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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

  • verified exact0
  • 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:df1a0fc1ef8ac197ab84d2ef390abd5c7965baa2246259e3c9f388684a9968c1

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=sha256:98d4d0557bdb8db2dffaa4f9317298e565914e7772deaa40e8d30892cb5ac65e

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:db2daee15846b099be7844c0efe8f0e418890c11e9b532366fec1b8f0c9bc190

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=sha256:037e17fbcf007725bd08dd7f2083e4a099836fde95bdff4948af225f34cb049d

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

Resolution
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.

source=pdf_text observed=2026-08-11T22:36:24.301949Z digest=sha256:eb2ab75c4898de7b1018d6870a427ec009c1348a6aacc045c833511a24ab3756

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.

source=pdf_text observed=2026-08-11T22:36:24.307663Z digest=sha256:cd318a0ecfb98bdda9e4fb1275e3780f5d80708fa6c8a92f7e695c3ca83490af

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=sha256:894392ca615e2b44a7139a32eb482a400482db0d618e4809d820ebf5021a9bed

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.

source=pdf_text observed=2026-08-11T22:36:24.318707Z digest=sha256:cb3f0df4d1787de7b4b6b7efe6fd970ae1f2f395d8026b9630d34d0895f90c06

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

Resolution
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.

source=pdf_text observed=2026-08-11T22:36:24.323670Z digest=sha256:d77ed518b61e83d69bad957413e8f0ede02bec72b172bf628f9fe1b4c3d7fdad

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

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

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 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=sha256:920a368f21ae478fa64ebc0af78cb0811de1eac1e0dc501e72003ad15addbbf8

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:fc318b986288a940f13590bc529340ca74817990db0cf0603c50e5ef73e81dfe

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=sha256:38434ca1466508285f866de1b9eaeed75e6c41b7d50466c7a93502475b7a94f5

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=sha256:050b06f50cc93a5a7193fc7c5a5b5a1c5d76aba6a00aa2bdd4f3cdf14dc54f86

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=sha256:643fbd72cb94aa7092b78a8c11d45c3ff00227b1997eaccae77ca12741242e21

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:d37ff49b6cd4c5d469b98b7b3da1c204078af3444d0c7c92e6bd2e2814e34cdc

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.

source=pdf_text observed=2026-08-11T22:36:24.364913Z digest=sha256:dd769255a099dc35d5456e22a15f4a6d794c1c33bf2c8ac7ec1c48d33f1e54f1

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=sha256:8e1ad186c4c3423bd239c2a4882768dd016c9b741e64d7c63f8d5719d518ba72

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

Resolution
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:eb54fab2478a6c93aaa1a02c6579de1883df054104b97eb08fd7e8028ce0973f

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.

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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

Resolution
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=sha256:04a9d5eba9cac591f45204f11c58ba0baf3f94b36d3278ffabe46513483309af

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:d1fcb3c4e1896ac5867b6632d97ff1ffc5a6fa902fb894619b09bf1dc339d38a

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:fdfb32eedc01c7dc679516df0c391617a178559e60bc7a9ecaf416ad8ddf73e0

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.

source=pdf_text observed=2026-08-11T22:36:24.403847Z digest=sha256:6350e3afb6ee4861487359db3bbf901d535449773228086c1b0d5b1d6fdd027d

Pith citing papers

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