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Paper Citation Record · LEDGER

On Lagrangian Tori in $S^2\times S^2$

As of 13 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 3 inbound Pith citation observations for arXiv:2412.16356.

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

pith.paper-citation-record.v1
2412.16356 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T10:50:04.673205Z

measured 20 of 20 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 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T05:14:35.162561Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T13:12:02.371925Z

Reference resolution

17 of 17 outbound references displayed

  • verified exact1
  • verified fuzzy5
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ce1f6b00-99dc-4599-abf1-a603142ce4e2 · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:05.300061Z

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=arxiv_source observed=2026-08-11T10:50:04.514546Z digest=sha256:5e294735e0e5c2e7c518d73db39f75ee3c7058c727014ce3211804cad2c9c578

Observation eefd5062-b3c1-4065-a9b1-00f73655284e · outbound

This paper cites 8, 1046--1051.

On Lagrangian Tori in $S^2\times S^2$ 8, 1046--1051

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:50:05.260443Z

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=arxiv_source observed=2026-08-11T10:50:04.522291Z digest=sha256:b2f9013409e7af93168673d2834e8ecc7655b0b27a0c1d2455549193d44dc40b

Observation 09afb641-ebad-483c-b03a-de6830b2367c · outbound

This paper cites 7, 3851--3875.

On Lagrangian Tori in $S^2\times S^2$ 7, 3851--3875

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:50:05.236574Z

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=arxiv_source observed=2026-08-11T10:50:04.530409Z digest=sha256:f12833b3a164ca9e1482e1368b3e918f053d52f55a37337f8f1e1a978f1da068

Observation ccdae43f-69ba-4e8f-8f23-5b0bbb90eceb · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:05.203292Z

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=arxiv_source observed=2026-08-11T10:50:04.537205Z digest=sha256:b6b35df3db2190e82f4d575f54bb183a2278f67ba60277b9eb42243e38c651a5

Observation 785f82e9-3f93-416a-bc40-d896b3b590d1 · outbound

This paper cites Biran, Lagrangian non-intersections, Geometric & Functional Analysis GAFA 16 (2006), 279--326.

On Lagrangian Tori in $S^2\times S^2$ Biran, Lagrangian non-intersections, Geometric & Functional Analysis GAFA 16 (2006), 279--326

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:50:05.158221Z

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=arxiv_source observed=2026-08-11T10:50:04.546806Z digest=sha256:f20f5deec6bc46e4d76e3a1b90d90e29365748676cf1805d19299c8389115a53

Observation 89077d6b-0bf8-45bf-84f7-22307df5b0d8 · outbound

This paper cites Real Lagrangian Tori and Versal Deformations.

On Lagrangian Tori in $S^2\times S^2$ Real Lagrangian Tori and Versal Deformations

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-11T10:50:04.558780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-11T10:50:04.558780Z digest=sha256:86a08c63184e4c33815d5511882f33be63233d0d3da50b75d9f5b11c47699713

Observation c8f5f68c-8055-4416-9c99-3ceea727e26f · outbound

This paper cites Hamiltonian Classification of toric fibres and symmetric probes.

On Lagrangian Tori in $S^2\times S^2$ Hamiltonian Classification of toric fibres and symmetric probes

Reference 7

Resolution
verified exact
local_arxiv, observed 2026-08-11T10:50:04.763408Z

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=arxiv_source observed=2026-08-11T10:50:04.578683Z digest=sha256:2004de787edf9b0ed3d1a9df44167ea73048d157e3148159e3130a16e0652c6a

Observation e97ae7f2-2f3a-4673-a1aa-5dcb5e3a25bd · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:05.118837Z

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=arxiv_source observed=2026-08-11T10:50:04.587899Z digest=sha256:be99c4657488805cbe9b3d861ebc3ef22a2733cedd2991d70ed7e191295ed97b

Observation dc26de7f-fe6f-42f7-965f-269e61fca8a9 · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:05.090490Z

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=arxiv_source observed=2026-08-11T10:50:04.602036Z digest=sha256:f9e3305de4a3c527a4261584139d09e2ce0176f2003568b64c9a6d0889b0a6e7

Observation 359977e0-d417-4e9f-a0a7-db2f11407752 · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:05.044973Z

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=arxiv_source observed=2026-08-11T10:50:04.609203Z digest=sha256:7454537ada9f4f59e777eab5d3c56a1a160d989a261aad6c25113806a91bf88b

Observation b2618c50-3eca-44ae-8f15-80246193d84e · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:05.015728Z

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=arxiv_source observed=2026-08-11T10:50:04.618212Z digest=sha256:dc1f4973e0a8777ca4c9e2da2cf1cd982f5130524e2a8df52a841ce01f0fceea

Observation 3e7a3630-87f3-4444-b326-a93bcdbd3a86 · outbound

This paper cites 13, 2942--2993.

On Lagrangian Tori in $S^2\times S^2$ 13, 2942--2993

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:50:04.980761Z

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=arxiv_source observed=2026-08-11T10:50:04.629001Z digest=sha256:0436fa2e1aa1c1decb40312599326991694ab0aaa2288a3133665ac259984f00

Observation 11a6f7d4-3f3e-430f-85de-b5a1fe889ede · outbound

This paper cites 2, 343--361.

On Lagrangian Tori in $S^2\times S^2$ 2, 343--361

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:50:04.943294Z

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=arxiv_source observed=2026-08-11T10:50:04.636988Z digest=sha256:4f150d6d3594f0ff7575d6248555c4f2990637297e5c21c37a426b5c74276b2b

Observation 68dc1f78-e883-497e-b042-b4548487023c · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:04.910767Z

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=arxiv_source observed=2026-08-11T10:50:04.645485Z digest=sha256:02778526ab0ff2cd799baf0ee819f2dd30060b844f995e61313509adce3befec

Observation 9133392d-d897-423c-a13d-e67123c0e756 · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:04.883162Z

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=arxiv_source observed=2026-08-11T10:50:04.655161Z digest=sha256:467678a324bb45702e1fb32282d639550e9bb3ebdca9be8b87118b83bd83461a

Observation e065c449-1353-428b-a0b6-063067c8b962 · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:04.859465Z

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=arxiv_source observed=2026-08-11T10:50:04.666385Z digest=sha256:47ef4c57edda1f80801768b3ca858c82b81363babe68b14a0cc09e6cc9ac1fe9

Observation aab4c656-c35c-4c24-a539-36279c3120c0 · outbound

This paper cites an unresolved cited work.

On Lagrangian Tori in $S^2\times S^2$ Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:50:04.834768Z

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=arxiv_source observed=2026-08-11T10:50:04.673205Z digest=sha256:53d8077ae1f89c200f6d8de272081c47b716bc03de2f91c04333a546da2cc5ee

Pith citing papers

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

Lagrangian split tori in $S^2 \times S^2$ and billiards cites this paper.

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 28dd219e-890c-4301-8189-6a4d3155ec17 · inbound

Tightness of Chekanov's bound on displacement energy for some Lagrangian knots cites this paper.

Tightness of Chekanov's bound on displacement energy for some Lagrangian knots On Lagrangian Tori in $S^2\times S^2$

Reference 2347

Resolution
verified exact
local_arxiv, observed 2026-08-06T13:12:02.375850Z

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=2026-08-06T13:12:02.311228Z digest=sha256:45097ff0065d4575c1af22d2d3f3982f89cdc335437b231afeddc5a8dee5910b

Observation 58d04701-0980-490a-9974-500a6d2abba3 · inbound

Explicit Hamiltonian Classification in the $F_4(0)$ Toric Degeneration of $CP^2$ cites this paper.

Explicit Hamiltonian Classification in the $F_4(0)$ Toric Degeneration of $CP^2$ On Lagrangian Tori in $S^2\times S^2$

Reference 22

Resolution
unresolved
no resolver link, observed 2026-08-06T22:52:23.861459Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T22:52:23.861459Z digest=sha256:71af8b7a4f1785f19d3217504c32904fc43fcafcc32e28003614d3f0942213e7