Paper Citation Record · LEDGER

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$

As of 21 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2608.04357.

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

pith.paper-citation-record.v1
2608.04357 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T19:20:22.230304Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

46 of 46 outbound references displayed

verified exact3
verified fuzzy37
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8615252a-5603-44f8-a2b6-171d4b1b56fd · outbound

This paper cites Alphonse and N.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Alphonse and N

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.583625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 00faf21b-56de-4e94-bf96-8669304b1f3a · outbound

This paper cites Ammar-Khodja, A.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Ammar-Khodja, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.569821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9dc4dca1-f307-4dd3-aa89-6dd29167a762 · outbound

This paper cites Anantharaman and F.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Anantharaman and F

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.556251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 02e7204d-311f-4838-a9be-46603c1f4219 · outbound

This paper cites an unresolved cited work.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:20:23.542837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4fc8949f-6f51-4254-aede-596a148e5a5a · outbound

This paper cites Bardos, G.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Bardos, G

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.529373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b89cc6f1-6e6b-4c2c-b681-9527c78c3f16 · outbound

This paper cites Beauchard and C.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Beauchard and C

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.515459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3a34d83d-514c-4d8c-ad9f-dfb88aec3794 · outbound

This paper cites Benabdallah, P.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Benabdallah, P

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.502100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a842ae4a-df6d-4f53-8cbf-14f6ed873e8e · outbound

This paper cites Bonami and B.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Bonami and B

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.488287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f007db22-c7d6-4cd0-b4ae-3c39419aa711 · outbound

This paper cites Boscain, M.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Boscain, M

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.474506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 24c8e574-e354-4bfd-8f15-8bba5eb5503e · outbound

This paper cites Bourgain, On the control problem for Schr¨ odinger operators on tori, inGeometric aspects of functional analysis, Springer, Cham, 2014, 97–105.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Bourgain, On the control problem for Schr¨ odinger operators on tori, inGeometric aspects of functional analysis, Springer, Cham, 2014, 97–105

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.460708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 40c315b9-49e6-400d-8eb0-84036043de6a · outbound

This paper cites Bourgain, N.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Bourgain, N

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.446893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9ef0ce6c-c135-40de-ae2c-79c27b6355b2 · outbound

This paper cites Burq and M.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Burq and M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.432811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 31331976-6fc3-44c0-afbd-8a3c134eeb19 · outbound

This paper cites Burq and M.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Burq and M

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.419046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1514041e-2bce-4f93-8d57-b82184e29205 · outbound

This paper cites Burq and H.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Burq and H

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-08T19:20:22.087617Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9bec635b-6a0f-4caf-9b32-76f7878c095b · outbound

This paper cites Burq and H.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Burq and H

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-08-08T19:20:22.829690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d8257b58-2d95-40f2-bf46-3bd181194f7f · outbound

This paper cites Chambrion, P.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Chambrion, P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.404805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2e0009da-cf11-435f-9fd1-8aa576f04453 · outbound

This paper cites Coron,Control and nonlinearity, Mathematical Surveys and Monographs, vol.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Coron,Control and nonlinearity, Mathematical Surveys and Monographs, vol

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.390456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 35887b51-a201-48cd-96bb-744e98fe1f69 · outbound

This paper cites Dard´ e and S.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Dard´ e and S

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.376146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 664a02d4-755a-45e2-972b-af074dcae239 · outbound

This paper cites Fern´ andez-Cara, M.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Fern´ andez-Cara, M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.361838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4616202f-0bac-4529-afd8-b168b45809b9 · outbound

This paper cites Fontes-Merz, A multidimensional version of Tur´ an’s lemma,J.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Fontes-Merz, A multidimensional version of Tur´ an’s lemma,J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.347359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b616852f-3413-492a-9516-44b9687d293e · outbound

This paper cites Observability from measurable sets for strongly coupled parabolic systems via single-component observation.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Observability from measurable sets for strongly coupled parabolic systems via single-component observation

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-08T19:20:22.603725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 351a976a-9652-4b67-a86f-960cd0d91cac · outbound

This paper cites Guerrero, Null controllability of some systems of two parabolic equations with one control force,SIAM J.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Guerrero, Null controllability of some systems of two parabolic equations with one control force,SIAM J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.333261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9ec5f061-56ad-4876-98e2-ebda0bbf9c01 · outbound

This paper cites an unresolved cited work.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Unresolved cited work

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-08-08T19:20:22.582404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f92896c7-f9e1-4ec4-aa6c-13d6baeecb1e · outbound

This paper cites Haraux, S´ eries lacunaires et contrˆ ole semi-interne des vibrations d’une plaque rectangulaire,J.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Haraux, S´ eries lacunaires et contrˆ ole semi-interne des vibrations d’une plaque rectangulaire,J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.319298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e4b688f2-300b-4d85-9615-cbe61dc0bdae · outbound

This paper cites Hartmann, K.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Hartmann, K

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.305402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a97c18b2-7b3e-4ad2-97b9-5a7375da9982 · outbound

This paper cites Havin and B.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Havin and B

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.291272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 09d184b6-cbf7-4970-a4e2-53d2b098c870 · outbound

This paper cites Huang and C.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Huang and C

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.277663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ec68076a-8fab-45ad-9295-d9f12abb13d1 · outbound

This paper cites an unresolved cited work.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:20:23.263313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 15df72ba-e94d-4bc1-9d5f-13effebaac19 · outbound

This paper cites Jaffard, Contrˆ ole interne exact des vibrations d’une plaque rectangulaire,Port.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Jaffard, Contrˆ ole interne exact des vibrations d’une plaque rectangulaire,Port

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.249413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 383cdce3-7551-430a-8ceb-ee73428c1952 · outbound

This paper cites Kahane, Pseudo-p´ eriodicit´ e et s´ eries de Fourier lacunaires,Ann.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Kahane, Pseudo-p´ eriodicit´ e et s´ eries de Fourier lacunaires,Ann

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.235380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation aef54cc8-283b-41c5-9286-0b3c94dd3e19 · outbound

This paper cites Komornik, On the exact internal controllability of a Petrowsky system,J.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Komornik, On the exact internal controllability of a Petrowsky system,J

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.221302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 943fb9a8-e2f6-48c5-b370-61f07476a464 · outbound

This paper cites Laurent, Internal control of the Schr¨ odinger equation,Math.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Laurent, Internal control of the Schr¨ odinger equation,Math

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.207857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 84b3be4a-c854-47a8-98a7-8ef625ae018d · outbound

This paper cites Observability estimates for the Schr{\"o}dinger equation in the plane with periodic bounded potentials from measurable sets.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Observability estimates for the Schr{\"o}dinger equation in the plane with periodic bounded potentials from measurable sets

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-08T19:20:22.172050Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 126db110-5bc2-45df-bd42-646f228d8f3e · outbound

This paper cites Li and J.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Li and J

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.194536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 994467d8-b8ac-4446-bd4b-946007797bc4 · outbound

This paper cites Lions,Contrˆ olabilit´ e exacte, perturbations et stabilisation de syst` emes distribu´ es.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Lions,Contrˆ olabilit´ e exacte, perturbations et stabilisation de syst` emes distribu´ es

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.180735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 230ae6b9-ff49-403d-a275-4d0a138b999f · outbound

This paper cites Lissy and E.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Lissy and E

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.167003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 88d51a13-1822-4e58-9963-3d2c34ee010b · outbound

This paper cites an unresolved cited work.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:20:23.152918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0bd97fb7-c868-429a-b45f-70c6fff5c6d0 · outbound

This paper cites Maci` a, High-frequency propagation for the Schr¨ odinger equation on the torus,J.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Maci` a, High-frequency propagation for the Schr¨ odinger equation on the torus,J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.139214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 01694dc8-8ad8-4a91-8bcf-243c19d9eafb · outbound

This paper cites an unresolved cited work.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:20:23.125284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation de51b585-559f-431b-ab33-b164d7c5f5d8 · outbound

This paper cites Rauch and M.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Rauch and M

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.111750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 005d2d26-139a-41c7-9afc-b3ea35fb5b96 · outbound

This paper cites Schechter and B.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Schechter and B

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.097777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2dbd350e-3161-4d6c-bd15-013c6d2b589b · outbound

This paper cites Tao, Exact control for the Schr¨ odinger equation on the torus from small balls,Pure Appl.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Tao, Exact control for the Schr¨ odinger equation on the torus from small balls,Pure Appl

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.082440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9b96ca9b-6a9b-4298-9b09-47c3c76028fd · outbound

This paper cites T¨ aufer, Controllability of the Schr¨ odinger equation on unbounded domains without geometric control condition,ESAIM Control Optim.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ T¨ aufer, Controllability of the Schr¨ odinger equation on unbounded domains without geometric control condition,ESAIM Control Optim

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.068140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6a6775be-2f3a-4dc5-b381-88767af9148a · outbound

This paper cites Tucsnak, Reachable states for infinite-dimensional linear systems: old and new, inProceedings of the International Congress of Mathematicians 2022, Vol.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Tucsnak, Reachable states for infinite-dimensional linear systems: old and new, inProceedings of the International Congress of Mathematicians 2022, Vol

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.054083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c3fc8a9f-665b-4ea3-a98b-06a7e409a29d · outbound

This paper cites Wunsch, Periodic damping gives polynomial energy decay,Math.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Wunsch, Periodic damping gives polynomial energy decay,Math

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.039819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b4fbda65-0d3d-41ff-94f8-824f83a5a413 · outbound

This paper cites Zygmund, A Cantor–Lebesgue theorem for double trigonometric series,Studia Math.43 (1972), 173–178.

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$ Zygmund, A Cantor–Lebesgue theorem for double trigonometric series,Studia Math.43 (1972), 173–178

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:20:23.025285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.