Paper Citation Record · LEDGER

All Hilbert spaces are the same: consequences for generalized coordinates and momenta

As of 14 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2502.08494.

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

pith.paper-citation-record.v1
2502.08494 v4

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T04:59:16.562143Z

measured 52 of 52 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T00:44:31.183958Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-02T14:07:02.624693Z

Reference resolution

51 of 51 outbound references displayed

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External citation measurements

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Outbound references

Observation 4c83c8b6-e6e7-4552-a356-70a70ded633b · outbound

This paper cites That this is so, follows, in physicists’ notation, from ⟨p′|p⟩ = δ(p′ −p).

All Hilbert spaces are the same: consequences for generalized coordinates and momenta That this is so, follows, in physicists’ notation, from ⟨p′|p⟩ = δ(p′ −p)

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:17.196437Z

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Observation 98933b6a-d712-4e96-ae4a-16a452431fb4 · outbound

This paper cites doubled” the total Hilbert space: in the ﬁrst case by extending the semi-inﬁnite real axis to the whole real axis, in the second case by using an extra (“ancilla.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta doubled” the total Hilbert space: in the ﬁrst case by extending the semi-inﬁnite real axis to the whole real axis, in the second case by using an extra (“ancilla

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:17.184512Z

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Observation 48d556a4-ad30-4d89-a525-cf1d666c0c19 · outbound

This paper cites wrap around.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta wrap around

Reference 3

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Observation 0a16e4fb-40d5-4b87-8a82-34f7eed32a06 · outbound

This paper cites delta-function normalized.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta delta-function normalized

Reference 4

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Observation 620f1379-2ea5-4329-a253-3559b8f9ce8e · outbound

This paper cites This case nat- urally describes a quantum system moving on the semi- inﬁnite real axis.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta This case nat- urally describes a quantum system moving on the semi- inﬁnite real axis

Reference 5

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Observation bf673a24-378a-40dc-a6d3-2efc2624fa9c · outbound

This paper cites momentum.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta momentum

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:17.141996Z

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Observation cb303a07-8ab3-4368-8a3f-aa941b5b288f · outbound

This paper cites That is, whenever xn < xk < xn′ we have n < k < n′.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta That is, whenever xn < xk < xn′ we have n < k < n′

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:17.132210Z

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Observation d2860d6d-0fe5-449e-ab34-6fad1a716ae6 · outbound

This paper cites ﬁnest” possi- ble measurements. That is, we do not include POVMs that are “coarser.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta ﬁnest” possi- ble measurements. That is, we do not include POVMs that are “coarser

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:17.122092Z

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Observation db7ab66f-1316-4bbb-852a-e3d07ddc15ec · outbound

This paper cites paradox” of the type discussed in [ 2], in the sense that a mathematical property that at ﬁrst sight might seem unimportant and “merely a technical detail.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta paradox” of the type discussed in [ 2], in the sense that a mathematical property that at ﬁrst sight might seem unimportant and “merely a technical detail

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:16.950507Z

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Observation 6a50ba56-877c-4791-b32a-f53e56df586a · outbound

This paper cites Thus, the POVM {Π α } de- scribes a physically acceptable simultaneous measure- ment of X3 and ˜P3.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Thus, the POVM {Π α } de- scribes a physically acceptable simultaneous measure- ment of X3 and ˜P3

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:17.111513Z

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Observation 0f309142-dc62-4f53-abd5-32ebb70d2da2 · outbound

This paper cites an unresolved cited work.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 11

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Observation 5c3dd522-b7d0-475b-8703-9e7ccbff56cb · outbound

This paper cites Canonical quantization on the half-line and in an interval based upon a new concept for the momentum in a space with boundaries.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Canonical quantization on the half-line and in an interval based upon a new concept for the momentum in a space with boundaries

Reference 12

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Observation aded771a-4173-451e-a18d-dcdff4fd1715 · outbound

This paper cites Since there are well-documented dangers in Dirac’s formalism [ 2], in the following we will, when appropriate, indicate such dangers.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Since there are well-documented dangers in Dirac’s formalism [ 2], in the following we will, when appropriate, indicate such dangers

Reference 13

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Observation 871d601e-99f8-4c0b-964d-c00a99a160e4 · outbound

This paper cites Mathematical surprises and Dirac's formalism in quantum mechanics.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Mathematical surprises and Dirac's formalism in quantum mechanics

Reference 14

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Observation 2ee167a9-7b1b-46aa-b126-7a1b9ca4deec · outbound

This paper cites Self-adjoint extensions of operators and the teaching of quantum mechanics.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Self-adjoint extensions of operators and the teaching of quantum mechanics

Reference 15

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Observation ac747193-5282-408a-8216-84153870358a · outbound

This paper cites Canonical Quantization and Impenetrable Barriers.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Canonical Quantization and Impenetrable Barriers

Reference 16

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 17

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Observation 2ba2e065-b4c0-4b10-bd00-b53889389d2f · outbound

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 18

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Observation 373c2ec4-a522-4311-af4f-ff49451e92c7 · outbound

This paper cites Becnel and A.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Becnel and A

Reference 19

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Observation cd8d1fff-1b6a-488d-9613-ea638a67b3d6 · outbound

This paper cites Talagrand, What Is a Quantum Field Theory? (Cam- bridge University Press, 2022).

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Talagrand, What Is a Quantum Field Theory? (Cam- bridge University Press, 2022)

Reference 20

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 21

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Observation 80639dcc-062f-4b0a-a4e0-0f34fdd1caee · outbound

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 22

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Observation a312ff58-c2f1-4a7f-8b09-382bca5bcb34 · outbound

This paper cites Daubechies, A.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Daubechies, A

Reference 23

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Observation 269c55c3-ed47-4d60-bafd-612bd9a33c41 · outbound

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 24

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Observation 25aeaa45-98f7-451c-8749-138c41323488 · outbound

This paper cites A New Concept for the Momentum of a Quantum Mechanical Particle in a Box.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta A New Concept for the Momentum of a Quantum Mechanical Particle in a Box

Reference 25

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Observation 196f536c-3247-41e3-b44c-36264dcfb98a · outbound

This paper cites Judge, On the uncertainty relation for lz and φ , Physics Letters 5, 189 (1963).

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Judge, On the uncertainty relation for lz and φ , Physics Letters 5, 189 (1963)

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T04:59:16.844288Z

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Observation 0357f687-77f8-40b7-8b0f-dbf1f381252d · outbound

This paper cites Judge, On the uncertainty relation for angle variabl es, Il Nuovo Cimento 31, 332 (1964).

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Judge, On the uncertainty relation for angle variabl es, Il Nuovo Cimento 31, 332 (1964)

Reference 27

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Observation a59b38fb-3ee8-4766-abe0-af0c606dd6cb · outbound

This paper cites Bouten, N.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Bouten, N

Reference 28

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 29

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Observation c5f1963e-a1ed-44f8-b8e7-d54d12785566 · outbound

This paper cites Vourdas, Quantum systems with ﬁnite Hilbert space, Reports on Progress in Physics 67, 267 (2004).

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Vourdas, Quantum systems with ﬁnite Hilbert space, Reports on Progress in Physics 67, 267 (2004)

Reference 30

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 31

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Observation 9ca91b3e-d430-45d5-b376-21b37e8bf7f5 · outbound

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta She and H

Reference 32

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Observation 913a2860-1e37-4979-998e-352b173d7fc9 · outbound

This paper cites Kraus, A.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Kraus, A

Reference 33

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 34

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Observation c785f485-c941-4c2d-89a3-f4efad77e3dd · outbound

This paper cites Roman, Introduction to Quantum Field Theory (Wi- ley, 1969).

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Roman, Introduction to Quantum Field Theory (Wi- ley, 1969)

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-08T04:59:16.548014Z

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 36

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Observation 7f2da778-3fdf-4bca-ad5e-5b0a10155f24 · outbound

This paper cites Linear stochastic wave-equations for continuously measured quantum systems.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Linear stochastic wave-equations for continuously measured quantum systems

Reference 37

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 38

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Observation 3adc68e7-b93d-4f98-95bf-e17f8201e4ab · outbound

This paper cites Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups

Reference 39

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Observation cb0ebe07-f88e-4339-9f2b-37cdfafa13b2 · outbound

This paper cites How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of $\mathrm{SL}(2,\mathbb{C})$.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of $\mathrm{SL}(2,\mathbb{C})$

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-08T04:59:16.521669Z

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Observation 53fa5d03-cfd0-4d00-9855-45c2520a06a0 · outbound

This paper cites Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

Reference 41

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Observation 10cf9008-8731-481e-8758-9eb9225b1a76 · outbound

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 42

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Observation 22df835d-4351-4791-a656-5112c9540b04 · outbound

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All Hilbert spaces are the same: consequences for generalized coordinates and momenta Unresolved cited work

Reference 43

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Observation c0e7cec2-5b49-45be-ab05-5314c40d28c1 · outbound

This paper cites Separable Hilbert space in Loop Quantum Gravity.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Separable Hilbert space in Loop Quantum Gravity

Reference 44

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Observation a4cf1425-76bb-4c41-9c70-d434be91dfb3 · outbound

This paper cites Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?

Reference 45

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Observation 494e4622-51b8-4279-a31f-ad289aa4401d · outbound

This paper cites These four operators thus form a POVM on H and thus describe a generalized measurement on the quantum system described by H.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta These four operators thus form a POVM on H and thus describe a generalized measurement on the quantum system described by H

Reference 46

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Observation 70dac458-0b38-421c-9291-ba696822d845 · outbound

This paper cites parti- cle in a box.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta parti- cle in a box

Reference 47

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Observation 6c4a0b77-5f7d-453a-b798-aac1e40d9405 · outbound

This paper cites Haag, On quantum ﬁeld theories, Matematisk-fysiske Meddelelser 29, no.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Haag, On quantum ﬁeld theories, Matematisk-fysiske Meddelelser 29, no

Reference 48

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Observation f387f97a-5ad5-4667-8d75-ba69b4e63a5c · outbound

This paper cites Even though [the Hamiltonians for the two ﬁeld theories] both make perfect sense, it is the (implicit) assumption that they operate on the same state space that does not.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Even though [the Hamiltonians for the two ﬁeld theories] both make perfect sense, it is the (implicit) assumption that they operate on the same state space that does not

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-08T04:59:16.554861Z

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Observation e8152d3c-b3b8-422b-8ea5-9a86a0c26831 · outbound

This paper cites Simulating quantum field theory with a quantum computer.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Simulating quantum field theory with a quantum computer

Reference 50

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Observation 953d3420-2d7e-4b48-94a1-90e538884e89 · outbound

This paper cites Quantum Simulation for High Energy Physics.

All Hilbert spaces are the same: consequences for generalized coordinates and momenta Quantum Simulation for High Energy Physics

Reference 51

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Pith citing papers

Observation 72e1f5bc-9079-400b-b292-626a0b321582 · inbound

Polymer quantum mechanics on compact configuration spaces cites this paper.

Polymer quantum mechanics on compact configuration spaces All Hilbert spaces are the same: consequences for generalized coordinates and momenta

Reference 47

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Source-reported events for the cited work

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