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Paper Citation Record · LEDGER

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate

As of 22 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 2 inbound Pith citation observations for arXiv:2411.19864.

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

pith.paper-citation-record.v1
2411.19864 v4

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T05:51:02.747441Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T08:29:07.166426Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

15 of 15 outbound references displayed

  • verified exact0
  • verified fuzzy9
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 81d74c9c-d879-47ff-b4fd-e10954c231c0 · outbound

This paper cites Ueber eine neue Methode zur Bestimmung vielfacher Integrale.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Ueber eine neue Methode zur Bestimmung vielfacher Integrale

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.989014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.679771Z digest=sha256:6794ce04a1be215454b505e64b4c1e8b69f11a5a33122d71cc78d2f67e9ca808

Observation 4d3f6a60-641e-4827-87ed-9b9131ba1759 · outbound

This paper cites an unresolved cited work.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-12T05:51:02.974644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.685249Z digest=sha256:a10d5476493ec052bdd43f4f7c7a59e107bf92bfa07e644ec04390da33e9bc56

Observation 4b02bb12-02d1-4b52-b09b-cfd6b4a30e89 · outbound

This paper cites A Geometric Interpretation of an Infinite Product for the Lemniscate Constant.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate A Geometric Interpretation of an Infinite Product for the Lemniscate Constant

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.960351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.689766Z digest=sha256:f196afd0bd07e64a7c5f1f03eff1dc26626828b8347e8cca0bf44a46c5898fc5

Observation ae17759f-e4b3-42b9-aa05-b6feae29064f · outbound

This paper cites What is the area of a Squircle?.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate What is the area of a Squircle?

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.946067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.694699Z digest=sha256:9f1eeb4a9dced71dda6ef9d88b4fe3b0113df057ece090d7d7b73971c109f94f

Observation bab90852-0558-42c7-b597-461240033d49 · outbound

This paper cites an unresolved cited work.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-12T05:51:02.932115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.699430Z digest=sha256:1e2d62c40542564879bc24821693c0d1aba4479bfbefeaa3af508c85f5e0fd1a

Observation 7e65d3a8-ae8d-4f28-aab7-255b85568f4f · outbound

This paper cites Squigonometry, hyperellipses, and supereggs.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Squigonometry, hyperellipses, and supereggs

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.918075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.704006Z digest=sha256:02ea7aee099d77f99657f8db9685d61e57fec7beaff324cba8ada7d4db4f8830

Observation c5bd1fcc-5b27-46b8-8b1a-93524d0f275f · outbound

This paper cites Bernoulli Lemniscate and the Squircle || A remark- able Geometric fun fact!!?.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Bernoulli Lemniscate and the Squircle || A remark- able Geometric fun fact!!?

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.903027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.709309Z digest=sha256:f0ee38a73007a43f06653da961de8128fcacbb4de03fd9fa5d7b63c6037bbb61

Observation 0f093944-dd9b-45fb-b0fa-162374a11bd8 · outbound

This paper cites Topics in Complex Function Theory – Elliptic Functions and Uniformization Theory, Volume 1, Wiley.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Topics in Complex Function Theory – Elliptic Functions and Uniformization Theory, Volume 1, Wiley

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.888947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.714314Z digest=sha256:24fe3656e54c4dabc89d703b89800bda48e116f1bb834bfdf58ae0eeef36d63a

Observation 8309ad55-418d-4a49-bf70-88bd32971f9f · outbound

This paper cites an unresolved cited work.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-12T05:51:02.873649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.718956Z digest=sha256:5b3798ce1e77672cdc64f140eb84ce08b0ad2753d7e0355df1efc26982a7267c

Observation 402ce801-e349-46b9-be8e-36a42a653c49 · outbound

This paper cites an unresolved cited work.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-12T05:51:02.858683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.723438Z digest=sha256:a7d35938289516075667def1dcf86e71cc4fc2937337a044fbd61328e026282b

Observation 01d81bb7-e830-4e4c-9641-b733a2b64476 · outbound

This paper cites an unresolved cited work.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-12T05:51:02.842991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.728836Z digest=sha256:18262bf882e8c7f39b6de30924c0dd29d9880fca03e2edc8f60928e9b56fa136

Observation 35d15e09-6d86-488d-af90-a2794f51ccec · outbound

This paper cites /external-link-alt.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate /external-link-alt

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.828022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.733258Z digest=sha256:d4639d2a276016a54ce0a68673d57d6983099d5b79e2ed6862c15807d277e406

Observation dc847895-ac0d-4ee1-bde6-0badf92bba25 · outbound

This paper cites an unresolved cited work.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-12T05:51:02.813543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.737922Z digest=sha256:72d0105b04b697b17de7e264f51eb6a3675b62c61cc20f953a3ebce24726ab17

Observation dc6c4f0f-e890-425d-9c1a-51f03577b52a · outbound

This paper cites N.(1978), A Course of Modern Analysis, Cambridge University.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate N.(1978), A Course of Modern Analysis, Cambridge University

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.798554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.742764Z digest=sha256:a82a556216df0d4e6b833cc5e5561992defe3b8ec70c8cca0196f71b2727cbf6

Observation c8c6a88a-fdd3-4a9a-9d35-877aea965683 · outbound

This paper cites Squigonometry.

An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate Squigonometry

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T05:51:02.782851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-12T05:51:02.747441Z digest=sha256:3828d1128875d9fb6e7197a9f97a3d8d98de32a946f7ca5232813bf8fdfd70cf

Pith citing papers

Observation fa4672a4-4540-4358-9617-de40edc49cfb · inbound

Generalizations of the Squircle-Lemniscate Relation and Keplerian Dynamics cites this paper.

Generalizations of the Squircle-Lemniscate Relation and Keplerian Dynamics An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-03T08:29:07.166426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-03T08:29:07.166426Z digest=sha256:f793c0c8c76169384f31322f6a4d8a12a9319e44ca377074b3218118d3d87c13

Observation 87710ff1-3e8f-45a5-87ad-ba7abfd40dec · inbound

Hypergeometric Series Representations for the Perimeter of Lam\'e Superellipses cites this paper.

Hypergeometric Series Representations for the Perimeter of Lam\'e Superellipses An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate

Reference 18

Resolution
unresolved
no resolver link, observed 2026-07-13T00:43:39.480584Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-13T00:43:39.480584Z digest=sha256:e46a8a83d7c8c3de68dcdbd8b005c43ef88a08650f0783393ba386bf7d1dea45