Pith. sign in

Paper Citation Record · LEDGER

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

As of 20 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 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.046427Z digest=sha256:a3b3d7c8631e608e30a5886f80ce03e80a05817a3e157c1ea392e969dc0b6912

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.052011Z digest=sha256:174976fec38f523d5666f04f72c0c9b3043745e5151c3dcbc324276599aee482

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.057669Z digest=sha256:9500de4623d47850ed73df14d5a0d9f2f2c520149b17c3ed0a0c163a14c6ccd6

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.063098Z digest=sha256:b2f108da6fe7d6c6a7dc48c542a4b02a8bdf721fadc2016a70ef75271ce8e583

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.068243Z digest=sha256:659eb5e649cb73e28f9ca5ad5648636c515b2cd96fb4c430f99e4d7e9d7d19f6

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.073354Z digest=sha256:04b1a985dd2a617976fe22116b82e217652504d8c7ae05cd1a994e0ab98cf161

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.078940Z digest=sha256:918dc0246d9888eb57e6a8561cb0c0361da9bed24c2bf06507be3e2f066de31d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.083642Z digest=sha256:38b4bff55462647908c07fa4e237f16d3d7ff77ade68ede291f0944ab4607fe7

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.088510Z digest=sha256:eb5bdf3705bd1dcc4e86d81a2b223ab1738de3542eb6d48ab1d37b45ee815aa3

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:a9b2f290a1d5852bd35c0596d600e20b98258075102c2ad609430b9dce2986ce

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=sha256:16dd47209b3c33c24d0d7081a59fddd6d21c2c7a9c50ea720f0f86e8d23e1133

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.103853Z digest=sha256:77c4656843ab4b241d6b01a008fec35523761a50408308afc4ec0acfe2ade415

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.108127Z digest=sha256:36dcc4021b05deead32a921296e2e89b51a959ce3e55c35981d79b0a019bc421

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.112107Z digest=sha256:f3b4e3d896a13cb976b73dbeae8afd885a8471b8e18c3268baf380e9c8608be6

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.116084Z digest=sha256:1d9c9e58229174c936f346a5cde73970818c70905742c3fc85dac9b1b932d14c

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.120234Z digest=sha256:3cceb40136b2e76a17ff6229519a28df73d286f04fe37cdd33181ec9e4fe407f

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.124473Z digest=sha256:7f9c8fd270a365b2c1dc4c89e6f17306b1b291e11cdcb0f57ef5a86db3fa270e

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.128633Z digest=sha256:16c0e428402ca307fc29d96c26e536a62c931d3f43b26f78cbbff966070896f3

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.133014Z digest=sha256:48642bccf93934036a6f42cceefed0a3aaa49446be10b2a1a465c47ee95dafa4

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.137935Z digest=sha256:1fe3fc46bdd18fd65493942231ad9a011e67385cc1b79327dd919bd47b39a770

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.142919Z digest=sha256:2e9dfd4f66de2e33f297613b9bc06ea1494b22c9ebe1bbc3e5a7ef470ba84b93

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.147963Z digest=sha256:ad171011350daafb042adc33bbc85d440f21e9842c7a0aa663875422912ee72d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.152795Z digest=sha256:afbbe1d0e63a45c7972554601ba975f044f28db10edf045d711876a3f3c0e0fe

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.157684Z digest=sha256:10d4fba1ab102132eaab6c9586fc09c679bf445548d95b60264dd9901cec33b7

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:b3786ea0836ad35500d98280a1cbb583f98e8ffcf676b0a9899028968031d244

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.167485Z digest=sha256:7e57b72d7de92779a6598092a6057b12bb4b3f49e74aa3ec4a5a0f28821d72cf

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.172080Z digest=sha256:cd0c60a8c3a136599d0b21edfbb515b747afa4f5728df99d4ee3eace5d5ded52

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.177921Z digest=sha256:495fb61a4f29c5f1f5215bcc0872faa33c9af8394f9fda92cb86b46b7686127d

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.182917Z digest=sha256:5acdcf4a5d75529acfc8d9767b5e60905489d773daf9cd154c51ce0e4b377492

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.187620Z digest=sha256:fa03ee7caeab3f03def1fd554c6bb2e9af80bf45440e86bfbfb7f018f03054f8

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.192271Z digest=sha256:04cfa0c0b91d8f0e171b91ba6e66f94e21a8abbf27d013678ac60e5ba49b30a8

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=sha256:7045f7824e5dc0c51de23b1ed763b12a9b8d5c25bb5c7a8fd1e79827cb3385ef

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.202124Z digest=sha256:7ff91f811d64f2e7c88564089c2c07d9e120a41ad0782c7b3c3afcc04a602f0a

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.206804Z digest=sha256:343d11a11df03623c675bb8f05b58ab16e4a3b4874f439cc66c2a513122dfa52

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.213141Z digest=sha256:a8834a424fa6c9f549fe12dbb52db100ac174c3cd7431fa618c01bdeeefcc790

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-09T05:14:35.219408Z digest=sha256:e3d6a938550ec9f5a89be2471d38ac3a0cffa2e6a67657fb54015fd9a7eb58e4

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 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-06T21:47:52.607500Z digest=sha256:7f8563e273764807365700e1a9049090b32231933f51e92016729075033f93dd