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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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.514546Z digest=sha256:3b6b6176ff5177017e59b1241a42cf1e4040566eb280d9f3a13e786a644a6db2

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.522291Z digest=sha256:f73bf54bac82495ffe8153c1b5f49c99a373c0ff0998d1be213d787248f8b1e6

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.530409Z digest=sha256:76188463bff90ef25d6969df00402f9ed66832d2d388ba733df81a31e1cc3df6

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.537205Z digest=sha256:1876583b0ca3b8d6eb4f6febfce76c936aaf6fcfb914717fa795718dd6e90873

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.546806Z digest=sha256:187ac5258d7459315f8817232335a0f857e3cd1f829bee6407f38aeb05481152

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:fb071156fdf0c33a9da6d845dd57a624161a56a0c03bedb54570947147638fd6

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.578683Z digest=sha256:808c41b88078cac31f4fb794a93129375fe06dbea4594c46d7dc4d109905645b

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.587899Z digest=sha256:aa5b10074eee70dc94840bed198ac4ca90e9626c1ce7ae406fb87e2b06eef4cf

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.602036Z digest=sha256:aa563d462a646ec9c2adadf752cb474830885eaeb063f32bfd99846b4118320a

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.609203Z digest=sha256:5020045b160e2cf29a949d94db9d93d42027737e6b7181d6d75d5e4f69c9f967

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.618212Z digest=sha256:dae016e2edb0205f111a68b82af5d91c4dffd389acfcb7eecf7facf374453475

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.629001Z digest=sha256:7809caabd3bcfe7803f9c79448963c8c29bf30b1ed501126fc5f5173164fc5b1

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.636988Z digest=sha256:ba4b7f978bfdc7e1d4f9852caf7e19dcfd30399b43993814a85ac9f8110433a1

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.645485Z digest=sha256:99bbe47628e71e025f7f60df3489a04ffb16bd0704ec109ad36ced7985118bf5

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.655161Z digest=sha256:ba3ffb90cda65661631d7bc4a7f81fea17b7ec6a83c8bbd46df2394485336ca1

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.666385Z digest=sha256:ae46a55ead8f0557e106f87dec241472e23c6cc22340751628044b658924227b

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 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.673205Z digest=sha256:96c90d7ffd25f98a2375246e4d248eeb0e75e632e068e560cdd3a7585d66510e

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-06T13:12:02.311228Z digest=sha256:e998d953f4fabe8ae4e60811f1a2fcd7c790b964476907892ee87a2e8b0ddade

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