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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=sha256:8c6e97d714396be52fb54c156ed9b327399069db1c735b947dadc0ad995d4d34

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=sha256:1a7ab4f4e46f9c2302f2fa2404cd27b5e42450cb05d88fbe2a5de277204433b9

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:db0280b83eef48d5e76cf2bdbccda5bb8e14cafd668a840a034a50eb23e31654

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:c292f8e046b83cfa65b9a352cba13394ed64d2220135834b16eb7a185ff4b89c

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=sha256:63fda30ef2c49e26dc1b4a7390465ff0a295b2520dc89ae548bc1c22cae670c8

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=sha256:80b893c19aad08e6638ef6aa41ae38d2b03a4948f3d9853e6211bd22aa815b7c

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.

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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

Resolution
unresolved
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=sha256:288027c7d0e1b9b268b693480455f6de761d3c93f732b3adc72e457ea2aaf778

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=sha256:0f2ddd3a260b6227f2f2522c17d7d5e68d076b9625d81484fcfe2c6f2039a7d0

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=sha256:506e0e224910931a733283b79d0bea24eca565f072724eb2967e4d32b907b161

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=sha256:0c7fbfa999c7f009e6ed77a164bc300ae566c460bf99a95a1d434e838b0c2151

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:b7799bc92a62553cea51d16c16d2837ffcd28490228447d6b1c77a47fa42b45a

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:e5346eb46483ff030021fc74823df541359df3e0c0b7d0aad40ed5fbc12c40ee

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=sha256:2a73bbc296628164f42731563376dc241fe116766afc2838e9e42636756b1ec3

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=sha256:012c1149b3bce4585f74505cafd1575bb6aff7a3cbfb9bf51f6277400bb4661c

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:ea79cd1829fe804ca5c1a1f52e8328c6955a106edb32dc731ffc30e611be022d

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=sha256:7acd67fcca1ed634b6f527560be053a27112e1faf6371c63f015a4a191d877bf

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=sha256:03d2ad1f2513d78df1e5b6266fc651e17050d012d096b7d5336c9f0a2439d39a

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:f5197ed63cea46d0cda5ccc84534a86f0de5a40720757abc0292779c5dd3f494

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:fe7d85c126a7f7bc9d27a2345c94eae7dc2f1469fd4438cc236bbcabe8c60325

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