The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity | Paper Citation Record

Observation 24c693c6-038e-4fd6-9bca-354406934376 · outbound

This paper cites ”Books, Hallways, and Social Butterflies: A Note on Sliding Block Puzzles.” The Mathematical Intelligencer (2024): 1-14.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Books, Hallways, and Social Butterflies: A Note on Sliding Block Puzzles.” The Mathematical Intelligencer (2024): 1-14

Reference 1

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This paper cites ”New progress in real and complex polynomial root-finding.” Computers & Mathematics with Applications 61.5 (2011): 1305-1334.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”New progress in real and complex polynomial root-finding.” Computers & Mathematics with Applications 61.5 (2011): 1305-1334

Reference 2

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Reference 3

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Observation 5db90211-c245-4a2c-bf2f-1397f95db548 · outbound

This paper cites A., and Joseph Frederick Traub.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity A., and Joseph Frederick Traub

Reference 4

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Observation ea4bb9c3-f446-4bdb-97a7-052004c1b886 · outbound

This paper cites ”The history and status of the P versus NP question.” Proceedings of the twenty-fourth annual ACM symposium on Theory of computing.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The history and status of the P versus NP question.” Proceedings of the twenty-fourth annual ACM symposium on Theory of computing

Reference 5

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Observation 03893946-6349-44fa-9dd1-da2cc5ffb16d · outbound

This paper cites ”Introduction to the Theory of Computation.” ACM Sigact News 27.1 (1996): 27-29.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Introduction to the Theory of Computation.” ACM Sigact News 27.1 (1996): 27-29

Reference 6

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Observation 6f88a8a7-f88d-4af5-a263-26b1b6759c0b · outbound

This paper cites ”Borel sets and circuit complexity.” Proceedings of the fifteenth annual ACM symposium on Theory of computing.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Borel sets and circuit complexity.” Proceedings of the fifteenth annual ACM symposium on Theory of computing

Reference 7

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The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

Reference 8

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Observation 5196420e-8975-440b-968f-e72fb9deb4b6 · outbound

This paper cites Ryan Williams.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Ryan Williams

Reference 9

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Observation dd02b0e5-be6e-447c-8ba0-857419df841c · outbound

This paper cites ”Relativized circuit complexity.” Journal of Computer and System Sciences 31.2 (1985): 169-181.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Relativized circuit complexity.” Journal of Computer and System Sciences 31.2 (1985): 169-181

Reference 10

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Observation 33925d82-bea5-4a72-8aae-6e83ae7cb0db · outbound

This paper cites Introduction to circuit complexity: a uniform approach.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Introduction to circuit complexity: a uniform approach

Reference 11

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Observation 4046af1f-4013-46dd-b192-32e146ff5c1c · outbound

This paper cites ”Circuit complexity before the dawn of the new millennium.” International Conference on Foun- dations of Software Technology and Theoretical Computer Science.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Circuit complexity before the dawn of the new millennium.” International Conference on Foun- dations of Software Technology and Theoretical Computer Science

Reference 12

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This paper cites ”Derandomizing polynomial identity tests means proving circuit lower bounds”.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Derandomizing polynomial identity tests means proving circuit lower bounds”

Reference 13

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Observation 5ae3d22d-9782-400f-9de7-3baa857af2c6 · outbound

This paper cites ”Michael A.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Michael A

Reference 14

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Reference 15

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Observation 669e1373-0afc-4692-8962-442856528ddf · outbound

This paper cites ”A quaternion QR algorithm.” Numerische Mathematik 55 (1989): 83-95.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”A quaternion QR algorithm.” Numerische Mathematik 55 (1989): 83-95

Reference 16

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This paper cites ”Horner’s method of approximation anticipated by Ruffini.” (1911): 409-414.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Horner’s method of approximation anticipated by Ruffini.” (1911): 409-414

Reference 17

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Observation 36f21786-e400-47a9-be83-0eb0b6f42408 · outbound

This paper cites ”The Fifteen Puzzle—A New Approach through Hybridizing Three Heuristics Methods.” Computers 12.1 (2023): 11.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The Fifteen Puzzle—A New Approach through Hybridizing Three Heuristics Methods.” Computers 12.1 (2023): 11

Reference 18

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Observation 4683f929-c1df-40be-b0bb-204ecaa93c45 · outbound

This paper cites Approximately Optimal Search on a Higher-dimensional Sliding Puzzle.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Approximately Optimal Search on a Higher-dimensional Sliding Puzzle

Reference 19

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This paper cites Precise numerical methods using C++.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Precise numerical methods using C++

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Observation 482161a6-8e7d-41c8-8908-c260c1faa4bb · outbound

This paper cites Introduction to precise numerical methods.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Introduction to precise numerical methods

Reference 21

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The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

Reference 22

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Observation 438711ed-73eb-4a6e-9634-fabc4c46b9ea · outbound

This paper cites ”A new look at the fifteen puzzle.” Mathematics Magazine 40.4 (1967): 171-174.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”A new look at the fifteen puzzle.” Mathematics Magazine 40.4 (1967): 171-174

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This paper cites ”A modern treatment of the 15 puzzle.” The American Mathematical Monthly 106.9 (1999): 793-799.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”A modern treatment of the 15 puzzle.” The American Mathematical Monthly 106.9 (1999): 793-799

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Observation 0e14ed3a-08f8-457c-a5a0-7446f651f3d3 · outbound

This paper cites ”Sliding Puzzles Gym: A Scalable Benchmark for State Representation in Visual Reinforcement Learning.” arXiv preprint arXiv:2410.14038 (2024).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Sliding Puzzles Gym: A Scalable Benchmark for State Representation in Visual Reinforcement Learning.” arXiv preprint arXiv:2410.14038 (2024)

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Observation a6eaa3f3-8131-4dfa-9b43-5cd08c18bd00 · outbound

This paper cites ”Some numerical methods for locating roots of polynomials.” Quarterly of Applied Mathe- matics 3.2 (1945): 89-105.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Some numerical methods for locating roots of polynomials.” Quarterly of Applied Mathe- matics 3.2 (1945): 89-105

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This paper cites ”Unmasking Dunning-Kruger Effect in Visual Reasoning & Judg- ment.” IEEE Transactions on Visualization and Computer Graphics (2024).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Unmasking Dunning-Kruger Effect in Visual Reasoning & Judg- ment.” IEEE Transactions on Visualization and Computer Graphics (2024)

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Observation b8d26b4f-f84e-4877-8885-809475d53f17 · outbound

This paper cites Numerical Methods for Roots of Polynomials-Part II.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Numerical Methods for Roots of Polynomials-Part II

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Observation e4765f02-38b8-4322-bbdb-faafa17e3020 · outbound

This paper cites ”Global convergence of the basic QR algorithm on Hessenberg matrices.” Mathematics of Computation 22.104 (1968): 803-817.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Global convergence of the basic QR algorithm on Hessenberg matrices.” Mathematics of Computation 22.104 (1968): 803-817

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Observation f5c57411-e10c-48db-8222-c7cdebebdba2 · outbound

This paper cites ”The 15 puzzle: how it drove the world crazy.” The puzzle that started the craze of (1880).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The 15 puzzle: how it drove the world crazy.” The puzzle that started the craze of (1880)

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Observation 07edcb39-8fc7-43df-8ab0-a87f409c26a7 · outbound

This paper cites ”Depth-first iterative-deepening: An optimal admissible tree search.” Artificial intelligence 27.1 (1985): 97-109.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Depth-first iterative-deepening: An optimal admissible tree search.” Artificial intelligence 27.1 (1985): 97-109

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This paper cites ”Computational complexity of puzzles and related topics.” Interdisciplinary Information Sciences 29.2 (2023): 119-140 28 R.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Computational complexity of puzzles and related topics.” Interdisciplinary Information Sciences 29.2 (2023): 119-140 28 R

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This paper cites ”Open problems related to quantum query complexity.” ACM Transactions on Quantum Computing 2.4 (2021): 1-9.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Open problems related to quantum query complexity.” ACM Transactions on Quantum Computing 2.4 (2021): 1-9

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This paper cites ”Quantum computational complexity from quantum information to black holes and back.” The European Physical Journal C 82.2 (2022): 128.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Quantum computational complexity from quantum information to black holes and back.” The European Physical Journal C 82.2 (2022): 128

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This paper cites ”DSolving: a novel and efficient intelligent algorithm for large-scale sliding puzzles.” Journal of Experimental & Theoretical Artificial Intelligence 29.4 (2017): 809-822.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”DSolving: a novel and efficient intelligent algorithm for large-scale sliding puzzles.” Journal of Experimental & Theoretical Artificial Intelligence 29.4 (2017): 809-822

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Observation f2e8bd4c-f93f-4cd6-bdc9-903ff4ce52e3 · outbound

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The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Large-scale parallel breadth-first search.” AAAI

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The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

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Observation ecd785f7-6ec8-44b0-953f-8e31634589da · outbound

This paper cites ”On Computing Makespan-Optimal Solutions for Generalized Sliding-Tile Puzzles.” Proceedings of the AAAI Conference on Artificial Intelligence.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”On Computing Makespan-Optimal Solutions for Generalized Sliding-Tile Puzzles.” Proceedings of the AAAI Conference on Artificial Intelligence

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Observation 37335d3b-e4a0-4838-9055-68bc1339677c · outbound

This paper cites ”Geometric complexity theory.” An approach (2007).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Geometric complexity theory.” An approach (2007)

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The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

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Observation ad79c611-d3f1-4838-a9b2-cce656b683a4 · outbound

This paper cites ”P, NP and mathematics–a computational complexity perspective.” Proceedings of the ICM.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”P, NP and mathematics–a computational complexity perspective.” Proceedings of the ICM

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Observation b850b319-ffb9-4798-a34e-042026542fca · outbound

This paper cites ”A short history of computational complexity.” Bulletin of the EATCS 80.01 (2003): 2003.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”A short history of computational complexity.” Bulletin of the EATCS 80.01 (2003): 2003

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Observation 0febc4b7-3c3f-4ae4-8eee-1930e0cee30b · outbound

This paper cites ”The P versus NP problem.” Clay Mathematics Institute 2.6 (2000): 3.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The P versus NP problem.” Clay Mathematics Institute 2.6 (2000): 3

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This paper cites ”The importance of the P versus NP question.” Journal of the ACM (JACM) 50.1 (2003): 27-29.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The importance of the P versus NP question.” Journal of the ACM (JACM) 50.1 (2003): 27-29

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This paper cites ”The P versus NP Problem, April 2000.” Clay Mathematics Institute at http://www.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The P versus NP Problem, April 2000.” Clay Mathematics Institute at http://www

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This paper cites ”Scheduled relaxation Jacobi method: improvements and applications.” Journal of Computational Physics 321 (2016): 369-413.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Scheduled relaxation Jacobi method: improvements and applications.” Journal of Computational Physics 321 (2016): 369-413

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Observation 37a0fa65-4132-49cc-b351-9346f3c2eb8b · outbound

This paper cites ”Parallel multigrid smoothing: polynomial versus Gauss–Seidel.” Journal of Computational Physics 188.2 (2003): 593-610.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Parallel multigrid smoothing: polynomial versus Gauss–Seidel.” Journal of Computational Physics 188.2 (2003): 593-610

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Observation 1c4b58d4-ab26-4db2-bb44-3b8fa0c9dbc9 · outbound

This paper cites Pulliam, and David W.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Pulliam, and David W

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Observation d9154366-a352-476c-a985-9af9407e00d1 · outbound

This paper cites C., and R.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity C., and R

Reference 50

Resolution: malformed identifier; raw_fallback, observed 2026-08-10T19:40:47.772899Z

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Observation e4ab4698-11d8-430e-84bb-ef962f541f9e · outbound

This paper cites ”Reheating and thermalization, linear vs.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Reheating and thermalization, linear vs

Reference 51

Resolution: verified exact; raw_fallback, observed 2026-08-10T19:40:47.169735Z

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Observation 952c2349-1cc4-4a2d-acda-27f738c9c4a1 · outbound

This paper cites an unresolved cited work.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

Reference 52

Resolution: unresolved; raw_fallback, observed 2026-08-10T19:40:47.760953Z

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Observation 2e17e959-998c-4b2d-b8ab-dbfd74c3e9e0 · outbound

This paper cites ”The general theory of relaxation methods applied to linear systems.” Proceedings of the Royal Society of London.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The general theory of relaxation methods applied to linear systems.” Proceedings of the Royal Society of London

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.749377Z

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Observation a8974b29-272b-48dd-9ae3-35f70a4b5a58 · outbound

This paper cites an unresolved cited work.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-08-10T19:40:47.735995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c64e6bae-679e-4aaa-a326-33107778bd37 · outbound

This paper cites ”Francis’s algorithm.” The American Mathematical Monthly 118.5 (2011): 387-403.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Francis’s algorithm.” The American Mathematical Monthly 118.5 (2011): 387-403

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.724436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7dce5430-33d8-4486-b71d-c84955bb4f73 · outbound

This paper cites ”The Compendious Book on Calculation by Completion and Balancing, al-Khw¯ arizm ¯ ı.” English Translation.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The Compendious Book on Calculation by Completion and Balancing, al-Khw¯ arizm ¯ ı.” English Translation

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.711303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d50c82f2-331c-4269-938d-f46f169c5c5e · outbound

This paper cites Richard Witmer, and Oystein Ore.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Richard Witmer, and Oystein Ore

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.698679Z

Source-reported events for the cited work

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Observation 67f64a18-d37a-4451-b402-61d0b5ae419b · outbound

This paper cites an unresolved cited work.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-10T19:40:47.686458Z

Source-reported events for the cited work

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Observation a8b35184-b019-4dbc-b6cd-1710a1aae3eb · outbound

This paper cites ”Sur les conditions de r´ esolubilit´ e des ´ equations par radicaux.” Journal de math´ ematiques pures et appliqu´ ees 11 (1846): 417-444.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Sur les conditions de r´ esolubilit´ e des ´ equations par radicaux.” Journal de math´ ematiques pures et appliqu´ ees 11 (1846): 417-444

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.674861Z

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Observation 5198feba-f0a6-4526-80cf-572822fb322f · outbound

This paper cites General recursion theory.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity General recursion theory

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.663690Z

Source-reported events for the cited work

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Observation 853ff4a8-7646-45ba-abb8-5c31f4a3dc34 · outbound

This paper cites ”Numerical solution of multivariate polynomial systems by homotopy continuation methods.” Acta numerica 6 (1997): 399-436.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Numerical solution of multivariate polynomial systems by homotopy continuation methods.” Acta numerica 6 (1997): 399-436

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.652226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 001f9c2d-c9a2-49b0-9c27-18b1efd77cd4 · outbound

This paper cites C., and James A.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity C., and James A

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.641660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e30b4aa3-7662-4131-ac8d-d36a52d2a18f · outbound

This paper cites ”Numerical polynomial homotopy continuation method and string vacua.” Advances in High Energy Physics 2011.1 (2011): 263937.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Numerical polynomial homotopy continuation method and string vacua.” Advances in High Energy Physics 2011.1 (2011): 263937

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.631000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 352fbafe-d286-4b13-9d74-d75f1ba6aead · outbound

This paper cites Introduction to numerical continuation methods.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Introduction to numerical continuation methods

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.619087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f0795b90-ac13-4460-a7cc-8b9703b7df44 · outbound

This paper cites ”PHCPACK: A general-purpose solver for polynomial systems by homotopy continuation.” Preprint (1997).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”PHCPACK: A general-purpose solver for polynomial systems by homotopy continuation.” Preprint (1997)

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.607723Z

Source-reported events for the cited work

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Observation 6cbe1509-9cb5-4bbe-acca-09fd5db0761a · outbound

This paper cites ”On the Ruffini–Abelian theorem.” (1896): 200-221.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”On the Ruffini–Abelian theorem.” (1896): 200-221

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.594787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d35727bc-da94-4d16-990d-c80b7ae23bc4 · outbound

This paper cites M´ emoire sur les ´ equations alg´ ebriques, o` u on demontre l’impossibilit´ e de la r´ esolution de l’´ equation g´ en´ erale du cinqui` eme d´ egr´ e.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity M´ emoire sur les ´ equations alg´ ebriques, o` u on demontre l’impossibilit´ e de la r´ esolution de l’´ equation g´ en´ erale du cinqui` eme d´ egr´ e

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.582565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1fac82ca-f8fd-4e1d-96da-fe8acfaebd46 · outbound

This paper cites Sidney, et al.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Sidney, et al

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.570305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 75ac4742-d548-4c84-abb9-a6fe9f6408ec · outbound

This paper cites ”Newton’s method in practice: Finding all roots of polynomials of degree one million efficiently.” Theoretical Computer Science 681 (2017): 146-166.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Newton’s method in practice: Finding all roots of polynomials of degree one million efficiently.” Theoretical Computer Science 681 (2017): 146-166

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.558331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a1cf7bb1-a563-47b7-9805-8623a5521322 · outbound

This paper cites E., and R.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity E., and R

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.546314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation eb7ab4eb-6f1b-4ed8-8664-f5486dda67b7 · outbound

This paper cites ”SYSTEM OF LINEAR ALGEBRAIC EQUATIONS AND METHODS OF THEIR SO- LUTION.” Multidisciplinary Journal of Science and Technology 4.1 (2024): 39-44.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”SYSTEM OF LINEAR ALGEBRAIC EQUATIONS AND METHODS OF THEIR SO- LUTION.” Multidisciplinary Journal of Science and Technology 4.1 (2024): 39-44

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.535440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 63efc47d-a78f-47aa-b30e-108cf5a3d1ec · outbound

This paper cites ”Solution of a System of Neutrosophic Linear Algebraic Equation by LU Decomposition Method.”.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Solution of a System of Neutrosophic Linear Algebraic Equation by LU Decomposition Method.”

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.523891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cee07418-f7d2-4a11-8ece-44ce1238cd16 · outbound

This paper cites an unresolved cited work.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Unresolved cited work

Reference 73

Resolution: unresolved; raw_fallback, observed 2026-08-10T19:40:47.512602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1488d8d6-f3fb-4e7a-92b6-45685cc734f1 · outbound

This paper cites ”Implicit schemes and LU decompositions.” Mathematics of Computation 37.156 (1981): 385-397.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Implicit schemes and LU decompositions.” Mathematics of Computation 37.156 (1981): 385-397

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.500388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b030979e-4a65-406d-8f4e-f78dd40ad698 · outbound

This paper cites ”Distributed localization using Levenberg-Marquardt algorithm.” Eurasip journal on advances in signal processing 2021 (2021): 1-26.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Distributed localization using Levenberg-Marquardt algorithm.” Eurasip journal on advances in signal processing 2021 (2021): 1-26

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.488361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 97e31011-c4f7-4561-8138-c6cef14607ff · outbound

This paper cites ”Improved computation for Levenberg–Marquardt training.” IEEE transactions on neural networks 21.6 (2010): 930-937.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Improved computation for Levenberg–Marquardt training.” IEEE transactions on neural networks 21.6 (2010): 930-937

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.476163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4ee5611c-de24-4f0b-9cb3-6d24b49fc852 · outbound

This paper cites ”The levenberg-marquardt algorithm.” Tutoral on LM algorithm 11.1 (2004): 101-110.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”The levenberg-marquardt algorithm.” Tutoral on LM algorithm 11.1 (2004): 101-110

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.464329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 01f42713-8180-45b0-a2b5-0d8a458e7532 · outbound

This paper cites ”A modified Newton method for solving non-linear algebraic equations.” Journal of Marine Science and Technology 17.3 (2009): 9.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”A modified Newton method for solving non-linear algebraic equations.” Journal of Marine Science and Technology 17.3 (2009): 9

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.452417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f488cfde-edb3-4b1d-a5d1-6f702ae2c295 · outbound

This paper cites ”Numerical experience with Newton-like methods for nonlinear algebraic systems.” Computing 58.1 (1997): 69-89.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Numerical experience with Newton-like methods for nonlinear algebraic systems.” Computing 58.1 (1997): 69-89

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.440356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4f98f1b0-02f1-483e-ad38-9d6c5d863671 · outbound

This paper cites ”Practical quasi-Newton methods for solving nonlinear systems.” Journal of computa- tional and Applied Mathematics 124.1-2 (2000): 97-121.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Practical quasi-Newton methods for solving nonlinear systems.” Journal of computa- tional and Applied Mathematics 124.1-2 (2000): 97-121

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.427098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 62519ee0-e810-46b0-93f3-3cd09b141a03 · outbound

This paper cites Thermodynamic Perspectives on Computational Complexity: Exploring the P vs. NP Problem.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity Thermodynamic Perspectives on Computational Complexity: Exploring the P vs. NP Problem

Reference 82

Resolution: verified exact; local_arxiv, observed 2026-08-10T19:40:47.063964Z

Source-reported events for the cited work

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Observation 66b63b59-1322-48ed-bae2-f0752ec61514 · outbound

This paper cites ”Thermodynamic Perspectives on Computational Complexity.” Thermodynamic Perspectives on Computational Complexity.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Thermodynamic Perspectives on Computational Complexity.” Thermodynamic Perspectives on Computational Complexity

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.415206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5ae85fd6-92e3-4735-947a-93ddce399033 · outbound

This paper cites ”On computable numbers, with an application to the Entscheidungsproblem.” J.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”On computable numbers, with an application to the Entscheidungsproblem.” J

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.403251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 920ca36c-9539-4923-baa4-8e22e29e4487 · outbound

This paper cites ”P vs NP.” (2014).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”P vs NP.” (2014)

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.392288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 678cbc47-e3a3-48b1-b633-94d540f13b79 · outbound

This paper cites ”On the P versus NP Problem.” (2024).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”On the P versus NP Problem.” (2024)

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.380894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 35b6c4ae-d636-48dd-80a6-7812cc5dabb5 · outbound

This paper cites ”NP on Logarithmic Space.” (2023).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”NP on Logarithmic Space.” (2023)

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.368989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d67f28d1-a669-4da2-8af7-c4e5a89a06a9 · outbound

This paper cites ”Hard problems of algebraic geometry codes.” IEEE Transactions on Information Theory 54.1 (2008): 402-406.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Hard problems of algebraic geometry codes.” IEEE Transactions on Information Theory 54.1 (2008): 402-406

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.357716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cb15f480-23a7-410a-b7f3-eb95c14a48e9 · outbound

This paper cites ”Parallel computation for well-endowed rings and space-bounded probabilistic machines.” Information and control 58.1-3 (1983): 113-136.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Parallel computation for well-endowed rings and space-bounded probabilistic machines.” Information and control 58.1-3 (1983): 113-136

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.345834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 27bcb3d7-49e2-4df6-af77-00befe0c868b · outbound

This paper cites P, NP, and NP-Completeness: The basics of computational complexity.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity P, NP, and NP-Completeness: The basics of computational complexity

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.889148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cf445cda-ba52-43eb-a4a0-0364b532f26c · outbound

This paper cites ”Evaluation of polynomials by computer.” Communications of the ACM 5.12 (1962): 595-599.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Evaluation of polynomials by computer.” Communications of the ACM 5.12 (1962): 595-599

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.331205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 64fe14bb-180d-4203-ad80-cdb248efae6c · outbound

This paper cites ”Another new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree.” (1983).

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Another new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree.” (1983)

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.318718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 81989dca-3ef6-4c01-a8e4-91636f0c0832 · outbound

This paper cites ”Gaussian elimination.” Wiley Interdisciplinary Reviews: Computational Statistics 3.3 (2011): 230-238.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Gaussian elimination.” Wiley Interdisciplinary Reviews: Computational Statistics 3.3 (2011): 230-238

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.305814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dcaa1cd7-61de-41b1-bf27-cdead8e1548d · outbound

This paper cites ”Scaling for numerical stability in Gaussian elimination.” Journal of the ACM (JACM) 26.3 (1979): 494-526.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Scaling for numerical stability in Gaussian elimination.” Journal of the ACM (JACM) 26.3 (1979): 494-526

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.293550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7a8995e5-d100-463f-a0bd-194a4eecaa51 · outbound

This paper cites ”On some pivotal strategies in Gaussian elimination by sparse technique.” SIAM Journal on Numerical Analysis 17.1 (1980): 18-30.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”On some pivotal strategies in Gaussian elimination by sparse technique.” SIAM Journal on Numerical Analysis 17.1 (1980): 18-30

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:40:47.281205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ac3125f7-5178-45ae-9b94-f66d119eeaa8 · outbound

This paper cites ”Gaussian elimination: when is scaling beneficial?.” Linear algebra and its applications 162 (1992): 309-324.

The sliding tile puzzle, roots to polynomials, and $\textbf{P}$ vs. $\textbf{NP}$ complexity ”Gaussian elimination: when is scaling beneficial?.” Linear algebra and its applications 162 (1992): 309-324

Reference 96

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