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Paper Citation Record · LEDGER

Fourier transform, Schr\"odinger representation, and Heisenberg modules

As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:1908.04514.

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

pith.paper-citation-record.v1
1908.04514 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:49:13.834798Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

21 of 21 outbound references displayed

  • verified exact4
  • verified fuzzy15
  • unresolved2
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3a7fc01d-51e5-4964-b1f0-2e6c552355dd · outbound

This paper cites Connes, C∗ -alg` ebres et g´ eometrie diff´ erentille, C.R.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Connes, C∗ -alg` ebres et g´ eometrie diff´ erentille, C.R

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.205690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.729405Z digest=sha256:0e946df3c9a1c8d9bdda5cec3c1f01b34947e24b484c2d7613ad51bb12b61ade

Observation a72e53f8-1ba8-468c-b764-04340430868b · outbound

This paper cites Boca, Projections in rotation algebras and theta functions , Comm.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Boca, Projections in rotation algebras and theta functions , Comm

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.190776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.734484Z digest=sha256:3c22eaa974fa712a02c6e57be78d129e30b21a1f2bf9ddafec1f2a3a964595cd

Observation 293c8849-d006-4ee4-bd15-6f56d14f565d · outbound

This paper cites Connes and M.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Connes and M

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.175202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.739870Z digest=sha256:97fdde92abb8b54010578167478d845c8c844d62ea962280ca0ec3885e17365d

Observation 69665673-b6a9-4e7a-a4d5-5ab884347f25 · outbound

This paper cites Dabrowski, T.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Dabrowski, T

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.158432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.745703Z digest=sha256:e5bd2aeb16341df23733d081ffcb74e3268c7ba6d4143f5c29c5bdd6de688c57

Observation af7a3dc4-558c-45e4-8364-79f0165cc0f6 · outbound

This paper cites Physics Lett.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Physics Lett

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.143144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.752054Z digest=sha256:c9318a2c31ed1e30716a29600c3dd496ea3f0ca10562762d29251a1c8a4dbc8d

Observation af64c20d-3170-4410-bf98-50fab6b72a19 · outbound

This paper cites Landi, and F Luef, Sigma-model solitons on noncommutative spaces , Lett.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Landi, and F Luef, Sigma-model solitons on noncommutative spaces , Lett

Reference 6

Resolution
verified exact
doi, observed 2026-08-14T13:49:13.914466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.759159Z digest=sha256:42e990e67950318d4025bb41c1dc1dea813c75f0fc6941fa0dd5aecb3d85291d

Observation 596cae57-f6fb-4c61-9c8c-8a574572ba67 · outbound

This paper cites Solitons of general topological charge over noncommutative tori.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Solitons of general topological charge over noncommutative tori

Reference 7

Resolution
verified exact
local_arxiv, observed 2026-08-14T13:49:13.939210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.765501Z digest=sha256:b5cb99477625f654fef798e816745cca6f244db57883db3be1907c704d2ae256

Observation 951a42a0-bf76-4227-9d46-cbf9a4424b00 · outbound

This paper cites an unresolved cited work.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:49:14.128284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.770810Z digest=sha256:cb5a96a8e56cf027e8f6cc34b07962a947fa29abf2f0653e55c19dd244631a40

Observation 4c9954db-3966-4dd5-9757-3a9c28489dde · outbound

This paper cites Frank and D.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Frank and D

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.114358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.775816Z digest=sha256:c42a7e0b7797efbfce147734eec099875a6b7dd84ad6011a6382f5cd36c99785

Observation c0d5b88b-f262-48e3-b254-730deffd6925 · outbound

This paper cites Gr¨ ochenig and Y.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Gr¨ ochenig and Y

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.099546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.780706Z digest=sha256:8e40eb20199c62e9092ff63217c4d9a6e04f86ca88812fbfba2882045bd3f909

Observation e1497cba-4159-4731-9fbe-5305a1656140 · outbound

This paper cites Gr¨ ochenig and J St¨ ockler,Gabor frames and totally positive functions , Duke Math.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Gr¨ ochenig and J St¨ ockler,Gabor frames and totally positive functions , Duke Math

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.084601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.785906Z digest=sha256:a6ee3458e88630805c2f6ace3c7110ebc7bbbbb1e770870fea885670de864928

Observation cb28caa3-7d36-4987-9d9c-e66e08fac147 · outbound

This paper cites Howe, On the role of the Heisenberg group in harmonic analysis , Bull.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Howe, On the role of the Heisenberg group in harmonic analysis , Bull

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.069230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.792815Z digest=sha256:9b281760f44801f0d424dc9c7ffd757d272505cd754dad5581740ed2ec4b1993

Observation 73338ecc-fbfa-4c43-81d1-de906b9b242c · outbound

This paper cites Jacobsen, On a New Segal Algebra:A Review of the Feichtinger Algebra , J.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Jacobsen, On a New Segal Algebra:A Review of the Feichtinger Algebra , J

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.053712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.797649Z digest=sha256:ff820cadd5192d804b8182559bd6a6712b02769f739b53f22d8dfa40e0d9c678

Observation e96d284d-9765-4ac9-8843-dc5a152477a5 · outbound

This paper cites Jakobsen and J.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Jakobsen and J

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.037091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.802026Z digest=sha256:d02f08d475f82974ddc1b01c0f5ea4efe2f696d01fc0b398d9ea79b94fbe95fc

Observation 790c62a2-038d-44ed-93a7-c9724b741adc · outbound

This paper cites Lee, A note on nonlinear σ -models in noncommutative geometry , IDAQP 19 (2016), no.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Lee, A note on nonlinear σ -models in noncommutative geometry , IDAQP 19 (2016), no

Reference 15

Resolution
verified exact
doi, observed 2026-08-14T13:49:13.897680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.806561Z digest=sha256:7693230b9a277ec6ec43484dd5f67a35c6ef89f743bb0dd62f3eb9eb29abd532

Observation 1ba46783-501c-4dd5-b11b-9d3c5bfbb2d1 · outbound

This paper cites 2, DOI 10.1142/S023902571850008X.

Fourier transform, Schr\"odinger representation, and Heisenberg modules 2, DOI 10.1142/S023902571850008X

Reference 16

Resolution
verified exact
doi, observed 2026-08-14T13:49:13.878735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.811092Z digest=sha256:23b7b777e88925032109ef8b6c4af347d6dbb2c90799e756fef354cb1765a56d

Observation 5188a39e-ed6d-4c5a-8bc0-8913865c66c1 · outbound

This paper cites Luef, Projections in noncommutative tori and Gabor frames , Proc.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Luef, Projections in noncommutative tori and Gabor frames , Proc

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:14.021134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.815928Z digest=sha256:8ba927d62b548e8406fb04fae0e5607c20accdea715af832054dadc8ddc463c5

Observation a7002a04-6a01-413f-a4c4-c05f49719a68 · outbound

This paper cites an unresolved cited work.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:49:14.005926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.821000Z digest=sha256:01cfdf2bebaa4edd3fbd320de669ca5870ac5f3b1b83f99d20031f3a3d7c4880

Observation 1246f402-670d-465d-87dc-e686a720e1ce · outbound

This paper cites Mathai and J.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Mathai and J

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:13.989662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.825547Z digest=sha256:e4831a3d64c2823f377ec15e526567c65a0741ea0d98124e1700d9f8cb57095a

Observation 4da92ee8-83ec-42bf-b35e-f065ff0702a5 · outbound

This paper cites Polishchuck, Analogues of the exponential map associated with complex st ructures on non- commutative two-tori , Pacific J.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Polishchuck, Analogues of the exponential map associated with complex st ructures on non- commutative two-tori , Pacific J

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:13.973633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.829978Z digest=sha256:97f75fae55834de16c21c70fa7f25dd10abbbd06130199b8b38998d2c2124a56

Observation 0fcb99b1-420f-4c05-8ac6-1855d4201dd2 · outbound

This paper cites Rieffel, Projective modules over higher-dimensional non-commutat ive tori , Canad.

Fourier transform, Schr\"odinger representation, and Heisenberg modules Rieffel, Projective modules over higher-dimensional non-commutat ive tori , Canad

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:49:13.957193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:49:13.834798Z digest=sha256:cee396b53f9ab80a8477a3eb58dc74479e1b51714fc0ec0eb15aa6ff438bb5d7

Pith citing papers

No inbound Pith citation observations are available.