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Paper Citation Record · LEDGER

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

As of 13 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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.046427Z digest=sha256:933b4d49c8fb7a5b7ecc5721c2786d126e128555230744959dd561f9bb12b11d

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.052011Z digest=sha256:3e198f55ef8475f56c4e11909de23aa9737a761c572245f76772ffb5f761d696

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.057669Z digest=sha256:5148be6d3c343bd0f6348711f696d459cda6ecca0fb9465a2420fb8eb12ff95c

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.063098Z digest=sha256:950320b794902452d78dabf0c4d74d71b34d84098e989bc7aab1bda73a14f5a2

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.068243Z digest=sha256:b3843ef23fa9bb3a8e246ba00202ed5704fbdf48ac4a4d18dba015c240225de4

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.073354Z digest=sha256:22f7498e864a3dd53da3439f2ae23776ee33c4555f2217629996bcfb240a5dc3

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.078940Z digest=sha256:2bc48f427da357d291ef7a4dcbcb53740c6e5cd91019a8b4ad7057619f89bed5

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.083642Z digest=sha256:84e49b8b8606f1fbdd0bb7f9f2b7e3b9782bd221991bacc771636f34a6ca7de9

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.088510Z digest=sha256:7dc871d7403d1f4ad6373eb51d3031c3e80df933f17b02ef965f2e4bd61fefb8

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=sha256:6e684dce7260f5f10d5fa6e7b2fd6bff28e658b5fd249b9aa0208d24eea6ceff

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.103853Z digest=sha256:a8ec030be523982e3b8bc965fa5ac56ed455f7b57f480c7a3ba8fdce59005c54

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.108127Z digest=sha256:7d880164ea24978be7f771c2deb3761bdd3653b42300f78231d88a94dd5c87f2

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.112107Z digest=sha256:7994a0c50760d54ab094b46472da38fb7c3436005fde7b5649202791ff2784d0

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.116084Z digest=sha256:3010e5162a1abd94e3e51f495adaf2876cdd6c5f3bf4e8b49685ccd555b2f819

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.120234Z digest=sha256:dc4a3c4561b3352b52f4f88f12bddb9409b244ac49eb330b3c03fa48a0652883

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.124473Z digest=sha256:ab74a804c92d4e6af7e85576bec6eb58efc84491a089de6c947e31561b642484

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.128633Z digest=sha256:feac185ef7ed87710dacff33a90f7471005205a3136aeb00f4aac66a7a2ab46c

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.133014Z digest=sha256:91f3f37bdeab6d16b0c08f36257a34a2c76f5534260f5c4c41be293ee4440f65

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.137935Z digest=sha256:958b69267baf4dfba2d6b3d3d32705b2c558972ffd1919687ffa7c78e21f5bb1

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.142919Z digest=sha256:c97c1aff9386e5268de2b1847d1a006e6130b105b80b5855f0bff8a446d82e64

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.147963Z digest=sha256:1ce0b913eab797f48f4b35b9186ee0777c8c2636bbf05c3dc06cf0d683abad2d

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.152795Z digest=sha256:14dbe56e1738b97d03eebc5a3f156737803df1af38663dc9d91d025c739d0e64

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.157684Z digest=sha256:0dc2c79000da387403609b1176f75b4816a37027de2c3d68b3145433ee085e2b

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.167485Z digest=sha256:6e24fbbd464160a13ef0c4ecfb48d0ee695486b273aaa4ec3941a9b2c805344e

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.172080Z digest=sha256:33f2fc6c09411fa0dd8ea83c83eca23f1f755f6ba81cc02d339626eee3c6e150

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.177921Z digest=sha256:298caa22b6d10ef517e5898367bfeb7a69ab9a43fa62f6f940228642a6cd9d65

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.182917Z digest=sha256:daf5c3ac78065581d62180825c755be55d3e5b68d87745b258670234c7d730ab

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.187620Z digest=sha256:cbd95064c0e2980c50d689fbe2bc8497ed32342485c1d000da4a1873b296d01b

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.192271Z digest=sha256:d2e1091da2fc6b82dfaafb0ae6b9d2310af71e3f475bff8d6865039c6c3677fc

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.202124Z digest=sha256:e59bd621af35dd871e9cbff5740b5405933f0dba9c878d1b7ed5734fc20ac188

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.206804Z digest=sha256:bc23bc49f8b3877c87d5244a9b095a12269f3cbaba6c7a11e0cd53dbdf908136

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.213141Z digest=sha256:c243b5baba9580b54c30391890e5d34c1463c69c2c791b9c556567a241bd2507

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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-09T05:14:35.219408Z digest=sha256:116a8551143c713512d5615a42adf95a3de7fd43d7e19a2d960259bbb6345d91

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
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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 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:47:52.607500Z digest=sha256:38bcca0a0c214ba98b6fd25cb280fbf5889249f3ba9e0ea677c7d321d34e95d3