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Paper Citation Record · LEDGER

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

As of 15 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.514546Z digest=sha256:067ae2f95debf62eaea8cbea6bae0aa9a3c89cb17d9954049e7ed71879db530a

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.522291Z digest=sha256:dbdfce4969d4748dbd3e644ef47c1ee2fc5a1b403d111421d5ecd12b9731b527

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.530409Z digest=sha256:9c1a1d8202eeb0e2f0ee17d70616564ebc136a0a8e9cfd7e0c2f8bd62c8d3b0a

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.537205Z digest=sha256:ad788911e8e7f7539f4fe293a1a3bb938af7fe58d3fe238d9d4032a51ca54060

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.546806Z digest=sha256:631dec1a8e1879c8fb2ef01f0404fdb564ea6652993e12a5ead06d3fff7c89f4

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=sha256:5722b4740bf1d821414fd3afc92b677a10eae8e59b5027c8c4f6e95f3da4c72d

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.578683Z digest=sha256:50c4bd59b9f0c87a802322c7d0601f371a7d8abf0f3e0170baa6ef3b03c7d3d1

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.587899Z digest=sha256:f29de41c46a4e272e2714ee10307461754e7b9af8879f9ad00b4ac8d2664d711

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.602036Z digest=sha256:6da34aac861f908be1752d344c0ade50699da0cdf57d8c375e5460ac1750ccde

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.609203Z digest=sha256:81057624ef2280e39fa9b87ecab3837587eadac60305ef0d36ef0663deeeeb4e

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.618212Z digest=sha256:892551d0073ac661da850c282505027cbada3de7d99c315399acf385cfa5a14d

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.629001Z digest=sha256:57318bd8bb2d7855e0843444a943f818b6da7eea6a9097cea851666a639d7923

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.636988Z digest=sha256:702ab2e0c8aa5896713de350f3f23a2401d2b9afebed0f95560300b7684ae2a8

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.645485Z digest=sha256:ba656d8686c2f04e9ac65929392d3c450517b45c9102eda4a40ad459affb7956

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.655161Z digest=sha256:db164c60fc951a3fb15a086a48d23af2f48a5083f0025ba7c2a0e02be2cd02bd

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.666385Z digest=sha256:7966deeef07648a3a7e08c142d92a0efb590dbb8924d6ee2028a1a51c628b816

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-11T10:50:04.673205Z digest=sha256:2889d1696460e182e419abe387ebb085f7f0d7ec63324b2f57c052b1aa41df75

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:fbdbc0e44a29099003a25802b247b19d3f81fe537edd4b2133836ad2f3305ca6

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T13:12:02.311228Z digest=sha256:60260dc2801872e078911fb14bc21a16fd4788c1ee4b7eef68b1d861645ff3af

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=sha256:1be42bb76d996bef71cb72d62e6a7fe7fcef6710fe13ff278c63f35839fb3fd0