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Paper Citation Record · LEDGER

Lagrangian split tori in $S^2 \times S^2$ and billiards

As of 12 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2502.03324.

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

pith.paper-citation-record.v1
2502.03324 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T05:14:35.219408Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:47:52.607500Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T21:47:54.675987Z

Reference resolution

36 of 36 outbound references displayed

  • verified exact0
  • verified fuzzy16
  • unresolved20
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 13e1a59c-99f5-4bee-8d8f-16a7fff1844f · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:36.219991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.046427Z digest=sha256:3f4c89812ad72111b3bdb0cedde8e8cf95baba2e6e3eb4e8b1592d3b1c33dbff

Observation 69b1d694-5164-4a5d-94f1-151f01982904 · outbound

This paper cites Abreu, M.

Lagrangian split tori in $S^2 \times S^2$ and billiards Abreu, M

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.206340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.052011Z digest=sha256:daa4a9a19778e3141562e26eef2c7a6bbd19fd7e10f4bc0102e428c935834ed7

Observation 5519b492-8bfa-4fcf-899a-f1680430fe17 · outbound

This paper cites Augustynowicz, J.

Lagrangian split tori in $S^2 \times S^2$ and billiards Augustynowicz, J

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.192413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.057669Z digest=sha256:2e8b9101c0078045e8a29a8f20cd9b81a8f7690c1d0b2d3027ca7aba6fc4eeb6

Observation 0c69d276-524c-450c-9498-a45461d74837 · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:36.176213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.063098Z digest=sha256:a402104c7b5cd85bdf75ade1e0e8871b378de27088c9a47004494efebf2206b6

Observation a6fb3724-ab88-4aa0-aa9b-6f4674e7201b · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:36.160240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.068243Z digest=sha256:f2f731ae2eab279bcbe3197555642a48aaa65c6b952d11b00c3487bbb379745c

Observation e5b6a507-6b1b-428e-836f-9dc02fbd459d · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:36.145018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.073354Z digest=sha256:82b8b591185ba580f0c8608cecbb71a217b7c315d071ced003381ed7b3d91144

Observation 92009717-99f3-43c6-b254-686e27425287 · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:36.129420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.078940Z digest=sha256:fb8df1f926aebcedf7cbc16b6036fcf530f9599ce409fdba8858c87101fc1c9a

Observation 1b0e4e20-e9c8-40e7-b1a5-a1fc5f90fe2a · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:36.114305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.083642Z digest=sha256:46f5f3c5e94e48b78309d82fbe348fe918552d577ba196b0fbc0b08364147be0

Observation 6817324a-03f6-45f9-a62c-762e9214d14a · outbound

This paper cites Brendel, J.

Lagrangian split tori in $S^2 \times S^2$ and billiards Brendel, J

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.099507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.088510Z digest=sha256:afd3b7e75aeaa216a9e3ff85c5798633f3cf156e544a785f3357ddbf7fbac03c

Observation 6c3f9ab1-1ffe-48f1-96d4-e1ecb24defdf · outbound

This paper cites A counterexample to Lagrangian Poincar\'e recurrence.

Lagrangian split tori in $S^2 \times S^2$ and billiards A counterexample to Lagrangian Poincar\'e recurrence

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-09T05:14:35.094013Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T05:14:35.094013Z digest=sha256:b84000f0befa8b6bc5ec9c214700125479e886871930af8783061239a6515cc0

Observation f00425c8-da3a-46d2-b0cb-704ae1cb3653 · outbound

This paper cites Chass´ e and R.

Lagrangian split tori in $S^2 \times S^2$ and billiards Chass´ e and R

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-09T05:14:35.099430Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T05:14:35.099430Z digest=sha256:0c3a45638d90dc2598d0750bb565ef7980a1a9e829ed6f15bffa0b5821249d51

Observation 163a70b9-544e-4635-bec8-704f55d6ffb2 · outbound

This paper cites Chekanov.

Lagrangian split tori in $S^2 \times S^2$ and billiards Chekanov

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.084509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.103853Z digest=sha256:8f3d95d61f06257ab5ddae988ebeef1439b5a268a6ed9b28907a2420993310e2

Observation 70d1cf02-efed-480d-af0d-4b5b89b00a31 · outbound

This paper cites Chekanov and F.

Lagrangian split tori in $S^2 \times S^2$ and billiards Chekanov and F

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.068205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.108127Z digest=sha256:fa6538d642d8139e6d3b38f60d217af8ad03cf074a60716c6f5b12938a796da4

Observation c826b0a4-7683-4f4d-923e-80b81968a12a · outbound

This paper cites Chekanov and F.

Lagrangian split tori in $S^2 \times S^2$ and billiards Chekanov and F

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.053307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.112107Z digest=sha256:0e95b70a7e9dd343115f83cf525ca8e09f2560346ce99d752f575ffcadefb443

Observation d65e17b8-2f0e-48a3-a443-d2d6a17e6139 · outbound

This paper cites Dimitroglou Rizell, E.

Lagrangian split tori in $S^2 \times S^2$ and billiards Dimitroglou Rizell, E

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.037691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.116084Z digest=sha256:c99f5ba44eafcb9dae7f42483b2f66d5fbbf27445955c37d60077d25b5334d7f

Observation dc9a7aba-5593-4dd2-9a8a-98771a16a9cf · outbound

This paper cites Eliashberg and L.

Lagrangian split tori in $S^2 \times S^2$ and billiards Eliashberg and L

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.023371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.120234Z digest=sha256:a3c0be50368b5e12ef1398de40d177e8e5eee0524d4b44eaf0b3b7bfafb7f459

Observation 78912251-a01e-4194-a746-031a9343f67f · outbound

This paper cites Entov and L.

Lagrangian split tori in $S^2 \times S^2$ and billiards Entov and L

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:36.009357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.124473Z digest=sha256:75b4ed3cee32181789c1436b0c363601edb3da4cbc5c087cfd460d20864ee2cb

Observation dcc51b3b-39b0-4c9c-abfb-08130272ac1a · outbound

This paper cites Fukaya, Y.-G.

Lagrangian split tori in $S^2 \times S^2$ and billiards Fukaya, Y.-G

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:35.994042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.128633Z digest=sha256:591d11af143b53b133e22cd0508d87618eea470f80f7632aec222bb34d63c20d

Observation 655d797b-074b-4c13-a57b-e08c36dc1ec9 · outbound

This paper cites Fukaya, Y.-G.

Lagrangian split tori in $S^2 \times S^2$ and billiards Fukaya, Y.-G

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:35.977902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.133014Z digest=sha256:3f7f02f7b35f25d541c6ec8dd682f3e12caa9a9720bdddb2024ce64b009e55e5

Observation fe74d63d-6cb0-47fd-94e3-e3aac4688adb · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.962231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.137935Z digest=sha256:eaf4fbaa728e6fdb096719768eb6ef614b604c481bd720a38c004656bbe01cb2

Observation ae52364e-e54f-46ad-b3bf-99b657fd90ab · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.946336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.142919Z digest=sha256:1c16bc28213138be9bb81f042c9c0706cab7ee3441550ef18deeefb450b9af48

Observation c43bb03d-f190-4008-8740-ed8510181a67 · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.929849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.147963Z digest=sha256:41ebf06325d0ca75b7103aa4133a4a14d893b6604c19b43a9251ec734204dc87

Observation 17bb3f9b-65b0-4050-ad6d-1df6ac723c46 · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.913914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.152795Z digest=sha256:ffe8e5bb6d30218e8b739c8e5adeb57b82c2b329dafeb6bba2faf93a40b566f4

Observation fe6988e2-442e-412c-a404-c075bdcdc5b9 · outbound

This paper cites Lalonde and D.

Lagrangian split tori in $S^2 \times S^2$ and billiards Lalonde and D

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:35.898340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.157684Z digest=sha256:bcf528ce024968ec9c22857bef9aa4023234e4259fa7a19e2731ca2c58401d18

Observation 0ff86a26-8ef4-441c-9a5c-2a94a103a194 · outbound

This paper cites On Lagrangian Tori in $S^2\times S^2$.

Lagrangian split tori in $S^2 \times S^2$ and billiards On Lagrangian Tori in $S^2\times S^2$

Reference 25

Resolution
unresolved
no resolver link, observed 2026-08-09T05:14:35.162561Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T05:14:35.162561Z digest=sha256:662f9a71bb2f0a8e6dbbc5059b0e3ec614428fb66c953cb6626195a1827893c1

Observation d248b90f-5682-4b13-8ba3-cd5108d7385f · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.882894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.167485Z digest=sha256:c7a42e03a7b6c6eb38d4fa1832e72389f26a180f68265926f362c18fb4d9ebf4

Observation f7042fc3-00f0-48b7-9c14-97bf0c76acc2 · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.866684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.172080Z digest=sha256:c81f1f0d05d5a3064c955cfa6fa3f26fb72a38686caee7e538dde511338d6ff3

Observation 49f83ba0-a608-4930-990a-5e128e9cc924 · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.851988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.177921Z digest=sha256:56254fb00322c7f07579543e050ee0d5a60f6ee4cc021229593c505d1b3de24b

Observation eeaac91e-5cf7-4b29-993c-7da0db8c6a0c · outbound

This paper cites McDuff and D.

Lagrangian split tori in $S^2 \times S^2$ and billiards McDuff and D

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:35.836041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.182917Z digest=sha256:70d155cbcf8815e0324d7e7f230dc67b4bd77ff8a6bfcab4676027c8f33482f4

Observation 3b156dad-daf7-4a0e-9668-7bfdd81fcebb · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.820811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.187620Z digest=sha256:c35bb7e6cfd1867957c76dbf099c7658abd52fc13a8ed6582f9a4e41599d576e

Observation dd5f7863-6d05-4056-9ff5-33f05259cae6 · outbound

This paper cites Polterovich and E.

Lagrangian split tori in $S^2 \times S^2$ and billiards Polterovich and E

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:35.804002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.192271Z digest=sha256:f55076c65f9b9fbbb27bb7bc9908ace90ae9cabe1245f1b39478e814cfb19b18

Observation b5231b3c-b7f6-445d-a3c7-1ca538c2850f · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 32

Resolution
unresolved
no resolver link, observed 2026-08-09T05:14:35.197157Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T05:14:35.197157Z digest=sha256:f85467e0d55a8d243e40f997edaa8955984f938d96fd0eae96d79b3d1c8a199a

Observation 8cb6778d-a0d1-4469-823e-71aab256de42 · outbound

This paper cites Symington.

Lagrangian split tori in $S^2 \times S^2$ and billiards Symington

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:35.787652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.202124Z digest=sha256:62e1d4f62526407f8cac157f6a50e5166555cd3066faa6d4dc9c6afef82af410

Observation 87478861-c449-4458-816a-e732f285457e · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.770706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.206804Z digest=sha256:e36e9617743467627a14559737739827b679b6b89ef05bbc7182170fd65f428a

Observation 35d42008-5354-4487-94e4-2dadb354a5e7 · outbound

This paper cites Welschinger.

Lagrangian split tori in $S^2 \times S^2$ and billiards Welschinger

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T05:14:35.754136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.213141Z digest=sha256:aaa4d5ed8cbc7957ca64eb5b56a7b229e730bd6429c2152f5946201e253c186b

Observation d2dbd388-0806-4e84-81ce-d1d441e6da2d · outbound

This paper cites an unresolved cited work.

Lagrangian split tori in $S^2 \times S^2$ and billiards Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-09T05:14:35.736146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T05:14:35.219408Z digest=sha256:cef7567aaabb220d6d1f34dad9ec112bf184fd78e3dcc59033983ed38582faa8

Pith citing papers

Observation f68d64c4-2c09-43f8-ae0f-4c78124df132 · inbound

Nodal Tangles cites this paper.

Nodal Tangles Lagrangian split tori in $S^2 \times S^2$ and billiards

Reference 2024

Resolution
metadata mismatch
local_arxiv, observed 2026-08-06T21:47:54.808661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-06T21:47:52.607500Z digest=sha256:b922b9563fb29bfcba7ed3881a843518115e87e0db970585e5a7d5edd6c83484