Paper Citation Record · LEDGER

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves

As of 23 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2412.02476.

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

pith.paper-citation-record.v1
2412.02476 v2

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T23:31:42.268332Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:23:19.779703Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T13:23:23.445684Z

Reference resolution

32 of 32 outbound references displayed

verified exact1
verified fuzzy16
unresolved15
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation df316140-3483-4daa-9708-bd806afc8dbd · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.876979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 30d694b5-9704-4243-83a3-853c921d0994 · outbound

This paper cites Armijo, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific J.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Armijo, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.864618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7132f9e9-5b3f-423a-8a2c-ff7dc33744e2 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.851476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 68be855a-f519-44a2-bbe1-033b6d8d19df · outbound

This paper cites Bendixon, Sur les courbes d´ efinies par des ´ equations diff´ erentielles, Acta Mathematica 1, 1–88, 1901.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Bendixon, Sur les courbes d´ efinies par des ´ equations diff´ erentielles, Acta Mathematica 1, 1–88, 1901

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.838846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e4d6a43a-1531-4286-ad9c-eedac21b8bf5 · outbound

This paper cites Bergweiler, Iteration of meromorphic functions, Bulletin of the American Mathematical Society, vol 29, number 2, October 1993, pp.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Bergweiler, Iteration of meromorphic functions, Bulletin of the American Mathematical Society, vol 29, number 2, October 1993, pp

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.826595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ebba0101-d905-4c92-980a-1af9d31a1476 · outbound

This paper cites Carleson and T.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Carleson and T

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.798298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8351823a-fe13-4065-9896-12cf1581369c · outbound

This paper cites Devaney, An introduction to chaotic dynamical systems, CRC Press, 2023.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Devaney, An introduction to chaotic dynamical systems, CRC Press, 2023

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.784736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a3c1197f-066a-44ef-8c35-1b02c1318a7b · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.769031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 255c552a-acb8-43ab-8131-33fd6be4f8d1 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.752927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 06c5b9a0-5765-481b-89f6-d1e5c7e1fe59 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.741102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fcad1d1a-c8d8-484e-b35e-b2998562035b · outbound

This paper cites Backtracking New Q-Newton's method, Schr\"oder's theorem, and Linear Conjugacy.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Backtracking New Q-Newton's method, Schr\"oder's theorem, and Linear Conjugacy

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T23:31:42.104307Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12b3296f-17b5-46e2-93d3-b60899387d63 · outbound

This paper cites von Haeseler, H, Kriete, The relaxed Newton’s method for rational func- tions, Random Comput.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves von Haeseler, H, Kriete, The relaxed Newton’s method for rational func- tions, Random Comput

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.705511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 21d97076-02a3-4c5f-8831-6c612b5074b1 · outbound

This paper cites Hubbard, D.Schleicher and S.Sutherland, How to find all roots of complex polynomials by Newton’s method, Inventiones mathematicae, vol 146, 1–33, 2001.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Hubbard, D.Schleicher and S.Sutherland, How to find all roots of complex polynomials by Newton’s method, Inventiones mathematicae, vol 146, 1–33, 2001

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.672715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4728fe73-253a-43e6-8ba5-5a3d6ae65ef3 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.650380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5cb61161-2e1f-487f-87d1-f9024f34daea · outbound

This paper cites Manning, How to be sure of finding a root of a complex polynomial using Newton’s method, Boletim da Sociedade Brasileira de Matematica, vol 22, no 2, 157–177, 1992.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Manning, How to be sure of finding a root of a complex polynomial using Newton’s method, Boletim da Sociedade Brasileira de Matematica, vol 22, no 2, 157–177, 1992

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.638199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ac635c0e-8049-4147-8d9a-a52d221bbdca · outbound

This paper cites McMullen, Families of rational maps and iterative root-finding algorithms, Ann.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves McMullen, Families of rational maps and iterative root-finding algorithms, Ann

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.624481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fc3ab349-854b-4798-b4fd-bcfe328acfb2 · outbound

This paper cites Meier, The relaxed Newton-iteration for rational functions: the limiting case, Complex Variables Theory Appl., 16, 239–260, 1991.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Meier, The relaxed Newton-iteration for rational functions: the limiting case, Complex Variables Theory Appl., 16, 239–260, 1991

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.607064Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 675ab82d-5c08-4328-902f-da473bb2e793 · outbound

This paper cites Milnor, Dynamics in One Complex Variable.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Milnor, Dynamics in One Complex Variable

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.591960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 223c4623-8878-447c-93f6-b946ffb83c7c · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.578839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 54ecc943-c84b-4605-9284-9d9850b78855 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.560637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 578bd88c-03ac-4771-b85d-38ced1e24761 · outbound

This paper cites Poincar´ e, Sur les courbes d´ efinies par un ´ equation diff´ erentielle, Oeuvres, vol 1, Paris, 1892.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Poincar´ e, Sur les courbes d´ efinies par un ´ equation diff´ erentielle, Oeuvres, vol 1, Paris, 1892

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.548616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f773e98f-7783-4f58-8f29-0799f93b84d5 · outbound

This paper cites Przytycki, Remarks on the simple connectedness of basins of sinks for it- erations of rational maps, in: Dynamical systems and Ergodic theory, ed.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Przytycki, Remarks on the simple connectedness of basins of sinks for it- erations of rational maps, in: Dynamical systems and Ergodic theory, ed

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.536744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 120a1fb0-ae76-4b29-881c-ebdd47b15e34 · outbound

This paper cites Schr¨ oder, Ueber iterirte Functionen.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Schr¨ oder, Ueber iterirte Functionen

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.524812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 84cf6ef8-0077-4836-88fb-d716d6f86be4 · outbound

This paper cites Shub, Global stability of dynamical systems , Springer Science and Business Media, 1987.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Shub, Global stability of dynamical systems , Springer Science and Business Media, 1987

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.508104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 33a9c702-4b2a-4bec-b83e-d97c7ee2c926 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.491170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 186b4e71-8a42-4cdc-97fc-1ec29f16eaea · outbound

This paper cites The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves The Riemann hypothesis and dynamics of Backtracking New Q-Newton's method

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-11T23:31:42.328472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fadf0410-6e96-431a-9203-c7ee88ff9155 · outbound

This paper cites Backtracking New Q-Newton's method: a good algorithm for optimization and solving systems of equations.

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T23:31:42.234228Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8af5a06c-164b-473e-a426-bee980a81cae · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.461698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5086d04f-b143-44fc-a93f-f62e5b37a4e5 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.431943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d52a8a98-1c94-4f0d-afa9-9b190f6d3772 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.404745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f0753d15-e373-47ed-b42c-25e597c06296 · outbound

This paper cites an unresolved cited work.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:31:42.374364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 895e3143-993d-4daa-b713-b466acfb72eb · outbound

This paper cites Yamagishi, On the local convergence of Newton’s method to a multiple root, J.

Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves Yamagishi, On the local convergence of Newton’s method to a multiple root, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:31:42.359658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation 61989f5d-8a4b-4a92-a47c-256d6051dbab · inbound

Some iterative algorithms on Riemannian manifolds and Banach spaces with good global convergence guarantee cites this paper.

Some iterative algorithms on Riemannian manifolds and Banach spaces with good global convergence guarantee Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:23:23.557472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.