Paper Citation Record · LEDGER

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer

As of 7 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2507.06685.

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

pith.paper-citation-record.v1
2507.06685 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:11:45.832888Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+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

22 of 22 outbound references displayed

verified exact0
verified fuzzy13
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e3623ed8-87bf-480c-b8ca-d6aac2f9fc1e · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:49.392858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation d52fc9d0-9ada-4cb9-849d-8bd9c98862f9 · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:49.118681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 62ceb62e-d433-4164-8a4e-2fd55bb19f42 · outbound

This paper cites K., A note on the discrete coagulation equations with collisional breakage, Acta Applicandae Mathematicae, 189(5), 2024.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer K., A note on the discrete coagulation equations with collisional breakage, Acta Applicandae Mathematicae, 189(5), 2024

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:48.850772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 9d5bd037-7336-4c54-853b-e93f2f8ba5a6 · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:48.601489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 75cfc741-5a09-4675-9333-7869a67d8a90 · outbound

This paper cites K., & Giri, A.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer K., & Giri, A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:48.390491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation a6a1b628-2abf-436e-8cb2-5bd1de805c72 · outbound

This paper cites K., & Giri, A.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer K., & Giri, A

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:48.160735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 960621f1-0c78-472a-bd69-c1161da319fb · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:47.999530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation af85205b-f9cf-40a0-b286-75d930757c78 · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:47.713694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 1a1aaa51-5eb0-4f72-ab9d-dcf7cc46744f · outbound

This paper cites K., & Lauren¸ cot, Ph., Weak solutions to the collision-induced breakage equation with dominating coagulation, Journal of Differential Equations , 288, 690–729, 2021.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer K., & Lauren¸ cot, Ph., Weak solutions to the collision-induced breakage equation with dominating coagulation, Journal of Differential Equations , 288, 690–729, 2021

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:47.497353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 8de8d106-78cd-49c2-8bf8-dcf85c4afb3d · outbound

This paper cites K., & Lauren¸ cot, Ph., Existence and non-existence for collision-induced breakage equation, SIAM Journal on Mathematical Analysis , 53(4), 4605–4636, 2021.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer K., & Lauren¸ cot, Ph., Existence and non-existence for collision-induced breakage equation, SIAM Journal on Mathematical Analysis , 53(4), 4605–4636, 2021

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:47.297531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation f9d54808-8aef-4098-97e4-4dcd87684746 · outbound

This paper cites K., Jaiswal, R.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer K., Jaiswal, R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:47.203728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 244bbf35-3415-499c-9f6c-4f28fa25549d · outbound

This paper cites G., & Giri, A.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer G., & Giri, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:47.058751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 67e1ce7e-055f-481c-847a-4545f0e95cda · outbound

This paper cites J., A study of the nonlinear breakage equation: Analytical and asymptotic solutions, Journal of Physics A: Mathematical and General , 33, 1221–1232, 2000.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer J., A study of the nonlinear breakage equation: Analytical and asymptotic solutions, Journal of Physics A: Mathematical and General , 33, 1221–1232, 2000

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:46.959798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation a6f5a683-7667-4574-9b6b-dcd104aceef1 · outbound

This paper cites J., A study of the collisional fragmentation problem using the Gamma distribution approximation, Journal of Colloid and Interface Science , 303, 419–429, 2006.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer J., A study of the collisional fragmentation problem using the Gamma distribution approximation, Journal of Colloid and Interface Science , 303, 419–429, 2006

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:46.781391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation d2bbba2e-95a9-4017-a257-dfda77dfe8c1 · outbound

This paper cites L., & Ben-Naim, E., Shattering transitions in collision-induced fragmentation, Physical Review E, 68(2), 021102, 2003.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer L., & Ben-Naim, E., Shattering transitions in collision-induced fragmentation, Physical Review E, 68(2), 021102, 2003

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:46.688177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 94b5772e-66a0-4d31-8a0f-7d50e3a6c336 · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:46.564522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 814108a1-4b18-4115-898a-cc10bec06cb9 · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:46.475273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 04d596bc-9efa-45bb-a882-84af92d89a0c · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:46.344422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 2a41489e-a6d0-4471-8a82-2a885508bcf9 · outbound

This paper cites 105, American Mathematical Society, Providence, RI, 2009.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer 105, American Mathematical Society, Providence, RI, 2009

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:46.227696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 556f5a62-d423-4e15-8b54-96c4d1dbc8b8 · outbound

This paper cites V., Drei Vortr¨ age ¨ uber Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Physikalische Zeitschrift , 17, 557–599, 1916.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer V., Drei Vortr¨ age ¨ uber Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Physikalische Zeitschrift , 17, 557–599, 1916

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:46.132987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 002c9f3a-74f1-4c8b-a0ce-39dfd13db2eb · outbound

This paper cites V., Versuch einer mathematischen Theorie der Koagulationskinetik kolloider L¨ osungen,Zeitschrift f¨ ur Physikalische Chemie, 92, 129–168, 1917.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer V., Versuch einer mathematischen Theorie der Koagulationskinetik kolloider L¨ osungen,Zeitschrift f¨ ur Physikalische Chemie, 92, 129–168, 1917

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:11:46.061882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 9ce72190-310e-4f41-b553-16f8e643a715 · outbound

This paper cites an unresolved cited work.

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:11:45.928856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Pith citing papers

No inbound Pith citation observations are available.