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Paper Citation Record · LEDGER

Theoretical analysis of the maximum range of a projectile released from a pendulum

As of 13 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2608.09157.

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

pith.paper-citation-record.v1
2608.09157 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T22:36:24.403847Z

measured 25 of 25 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

25 of 25 outbound references displayed

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  • verified fuzzy16
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 95a69a49-a303-4912-b705-57c8ae1bb420 · outbound

This paper cites (11) cannot be realized.

Theoretical analysis of the maximum range of a projectile released from a pendulum (11) cannot be realized

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.824239Z

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=2026-08-11T22:36:24.279779Z digest=sha256:00c4733493f66bf2a1ac1aa6ab61249e9423bf94c917edfd1f74fe80a8767e49

Observation 319e2a3f-466f-49c9-8cec-478ad8fff3ee · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-11T22:36:24.808287Z

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=2026-08-11T22:36:24.285590Z digest=sha256:0884b6654197039d1060e8ba01e17bb800e9309a14afd374784828cd2028c1c2

Observation da9a17a3-d65e-44bc-968a-b5be1122a58a · outbound

This paper cites Equation (14) is the governing equation of θmax and is analyzed in detail in the present study.

Theoretical analysis of the maximum range of a projectile released from a pendulum Equation (14) is the governing equation of θmax and is analyzed in detail in the present study

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.793392Z

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=2026-08-11T22:36:24.290919Z digest=sha256:084eccc77602b875fd20be08091565d952c8a3732faf9f1aef8d8d59f515f303

Observation c70a8159-da48-4b94-b9a3-88d209e8cfd8 · outbound

This paper cites In 0 < x < 1/ √ 2, no solutions exist because f (x) < 0.

Theoretical analysis of the maximum range of a projectile released from a pendulum In 0 < x < 1/ √ 2, no solutions exist because f (x) < 0

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.776560Z

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=2026-08-11T22:36:24.296553Z digest=sha256:ccc0b9d528b61b76b84809470dffa1c9b87b02fd40e86d438708315a7680a751

Observation 100e4b76-43e4-4056-a04a-50dcacce0158 · outbound

This paper cites Using x ≃ 1 − c˜v2 0 together with x = cos θmax ≃ 1 − θ2 max/2, the optimal angle is approximated as θmax ≃ √ 2 2 ˜H + 1 ˜v0 = v0√ g(2H + L).

Theoretical analysis of the maximum range of a projectile released from a pendulum Using x ≃ 1 − c˜v2 0 together with x = cos θmax ≃ 1 − θ2 max/2, the optimal angle is approximated as θmax ≃ √ 2 2 ˜H + 1 ˜v0 = v0√ g(2H + L)

Reference 5

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verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.759683Z

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.

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Observation ef9a0c22-f607-4765-a727-484b40308cdb · outbound

This paper cites (7) including a square root.

Theoretical analysis of the maximum range of a projectile released from a pendulum (7) including a square root

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.743421Z

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.

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Observation 25b9383c-7355-453e-8b2e-eb4607e772d3 · outbound

This paper cites Tarzan’s dilemma.

Theoretical analysis of the maximum range of a projectile released from a pendulum Tarzan’s dilemma

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.727658Z

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=2026-08-11T22:36:24.313406Z digest=sha256:5eca0f6a5af781b5beb68ac470d68abeaa343c1a83abf5f03a7f10ddabcb68ad

Observation 8b64c255-ecb9-4d55-93c4-067c6c707527 · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-11T22:36:24.712654Z

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.

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Observation c13db0c9-8131-41a7-999b-f54e0197001c · outbound

This paper cites Ganci and D.

Theoretical analysis of the maximum range of a projectile released from a pendulum Ganci and D

Reference 9

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verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.697307Z

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.

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Observation f3cec375-c524-4881-a486-c31dc6dc349e · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 10

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raw_fallback, observed 2026-08-11T22:36:24.681922Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 85fadaa8-ef5f-4525-aafa-dc2eaddeba57 · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-11T22:36:24.665810Z

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=2026-08-11T22:36:24.334686Z digest=sha256:bfc141f973376d3f6689d11231582eb0255a3b0e336637a1d8e62be1b36b080c

Observation d1f0e506-fc90-4559-bf87-995bfba17d09 · outbound

This paper cites Cohen, B.

Theoretical analysis of the maximum range of a projectile released from a pendulum Cohen, B

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.649700Z

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=2026-08-11T22:36:24.339721Z digest=sha256:4d9bfd888469880a97278862e51db4b8d1ba0e2d8972b88adf47095c978086b8

Observation c7b9ed26-051f-4239-943e-dc67169e58cf · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-11T22:36:24.634334Z

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=2026-08-11T22:36:24.344550Z digest=sha256:1f67fe76514d7c69c3920f8aeb8a053515e91bd51c04abb284775bc1d4786f38

Observation 2c6778c4-12f4-42de-a860-792527ec3a58 · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-11T22:36:24.618137Z

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=2026-08-11T22:36:24.349660Z digest=sha256:47f094117f081b208f3b335902b428d17e666b6407f077ddc56156881a235441

Observation 69dfab39-d2ea-49f4-8a07-eb0c0216f376 · outbound

This paper cites Bittel, Phys.

Theoretical analysis of the maximum range of a projectile released from a pendulum Bittel, Phys

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.602556Z

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=2026-08-11T22:36:24.355096Z digest=sha256:7da0b25c6557d788ca656723a0f386d7e6ba231ec47801e7c15e304ed4fd8419

Observation 9f79fc91-9f9d-4413-bedf-2f5c8693128e · outbound

This paper cites Rave and M.

Theoretical analysis of the maximum range of a projectile released from a pendulum Rave and M

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.587577Z

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=2026-08-11T22:36:24.360032Z digest=sha256:3e541f343c0500cea1bd4195e4163636889792f83ee9014aab68413cf1f6bdeb

Observation 5d5f3c94-8da2-474b-8a39-a23cda91ee32 · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-11T22:36:24.572570Z

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.

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Observation cf6b5b5a-c197-481f-85dc-9776964efc62 · outbound

This paper cites Shima, Eur.

Theoretical analysis of the maximum range of a projectile released from a pendulum Shima, Eur

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.556645Z

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=2026-08-11T22:36:24.369820Z digest=sha256:20cc5432485f87e60ca8acb5bcc190e631b955b83e4c7404f04fdce8129e7e08

Observation 1dfe077b-2791-4f11-93c3-4747b1b14b41 · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 19

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unresolved
raw_fallback, observed 2026-08-11T22:36:24.541356Z

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=2026-08-11T22:36:24.374545Z digest=sha256:fd469ed281a52eeec15369d26fca43062e42379509906550baa7e4410019ddd9

Observation a6785187-67c0-4964-8364-a2b28ba20a4f · outbound

This paper cites Tignol, Galois’ Theory of Algebraic Equations (World Scientific, Singapore, 2001).

Theoretical analysis of the maximum range of a projectile released from a pendulum Tignol, Galois’ Theory of Algebraic Equations (World Scientific, Singapore, 2001)

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.524344Z

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=2026-08-11T22:36:24.379391Z digest=sha256:b6fa433f732be5521973f7510b625c41a409b415fe9ca1b35e81f6067e7b4300

Observation 328582fa-c1a3-4903-8e75-f6109fdd4697 · outbound

This paper cites Anderson, J.

Theoretical analysis of the maximum range of a projectile released from a pendulum Anderson, J

Reference 21

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verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.506186Z

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.

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Observation a0291642-c1b6-429c-9a62-b88e7a593d49 · outbound

This paper cites Kovacic and M.

Theoretical analysis of the maximum range of a projectile released from a pendulum Kovacic and M

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.490376Z

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=2026-08-11T22:36:24.389253Z digest=sha256:9dac0bf42c542768a382a0711cb5c0e35e90d951b4fc5b73423dc0cf2843fa5a

Observation 4a0dfbf7-c786-4e69-a14d-c33d1f89695f · outbound

This paper cites Efremidis, K.

Theoretical analysis of the maximum range of a projectile released from a pendulum Efremidis, K

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.474361Z

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=2026-08-11T22:36:24.394166Z digest=sha256:e54eabae3ee98309ee5b3c837ceed9ef315f7dfafa8e2bba959676da70cacf38

Observation 5d0167ae-7ea0-466c-9f58-641ece780500 · outbound

This paper cites an unresolved cited work.

Theoretical analysis of the maximum range of a projectile released from a pendulum Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-11T22:36:24.458639Z

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=2026-08-11T22:36:24.398859Z digest=sha256:f6423dfffc0311cc9d8ba866c2d8b94c2f8157c87f85b67af767bcc2a5ed25b6

Observation 701874ec-4725-44d6-87ab-756e80552be1 · outbound

This paper cites Johannessen, Eur.

Theoretical analysis of the maximum range of a projectile released from a pendulum Johannessen, Eur

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T22:36:24.442396Z

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.

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