁 -step truncations

Reference 91

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Observation 5905e428-a776-4f1c-83e0-2431673481df · outbound

This paper cites Thus, equality𝑃=wlp(𝑆,𝑄) holds trivially, which implies𝑃⊒wlp(𝑆,𝑄).

Reasoning about Continuous-Variable Quantum Systems Thus, equality𝑃=wlp(𝑆,𝑄) holds trivially, which implies𝑃⊒wlp(𝑆,𝑄)

Reference 92

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Observation 28f08dc9-7fbf-4760-b4ba-3f9212b01dda · outbound

This paper cites By the monotonicity of the wlp transformer (Theorem C.2.1), wlp(𝑆 1,𝑅)⊒wlp(𝑆 1,wlp(𝑆 2,𝑄)).

Reasoning about Continuous-Variable Quantum Systems By the monotonicity of the wlp transformer (Theorem C.2.1), wlp(𝑆 1,𝑅)⊒wlp(𝑆 1,wlp(𝑆 2,𝑄))

Reference 93

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Observation abf7e4d3-a4e1-4da6-a7ea-260535ef30e5 · outbound

This paper cites By induction hypothesis,𝑃𝜈⊒wlp(𝑆 𝜈,𝑄) , which means 𝔱𝑃𝜈[v]≥𝔱 wlp(𝑆 𝜈,𝑄)[v] for allv.

Reasoning about Continuous-Variable Quantum Systems By induction hypothesis,𝑃𝜈⊒wlp(𝑆 𝜈,𝑄) , which means 𝔱𝑃𝜈[v]≥𝔱 wlp(𝑆 𝜈,𝑄)[v] for allv

Reference 94

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Observation 0ad88f5c-0ab3-46aa-a3b9-deea3bca392d · outbound

This paper cites By the induction hypothesis,𝑅⊒wlp(𝑆 𝑏𝑜𝑑𝑦,𝑃).

Reasoning about Continuous-Variable Quantum Systems By the induction hypothesis,𝑅⊒wlp(𝑆 𝑏𝑜𝑑𝑦,𝑃)

Reference 95

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Observation 51eceab7-ee70-4576-9ee5-77af61e8cf99 · outbound

This paper cites By the monotonicity of wlp,𝑄′⊒𝑄=⇒wlp(𝑆,𝑄 ′) ⊒wlp(𝑆,𝑄).

Reasoning about Continuous-Variable Quantum Systems By the monotonicity of wlp,𝑄′⊒𝑄=⇒wlp(𝑆,𝑄 ′) ⊒wlp(𝑆,𝑄)

Reference 96

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Observation 4c62d466-e449-4d6b-beee-8852d2a26608 · outbound

This paper cites For abort, the semantic weakest liberal precondition is wlp(abort,𝑄)= 0(by Definition C.4).

Reasoning about Continuous-Variable Quantum Systems For abort, the semantic weakest liberal precondition is wlp(abort,𝑄)= 0(by Definition C.4)

Reference 97

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Observation 94012bae-7b12-4274-9d4f-ac8658601f67 · outbound

This paper cites By the induction hypothesis, ⊢ {𝑃𝜈}𝑆𝜈{𝑄} is derivable for all𝜈∈Ω 𝑀.

Reasoning about Continuous-Variable Quantum Systems By the induction hypothesis, ⊢ {𝑃𝜈}𝑆𝜈{𝑄} is derivable for all𝜈∈Ω 𝑀

Reference 98

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Observation a8f0e1b4-71e9-4600-88f0-03e28f2b65f4 · outbound

This paper cites We must derive⊢{wlp(𝑆,𝑄)}𝑆{𝑄}.

Reasoning about Continuous-Variable Quantum Systems We must derive⊢{wlp(𝑆,𝑄)}𝑆{𝑄}

Reference 99

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Observation 7b8c83af-34aa-46a5-ab2e-3397d9292ba8 · outbound

This paper cites Evaluating its quadratic form yields 𝔱𝑃𝑠 𝑦𝑛[u]= 𝔱 𝑄[u]+𝜀 ∥u∥2.

Reasoning about Continuous-Variable Quantum Systems Evaluating its quadratic form yields 𝔱𝑃𝑠 𝑦𝑛[u]= 𝔱 𝑄[u]+𝜀 ∥u∥2

Reference 100

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Observation 7aa68c1e-414e-4fa9-9194-b0f0eec1f580 · outbound

This paper cites By the induction hypothesis, we have𝑃⊒wp(𝑆 1,𝑅) and𝑅⊒wp(𝑆 2,𝑄).

Reasoning about Continuous-Variable Quantum Systems By the induction hypothesis, we have𝑃⊒wp(𝑆 1,𝑅) and𝑅⊒wp(𝑆 2,𝑄)

Reference 101

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Observation 901021a3-9a14-4e39-abd1-90e52543764c · outbound

This paper cites The derived precondition is𝑃𝑝𝑟𝑒 =𝜀𝐼+ ∫ Ω𝑀 𝑀† 𝜈𝑃𝜈𝑀𝜈𝑑𝜇(𝜈).

Reasoning about Continuous-Variable Quantum Systems The derived precondition is𝑃𝑝𝑟𝑒 =𝜀𝐼+ ∫ Ω𝑀 𝑀† 𝜈𝑃𝜈𝑀𝜈𝑑𝜇(𝜈)

Reference 102

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