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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:ada604380654b61bca6be86c83746c4d04adc6b7fff46980efb61dd50e3cb3f8

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=sha256:17c8ea914e4c8fd626cd64fd8b01d67ddc7c01b562d7e413cfa9c3d24de356db

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=sha256:7768b4ad2420e7e3b341b5cff3a3e588a3a3cb216f0e994a0f79bed949400aca

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=sha256:5762d2ba6b0db171d5b0ccc1e7d550a5d28f275e9bebacb75f54d19f00058d1a

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:aa8da21d99aeca7c7a51131d433a5777ae547556abc8071db91d839c653225a2

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=sha256:14beac3f7401cd9fc66c08ebdab711daf6dfeee50f9d02ff49018eb02f551426

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:a422827fadf05928bfa623bfd1745d920621dfbbb2a51188de57959e00ed6cad

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:b5dd1f92076ffa002e25bc1b0acfa0229bbf41ede4194dc2cbcb3f07a6de65a1

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
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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=sha256:63acaf1973b431132349dbbb2aa51db41509fd0f251a73c3625c2a68541b508d

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=sha256:92a752462b0a0a7de91822ff7b1a48803e7012bf2f4c7073c615032f3deda52f

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:b75889e8faa3e1c605b7ac81aee8ea714c960128f05b0a9cc83493575a05e4ee

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=sha256:91a4ee6b04d358bb02933a070d2fa852249aefdd2d39bcb5aff76890c755f0cf

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=sha256:5ef75825f950d46b46329b5ca932143955c82c51147995c6d169d73855c4c425

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:fbcd45d9352a8f22cb0051dbea754c7157ab3e7fe5facc3585bc07645a32d570

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:f7e29269fe0f9880edf44b357629458606a36d9c32f625356d2d47942945c251

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:c4e9b501fa5275bbdd062f49daf03a0bbeab8186831dcb44bd4c1934815b92b8

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:f79451600718e1bb61b48bd0d6e6718f4e0bbca088fe19b4385345982f0c495f

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:a7fb1d408ab34197fb2ade93f56d3fb26695c999efe6240b66cf969a66c329d3

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.

source=pdf_text observed=2026-08-11T22:36:24.384173Z digest=sha256:23865ac2957e0dd44e4cd3de046c2d9333a346e40b159bfe1345a121aec9ee90

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:f3fd6b395c7a68a621f8638f1ee6b7eaccf95671517f446a05cb31281e5ce0f2

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=sha256:2b24c2fa12ca19ac86f7783b81be6f304f9c65a216bb4ac7abe26a09ff9e015a

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:b15621c818c4b5d7cfd7e9c86ef034c57fc3650879bce6dfe5075aafdb0bd5ac

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=sha256:92e184950dec883d4434b90eff95817bf45208bee33d33adfb325f14c00b3b93

Pith citing papers

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