INDEPENDENT RESEARCH
Root constructions, nonlinear systems and formal verification. A place to read the research, explore the methods and examine their limitations.
Open-access papers · downloadable code · clearly scoped proofs
01 / PUBLICATIONS
A ninth-order cubic construction and real-degree root solvers
Positive-root constructions: a fifth-order arc, a nested-radical support of order nine in the cubic case, and real-degree enclosures.
02 / SOFTWARE
One Python file.
One solver engine.
A solver for real and complex nonlinear systems, without requiring analytic derivatives. Integrated exploration, controlled evaluation budgets and NumPy as its only external dependency.
# Python + NumPy
from pandrosion_449_standalone import solve, Options
result = solve(
lambda z: (z - 5) * (z - 7) * (z - 12),
[8],
Options(mode="root"),
)
print(result.x, result.root_success)03 / APPROACH
Connect explicit geometric objects to iteration formulas, then state their domain of validity.
Distinguish the protocol, residual, evaluation budget and cases that still fail.
Distinguish mathematical results checked in Lean, written proofs and numerical observations.
The targeted mathematical proofs do not verify the Python program from end to end or guarantee convergence for every system.
Read the scope of the proofs →