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Paper Citation Record · LEDGER

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$

As of 14 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 0 inbound Pith citation observations for arXiv:2506.23119.

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

pith.paper-citation-record.v1
2506.23119 v1

Coverage vector

measured 56 of 56 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:58:55.497887Z

measured 56 of 56 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 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

56 of 56 outbound references displayed

  • verified exact2
  • verified fuzzy43
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 65879c64-0b31-4a3a-8442-fab70bb2cb49 · outbound

This paper cites Aizenman and S.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Aizenman and S

Reference 1

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raw_fallback, observed 2026-08-06T21:59:06.517103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 19e663f9-dc5b-4d21-ba2b-266f7de5958a · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 2

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raw_fallback, observed 2026-08-06T21:59:06.325740Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:49.674484Z digest=sha256:e9e3e9c2478e27b6fd8b22fe6b242c1ed21c6c646b57bcda18945a63ed715525

Observation 38620757-1af3-485c-9fcf-1a2b65e8501d · outbound

This paper cites Agmon, Spectral properties of Schr¨ odinger operators and scattering theory, Ann.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Agmon, Spectral properties of Schr¨ odinger operators and scattering theory, Ann

Reference 3

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raw_fallback, observed 2026-08-06T21:59:06.137110Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 057f51a6-0a24-4d42-84bf-d5a2df603a49 · outbound

This paper cites Boutet de Monvel and J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Boutet de Monvel and J

Reference 4

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:49.915948Z digest=sha256:5ad6da34e6fa8c64a6438d8cb6da171c1f350e3917dca1f871bf596e929f9cd3

Observation d7c88224-417c-4a1e-88dc-7cfc1a5f0566 · outbound

This paper cites Boutet de Monvel and J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Boutet de Monvel and J

Reference 5

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:50.009327Z digest=sha256:c5b4a1ccac3551ed5eaccdecc2c3419a97a80a9e62dab447f4e6d9232c99bebb

Observation a6c46c19-f281-4876-a189-c3d0f6726675 · outbound

This paper cites Bellissard and H.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Bellissard and H

Reference 6

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raw_fallback, observed 2026-08-06T21:59:05.543997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:50.108419Z digest=sha256:971d43603a5a6faed0748b622317dda32f73b128a97b9fda365529107d37c9e1

Observation eb6daf0b-abf1-4edf-8751-1a523039ed24 · outbound

This paper cites Pointwise estimates for the fundamental solutions of higher order Schr\"{o}dinger equations in low odd dimensions.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Pointwise estimates for the fundamental solutions of higher order Schr\"{o}dinger equations in low odd dimensions

Reference 7

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local_arxiv, observed 2026-08-06T21:58:55.901052Z

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source=pdf_text observed=2026-08-06T21:58:50.206973Z digest=sha256:f333fb5026eaa2bd1fa0bec789a6a53a1eb8208c9b540ded12cbdf4bb232562d

Observation c9290c19-d0b0-40b7-9b2a-3a79031edb90 · outbound

This paper cites Pointwise estimates for the fundamental solutions of higher order Schr\"{o}dinger equations in odd dimensions II: high dimensional case.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Pointwise estimates for the fundamental solutions of higher order Schr\"{o}dinger equations in odd dimensions II: high dimensional case

Reference 8

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local_arxiv, observed 2026-08-06T21:58:55.737029Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:50.313222Z digest=sha256:5b185b4f9242a4bfcdc031bfd54d0d89628dade91da6aca6f20887797cc9ddda

Observation 8425cb18-0ed2-4e7a-bf5a-ab7c77ab6cb1 · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 9

Resolution
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raw_fallback, observed 2026-08-06T21:59:05.379556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:50.414595Z digest=sha256:6b607a5cc0a6a5fd6b59d00db6d1163075400cf738c4f49b68f47700474fff4e

Observation 22a2fa5b-e2ef-488c-bf02-5521c6355d7a · outbound

This paper cites Cuccagna and M.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Cuccagna and M

Reference 10

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raw_fallback, observed 2026-08-06T21:59:05.191735Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:50.516395Z digest=sha256:8ebeb19de4cbeb45f9d6ed3dfae10d1229f2ce92687570646674fd22ae9011b3

Observation 5a51ee79-31c9-4c03-b56c-a41aad356bb7 · outbound

This paper cites Cuccagna, Lp continuity of wave operators in Z, J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Cuccagna, Lp continuity of wave operators in Z, J

Reference 11

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source=pdf_text observed=2026-08-06T21:58:50.637015Z digest=sha256:156a8aab28d145d7f3a008d04d3cceb0b0af4d33b4e8d48d780b6f7d7443ffd5

Observation bb024396-ae50-410a-9deb-d8e54e04d9ce · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 12

Resolution
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:50.753024Z digest=sha256:2794ac7fd3bc858f9b1df12d9bb6ffe6739cc8467ad2f9c98b89f4b857f020e0

Observation 2c991640-19f3-427a-8eb2-49bc3d633a34 · outbound

This paper cites Egorova, E.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Egorova, E

Reference 13

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source=pdf_text observed=2026-08-06T21:58:50.875282Z digest=sha256:f9fc2225c98885e97268b9b612e65a73818dd0aec681e0c400312ee31fbcc5a2

Observation 32a6bd49-5d83-4c9d-97c4-2733caa389f3 · outbound

This paper cites Erdo˘ gan, W.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Erdo˘ gan, W

Reference 14

Resolution
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raw_fallback, observed 2026-08-06T21:59:04.473875Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.015543Z digest=sha256:6b53cfaedf9dacd0cd61cdc2a2e5ee47196a9e9a588484a36f945a7de6a8d1c4

Observation 1ae17df3-961f-469e-9271-df6be6bc3fde · outbound

This paper cites Erdo˘ gan and W.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Erdo˘ gan and W

Reference 15

Resolution
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raw_fallback, observed 2026-08-06T21:59:04.258176Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.127940Z digest=sha256:29064ca4727aa5bd4360ccaa86e6ff5307b26ba18e33cd6be82b4f020bc4f1af

Observation 28384b72-3ba3-4ac9-85b9-a6c36dfec08e · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 16

Resolution
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.216012Z digest=sha256:cf66160f69bd163334b2b26bd0b78a32ad25498ae8bed6e49b780bad42cb770b

Observation 113d1996-bb27-4610-9a2e-73bb7e14aa25 · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 17

Resolution
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raw_fallback, observed 2026-08-06T21:59:03.792420Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.342062Z digest=sha256:f64be0ce26e392fe96bf604f7f2b447763ddbdf551089c425975e99362d32b0b

Observation a6f17260-b1bd-4385-967f-bcaa5129d30e · outbound

This paper cites Georgescu, C.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Georgescu, C

Reference 18

Resolution
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raw_fallback, observed 2026-08-06T21:59:03.633496Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.458693Z digest=sha256:d3e4b84b75cc488d7692054e135932491b7a3990fa8b9930db22ca24e879824f

Observation 6fe3d5ec-dc70-4976-9410-6bdd322b8bdc · outbound

This paper cites Goldberg and W.R.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Goldberg and W.R

Reference 19

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raw_fallback, observed 2026-08-06T21:59:03.433100Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.563989Z digest=sha256:344d0662e8f2a7710deb1785c35ffcb1628105cf307d241d00e3ea75ade7a2b3

Observation 6f5b1b87-898b-4cc7-879e-4a7b66da7ac2 · outbound

This paper cites Goldberg and W.R.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Goldberg and W.R

Reference 20

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raw_fallback, observed 2026-08-06T21:59:03.211111Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.664556Z digest=sha256:dccdf4ed3cf2df13b319fbdd36290cbfdc5f29f7b92c34f612a0102c00d0877e

Observation 07f0f214-0098-452a-bdb6-e7eb75840653 · outbound

This paper cites Hayashi, Y.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Hayashi, Y

Reference 21

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raw_fallback, observed 2026-08-06T21:59:03.008979Z

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source=pdf_text observed=2026-08-06T21:58:51.788745Z digest=sha256:c08ce6c7961a33cc158154fc53bafa229a2141f7548be8492011fa706cae9e85

Observation 074bbdf2-553d-4230-98ea-b3d26df22c4c · outbound

This paper cites Hiroshima and J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Hiroshima and J

Reference 22

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:51.903547Z digest=sha256:734f3c2080818a6cf845faaca539ab89874fc3d8b74838fbeac1fd53d9d4bb39

Observation 4df98b5f-f8ca-480a-85fa-753849570f02 · outbound

This paper cites Higuchi, T.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Higuchi, T

Reference 23

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raw_fallback, observed 2026-08-06T21:59:02.613169Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:52.042717Z digest=sha256:e545aba31ba48b4b3c99a3928d019703fd2e02bc770fd201a8458080927c4112

Observation 45e5892f-3ea0-4e7b-ab8a-00ea13f860fd · outbound

This paper cites Hiroshima, Z.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Hiroshima, Z

Reference 24

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raw_fallback, observed 2026-08-06T21:59:02.423155Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:52.154374Z digest=sha256:ff63921803f718f63baa595039dcc4825ed78501507d1ec34973c07501dec7e1

Observation e172dc45-19a4-498c-a854-d1778f6df6a0 · outbound

This paper cites Hiroshima, I.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Hiroshima, I

Reference 25

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raw_fallback, observed 2026-08-06T21:59:02.183796Z

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source=pdf_text observed=2026-08-06T21:58:52.281526Z digest=sha256:45be522717fffd0f170c9918c0e23e603e110f163e188dd8b6205e103d92d480

Observation e4968e4a-5892-4ef2-9fae-12578e6a22df · outbound

This paper cites Ito and A.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Ito and A

Reference 26

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raw_fallback, observed 2026-08-06T21:59:01.976235Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:52.422683Z digest=sha256:59471ddd9ef666ec4270951b9e2c4b8bf5d5d6511ef1d3ffb91e0d94dc2236c3

Observation d818a1f5-ceed-4bfb-a7be-d2fd0a4f5261 · outbound

This paper cites Isozaki and E.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Isozaki and E

Reference 27

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raw_fallback, observed 2026-08-06T21:59:01.786469Z

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source=pdf_text observed=2026-08-06T21:58:52.529249Z digest=sha256:9aac64b52d32edb908a71ebaaedd98e89c3b7a09a376dfa2b1eafed97fedcefd

Observation 896c3a55-55f6-46fd-b60d-4392cf99f41b · outbound

This paper cites Isozaki and H.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Isozaki and H

Reference 28

Resolution
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raw_fallback, observed 2026-08-06T21:59:01.587455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:52.630053Z digest=sha256:5caa8ef4706116afef02a0e723f45fefb1355634b3f469d4daab62863e104ec9

Observation 9ad60512-781c-4553-8688-8f4fd3a207f3 · outbound

This paper cites Jensen and T.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Jensen and T

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:59:01.424853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:52.728662Z digest=sha256:5cbed558bbe000783519415fd0299bdfe49ed575a5f8b2d1847cf37c52a1c78a

Observation a1c7cbb5-79c1-4b19-9c68-ccc905a92415 · outbound

This paper cites Jensen, E.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Jensen, E

Reference 30

Resolution
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raw_fallback, observed 2026-08-06T21:59:01.229234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:52.825726Z digest=sha256:a988933f663f66269cfb023a9e853279257d9193ac4360c924222f67a8b4e4c2

Observation dadd3614-4e01-4840-a3f4-1db63a1b4fcd · outbound

This paper cites Jensen and G.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Jensen and G

Reference 31

Resolution
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raw_fallback, observed 2026-08-06T21:59:01.008185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:52.935965Z digest=sha256:b2aa023c145edf42afe441532f3fc02173c7951bc6c8e08dccf6928a3fb80081

Observation f6ad3c53-a872-4adc-b36e-d30c63b5fef2 · outbound

This paper cites Journ´ e, A.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Journ´ e, A

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:59:00.800636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.034374Z digest=sha256:8844ad6a843359b992ddf83327ee66b53d59181308047d2691805608e3b6eb11

Observation 8b8ba707-eae1-42ad-a593-0fc3e6e6bd75 · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:59:00.577454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.146277Z digest=sha256:8dd5bc0454de3d5f3c63af30e15e00302ca885250cd6b8b5c66dac87f1e96732

Observation b61b36fb-34b3-44ed-afe7-52899d1d40f7 · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:59:00.281068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.301818Z digest=sha256:9c95cec8f7f794964364576bb357d864fce2bdc6b9597fdb23697cb66b9a7240

Observation 554d1aed-3417-4b3b-98ac-a5b8cbbcafa4 · outbound

This paper cites Korotyaev and J.S.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Korotyaev and J.S

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:59:00.061864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.421589Z digest=sha256:c60aa14b26e505a8a9a406780060f8956c2c401f5accf75c7a3ae2c5d04c569b

Observation 8ef5693d-2a8e-4d69-a7c1-1bb55e917723 · outbound

This paper cites Kr¨ uger, On the existence of embedded eigenvalues,J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Kr¨ uger, On the existence of embedded eigenvalues,J

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:59.852478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.527916Z digest=sha256:0f0cc94e1edd74031f82ac91ec7681d7b27a8702992a77bec4b061a2a6bb3bbf

Observation 4ce32345-dd75-449b-adb4-aaedd7aa0799 · outbound

This paper cites Keel and T.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Keel and T

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-06T21:58:53.621080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T21:58:53.621080Z digest=sha256:e6efda0df31a181e4c8acfc7871d79f94b310e4026a9e45c5fd9621ceb30a272

Observation 3f8c5394-cef1-4ec9-93eb-617587baaa6c · outbound

This paper cites Liu, Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators, J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Liu, Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators, J

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:59.621130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.709443Z digest=sha256:cf53cc783b56e77f9a692ffb9d86f2ff48acbe452a1abec7680f68937c781475

Observation b883c5a4-fd01-4384-8bbb-fd56299d4f50 · outbound

This paper cites Liu, Irreducibility of the Fermi variety for discrete periodic Schr¨ odinger operators and embedded eigenvalues, Geom.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Liu, Irreducibility of the Fermi variety for discrete periodic Schr¨ odinger operators and embedded eigenvalues, Geom

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:59.381911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.821907Z digest=sha256:ddcee72f2411560379141ff5d9431b4959e6460abad3d506c9f49005c62cd39e

Observation 12284203-f40e-4e84-9e26-b72e226ef756 · outbound

This paper cites Sharp decay rate for eigenfunctions of perturbed periodic Schr\"odinger operators.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Sharp decay rate for eigenfunctions of perturbed periodic Schr\"odinger operators

Reference 40

Resolution
unresolved
no resolver link, observed 2026-08-06T21:58:53.903675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T21:58:53.903675Z digest=sha256:4cd64f9aaa82a830d2b2ccea1283646ddc21fe310ae59716af893053bd0030fa

Observation 89919249-7a3c-4ad0-a45b-c86f3fbc32c9 · outbound

This paper cites Marklof, Arithmetic Quantum Chaos, Academic Press, Oxford, (2006), 212-221.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Marklof, Arithmetic Quantum Chaos, Academic Press, Oxford, (2006), 212-221

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:59.214155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:53.979209Z digest=sha256:63ee9e9af92628c61f984bfa8202e9d6c3814bb9a1a8a411fd1d29c592da91d1

Observation f0c956d0-ec37-4202-9ef1-ef54b1d9916d · outbound

This paper cites Mandich, The limiting absorption principle for the discrete Wigner–von Neumann operator, J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Mandich, The limiting absorption principle for the discrete Wigner–von Neumann operator, J

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:58.994242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.076684Z digest=sha256:2d6b62d8bcb65ab14cc01083acdffd87c1baa4e23886269406d7ca7908c40bda

Observation 8c3a8073-8023-403d-9a88-cd845e39936f · outbound

This paper cites Mandich, Sub-exponential decay of eigenfunctions for some discrete Schr¨ odinger operators, J.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Mandich, Sub-exponential decay of eigenfunctions for some discrete Schr¨ odinger operators, J

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:58.818159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.176087Z digest=sha256:5c6e10a4c79d6f989f2c324a5782494688d6c77654637492e90d1ce1f3435016

Observation a80a1f4f-0268-4ce5-84d0-1b27709abec6 · outbound

This paper cites Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:58.656049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.294140Z digest=sha256:4b3bbb84d1703e02a5e905ccfb5671a4e611835b36f5dc866b50894866abf717

Observation 5e377180-4741-4bd6-91e0-4dcba0361af5 · outbound

This paper cites Mourre, Operateurs conjugu´ es et propri´ et´ es de propagation,Comm.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Mourre, Operateurs conjugu´ es et propri´ et´ es de propagation,Comm

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:58.434144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.403401Z digest=sha256:00cac3594a97ce23b23f6a776429f0934c4438e82af0db3454f7500e310d42fa

Observation a14b2eed-e723-4f4b-9796-db0852e5ab81 · outbound

This paper cites Mi and Y.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Mi and Y

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:58.241999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.521135Z digest=sha256:49f3736108b271031a72b5276e0c979573ec7f98bf5f2985c456f9018bb63b6b

Observation fd2899ef-27f0-436d-a7e7-a5a389490529 · outbound

This paper cites ¨Ochsner, Classical Beam Theories of Structural Mechanics, Springer International Publishing, (2021), 7-66.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ ¨Ochsner, Classical Beam Theories of Structural Mechanics, Springer International Publishing, (2021), 7-66

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:58.030099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.629070Z digest=sha256:8ea9a4700befa79a90449ccc7fcfca59494d17be45838ba1d2cc5f4832bbfd48

Observation 96576110-9bfa-4cf3-a914-79382b1c8753 · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:58:57.808396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.721341Z digest=sha256:080fb4c2c43798d6f93268a5f70d257c7baf7aa7484d7c219b2d277d2b144f97

Observation 9949b29e-f87d-4ebd-8fed-22c05d545ec0 · outbound

This paper cites Reed and B.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Reed and B

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:57.574763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.800304Z digest=sha256:b7730ca0064ed9650d9edcc35f787f0dd9a14692b49c67c45608d886ff2690dc

Observation 9f3cd731-afd2-4a32-82dc-942b8e8e1b65 · outbound

This paper cites Rodnianski and W.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Rodnianski and W

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:57.368984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:54.925186Z digest=sha256:f98c9958505b2e760c2077c49ded1937fcd99b75d9b068a82f8fbcc5c5c02013

Observation 59b324b8-3576-4a68-8ad2-8efe785712a0 · outbound

This paper cites Stefanov and P.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Stefanov and P

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:57.186557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:55.051571Z digest=sha256:1c885de8afd86207394697105cce78788682da90c674867397d101efef297631

Observation 414fbfbd-2ad2-4fb6-a2d4-ff4f3c37d47a · outbound

This paper cites Soffer, Z.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Soffer, Z

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:57.016313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:55.151910Z digest=sha256:a78ddac1d4ae00e2ad0f3ca2f05d7fdaf5cee84025d302a3385f6be720d80029

Observation de83d00f-92b1-4e8b-9c3b-b9e3fef5134e · outbound

This paper cites Tao, Nonlinear dispersive equations.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Tao, Nonlinear dispersive equations

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:56.821854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:55.217935Z digest=sha256:dc72271449027f952a496c6764f611b8d30f097c25144f46dfe6f11eaadfb525

Observation 24fe0a13-612f-46a3-8d87-4ccab1ecb34d · outbound

This paper cites Schlag, Dispersive estimates for Schr¨ odinger operators: a survey Mathematical aspects of nonlinear dispersive equations, Ann.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Schlag, Dispersive estimates for Schr¨ odinger operators: a survey Mathematical aspects of nonlinear dispersive equations, Ann

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:56.599467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:55.309660Z digest=sha256:c0bac9ef17bf6c42c8930f8f3849181a80aee0a4206a45890a13037074f6afe0

Observation 6654516c-feb3-42e5-b1fb-0b4c024186a7 · outbound

This paper cites an unresolved cited work.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:58:56.370165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:55.414101Z digest=sha256:e0bbe37597f4ced7a4bc8ab6ed66d55be200c4af264f421b8e6f475aa5bdec6c

Observation ae18b356-513f-49d8-98c4-2b4fe3e70526 · outbound

This paper cites Shaban and B.

Decay estimates for discrete bi-Laplace operators with potentials on the lattice $\mathbb{Z}$ Shaban and B

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:58:56.165389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-06T21:58:55.497887Z digest=sha256:75efc667913b3c323b0f105685bc6e6d0188dff3368e97af07b6f6812caeec40

Pith citing papers

No inbound Pith citation observations are available.