Pith. sign in

Paper Citation Record · LEDGER

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues

As of 20 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2506.16378.

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

pith.paper-citation-record.v1
2506.16378 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:37:31.531275Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T15:52:32.848879Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

31 of 31 outbound references displayed

  • verified exact1
  • verified fuzzy22
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c5df658b-f3f2-4070-83ce-9cf5b81a00a1 · outbound

This paper cites The Lp-boundedness of wave operators for 4th order Schr¨ odinger operators on R2, I, preprint 2025, arXiv:2504.11753.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues The Lp-boundedness of wave operators for 4th order Schr¨ odinger operators on R2, I, preprint 2025, arXiv:2504.11753

Reference 1

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raw_fallback, observed 2026-08-15T19:37:31.702549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.397433Z digest=sha256:cfabf5db13b0875d6e23d6af4f574d195424593b5bb3bad746cc9b69439e4aca

Observation 4f0f5806-9600-4dba-bce2-72bcc0d2f33c · outbound

This paper cites The Lp-boundedness of wave operators for fourth order Schr¨ odinger operators on R4.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues The Lp-boundedness of wave operators for fourth order Schr¨ odinger operators on R4

Reference 2

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raw_fallback, observed 2026-08-15T19:37:32.277979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.402951Z digest=sha256:a048b3d9d4eb1c73a3d0fc970e1b7d07272cbedfd753d303eaf8d85084eecb97

Observation 249099e8-16cc-4eba-8ad6-3c8bbd5c3669 · outbound

This paper cites The $L^p$-boundedness of wave operators for higher order Schr\"odinger operator with zero singularities in low odd dimensions.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues The $L^p$-boundedness of wave operators for higher order Schr\"odinger operator with zero singularities in low odd dimensions

Reference 3

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no resolver link, observed 2026-08-15T19:37:31.407954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:37:31.407954Z digest=sha256:d207fe21c849b8b3b59fdb7d97c0217bbe8d501850efbae4c04497b81ff9eb43

Observation dda1bb1e-975e-42a1-84ea-5332edb3fc4b · outbound

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

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Agmon, Spectral properties of Schr¨ odinger operators and scattering theory.Ann

Reference 4

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raw_fallback, observed 2026-08-15T19:37:32.250575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.412769Z digest=sha256:2295f48c173423a29fefe6e204cfc821f476a9ee5e0db9c7a76e4dd7cba7d5bc

Observation 1cd5bc3c-8e70-4bcd-a8f0-3f92e8f69417 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 5

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raw_fallback, observed 2026-08-15T19:37:32.230255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.417840Z digest=sha256:97db7b2709304721281db071196246d66b58066e83759e07422383b826aedae7

Observation d8dfb834-379b-4524-a850-a670652ff2d4 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 6

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raw_fallback, observed 2026-08-15T19:37:32.207716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.421954Z digest=sha256:503e5490f2c86bed193ef0a6055cdc4b6167d186a0b387c326ca490f613d39fa

Observation c0b18c1c-2168-4893-a572-c015b070807e · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.426621Z digest=sha256:83b498bc142e8c465586b0ea758874837b30bf549ca899f51f76a83729dfe9a0

Observation 3b6e5099-f86c-47ae-a053-b1fabff7fa13 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 8

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raw_fallback, observed 2026-08-15T19:37:32.137610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.430826Z digest=sha256:72199965502e09ef4059b4fb1a60ab1edf7250ef89c9c0d2e76fd1ed4eb14e79

Observation 3fa0af78-a2ca-4c0e-ae42-a8e813e62d63 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:37:32.118631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.434475Z digest=sha256:fa28c2a79452770c12dfe8e434055d7dc6eb57964c4cee4d83b31d577474fc09

Observation 3a5d2027-ee93-487e-a2b5-73ae255b2aa6 · outbound

This paper cites Finco, and K.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Finco, and K

Reference 10

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raw_fallback, observed 2026-08-15T19:37:32.094114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.438171Z digest=sha256:20aea6eafb7aee8a63f8c3bcbc171ed55fba186bec91172c8fccbe5ee8d1efcb

Observation 3e9eeec2-bd98-4641-a21d-88a11ef9a8eb · outbound

This paper cites Galtbayar, and K.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Galtbayar, and K

Reference 11

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raw_fallback, observed 2026-08-15T19:37:32.075335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.442116Z digest=sha256:625ba8d48a76ded550e02c66da7b9c29401351871f03bb1388f9cb0d9b1b7312

Observation be46135d-0cde-4293-a5f5-87b3dc7c5b7a · outbound

This paper cites Goldberg and W.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Goldberg and W

Reference 12

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raw_fallback, observed 2026-08-15T19:37:32.056185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.446864Z digest=sha256:e823a12abeefc7c1826c1399284e3821f2962ce052b9bbbcf841a458edc199fc

Observation 1c5bb21b-2f3f-43c5-bb22-3d420768d20e · outbound

This paper cites Goldberg and W.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Goldberg and W

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.036244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.451337Z digest=sha256:15140ced805fd0861b424dcd9471be6301f85b30292885fbd7aac7e9661a9521

Observation 4fd53239-3fdf-4473-85db-4b385118f4ab · outbound

This paper cites Goldberg, and W.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Goldberg, and W

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.014994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.456070Z digest=sha256:476a0cdf056b6f027434eccfc5c0ca01499568bf2c490af3d91464b4021d0b13

Observation 6ec90b21-001a-44a4-8dc2-293bfd384a8f · outbound

This paper cites H¨ ormander,The existence of wave operators in scattering theory.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues H¨ ormander,The existence of wave operators in scattering theory

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.997091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.460579Z digest=sha256:0bc2eeb5afedc0d97331f8ddbfba4b42e992d3c4ab6e80deb989de0afbbca899

Observation 5479812e-55c9-4702-aef4-33d49b78fe93 · outbound

This paper cites Jensen, and G.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Jensen, and G

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.976753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.464490Z digest=sha256:08952a2109383cc27b4b6dfe990b0ee513c2702f1b4d6b89be1501fd91c90ad9

Observation 1ef8725c-a614-4403-be6b-c09f79bc014a · outbound

This paper cites Jensen and K.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Jensen and K

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.961721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.467763Z digest=sha256:9942ba731da5825011d3cfba97988f9ddf8de7c03d86a44321c54d499bbf4ede

Observation b07d2536-22b6-4797-84e4-cb6d818deee3 · outbound

This paper cites Mizutani, Z.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Mizutani, Z

Reference 18

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verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.945006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.471615Z digest=sha256:6ef0ee04f9e31154e150722849b5aa9cbeea04e2c722aaa7b635f73f32b723cf

Observation 84e420c7-ce00-461a-abb6-82b6b6aa944d · outbound

This paper cites Mizutani, Z.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Mizutani, Z

Reference 19

Resolution
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raw_fallback, observed 2026-08-15T19:37:31.926022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.476529Z digest=sha256:9bb1077b11b32968f59552182e2d7ad4549346220a90a29cc099cda391aafd4c

Observation a59e7619-3682-41cc-a69f-298e185a422d · outbound

This paper cites Mizutani, Z.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Mizutani, Z

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.909914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.480704Z digest=sha256:cbd5adb0ba2b820e607f75698e5cf17d57fb0570e4740b4166a16ca2ef82fd9d

Observation b9aa20ec-1a84-43ed-a1f1-d15fe114a12f · outbound

This paper cites Reed and B.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Reed and B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.891199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.486159Z digest=sha256:47616b10ea861cbb5893ad42f881cfd3fbf760fe42922cedcd767dae6de9f4df

Observation 6deb1edf-cb79-400f-bd3e-a15ea0c631b4 · outbound

This paper cites Schechter, Scattering theory for pseudodifferential operators, Quart.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Schechter, Scattering theory for pseudodifferential operators, Quart

Reference 22

Resolution
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raw_fallback, observed 2026-08-15T19:37:31.875205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.490275Z digest=sha256:7938f0388140add8b12b060bc2f9d53db5ddcbff490a95e2d51b32f41e217ae8

Observation f63ec354-1057-47c3-93e1-d3cb9100f122 · outbound

This paper cites Schechter, Scattering theory for elliptic operators of arbitrary order.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Schechter, Scattering theory for elliptic operators of arbitrary order

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.856602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.495239Z digest=sha256:55acd0d195682b6c93db438dba78a12fd93225a061e4de6c11f5d95398836d5a

Observation 77b125e4-3521-4a94-b2ae-35db290b3e9b · outbound

This paper cites Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.J.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.J

Reference 24

Resolution
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raw_fallback, observed 2026-08-15T19:37:31.836730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.500166Z digest=sha256:ef1beb1791edf53d5682931581fc747aee10e0d2a5f1b0fa5d5853983de3e5db

Observation c0e1527d-456d-4119-98bb-dd4061a214b3 · outbound

This paper cites Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.818852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.504050Z digest=sha256:23e103d1b53e1dfb84b8321bba600826f3a0244923bcb0367841c36a98d0c8fb

Observation bec6a9d5-fb3b-4f65-888e-2fd9c83957d8 · outbound

This paper cites Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.798531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.508680Z digest=sha256:81f6e1b5fa2b8e4ffdac7faabf0e2dfa09d420953c51b8a6ef3d698d9d81d64f

Observation ade1c6ab-5f28-472d-b14d-620c6626ba93 · outbound

This paper cites Yajima, The Lp boundedness of wave operators for Schr¨ odinger operators with threshold singularities I.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Lp boundedness of wave operators for Schr¨ odinger operators with threshold singularities I

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.778789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.513090Z digest=sha256:9e44ee78e71562fec792cac95612942f61dca0f86873ebedbb608705860ee622

Observation a1013de0-53e5-4720-ac38-4823759cdb4a · outbound

This paper cites Wave Operators for Schr\"odinger Operators with Threshold Singuralities, Revisited.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Wave Operators for Schr\"odinger Operators with Threshold Singuralities, Revisited

Reference 28

Resolution
unresolved
no resolver link, observed 2026-08-15T19:37:31.516897Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:37:31.516897Z digest=sha256:3b7ee3bbaddc1aedda68f0d6a58fcb6b9be9748a7d467ef54030882785218cd8

Observation 0bf1ab00-837a-4dd6-9204-492f45a1f7e7 · outbound

This paper cites Yajima, Remark on theLp-boundedness of wave operators for Schr¨ odinger operators with threshold singularities, Documenta Mathematica 21 (2016), 391–443.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, Remark on theLp-boundedness of wave operators for Schr¨ odinger operators with threshold singularities, Documenta Mathematica 21 (2016), 391–443

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.762282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.522022Z digest=sha256:b2c16f0799216f94687f27134e3cbfe2de665fe2e5d550c60b827f76fc90fea7

Observation 12b62085-5411-4ab8-8098-bd800917fab6 · outbound

This paper cites L1 and L∞-boundedness of wave operators for three dimensional Schr¨ odinger operators with threshold singularities, Tokyo J.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues L1 and L∞-boundedness of wave operators for three dimensional Schr¨ odinger operators with threshold singularities, Tokyo J

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.743688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.526755Z digest=sha256:88151d9c435396d9f50333e104ef7a8525d0eb0a37439c48f5f32134d3dc50d0

Observation 234b5f08-f038-475c-ae9e-22832bb6843a · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:37:31.724638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-15T19:37:31.531275Z digest=sha256:7d34a72a79997751840142af2e5f50db730159304abc283e174a1e3a2b0f2c19

Pith citing papers

Observation 61ba3b79-c896-4dd1-a61f-413d5e5c0b9c · inbound

The $L^p$-continuity of wave operators for fractional order Schr\"odinger operators cites this paper.

The $L^p$-continuity of wave operators for fractional order Schr\"odinger operators $L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-04T15:52:32.848879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T15:52:32.848879Z digest=sha256:68070bbdc6000cd5cc636c41657b388f81e083033797baf7ab0530527c7dd3fd