Jonathan ƒ(n) Reed

Goodbye to (ϕ) - Replacing the Galvani Potential with a Boltzmann Geometric State Equation for Next-Gen Battery Operation and Reduced-Gravity Molten Salt Electrolysis (Lean 4 and Python)

Classical electrochemistry relies on the macroscopic Galvani potential ($\phi$) to account for inner-phase electrical states, treating it as an unmeasurable primitive or operational convention. Here, we demonstrate that $\phi$ is an emergent property rather than an independent va...

Riemann Minimal Entropy Collapse - A Topological Proof by Contradiction of Non-Trivial Zeros via Spectral Rigidity in Lean 4 & Comparator

This paper presents a machine verified topological proof by contradiction of the Riemann Hypothesis via spectral rigidity. Departing from brute-force numerical sweeps and isolated analytic approximations, we establish a foundational topological equivalence ($\infty \sim 0$ on ${R...

Riemann Minimal Entropy Collapse - A Topological Proof by Contradiction of Non-Trivial Zeros via Spectral Rigidity in Lean 4 & Comparator

This paper presents a machine verified topological proof by contradiction of the Riemann Hypothesis via spectral rigidity. Departing from brute-force numerical sweeps and isolated analytic approximations, we establish a foundational topological equivalence ($\infty \sim 0$ on ${R...

Algebraic Closure and Composite Chord Symmetry of the Regular Nonagon via Cyclotomic Polynomial Resultants in Lean 4 with Comparator

Standard treatments of regular polygons rely heavily on continuous transcendental functions, obscuring the underlying discrete algebraic structures. This paper presents a first-principles algebraic derivation that isolates the composite $3 \times 3$ symmetry of the regular nonago...

Computer-Assisted Resolution of the Direct Product Conjecture via Kullback-Leibler (KL) Divergence Information Tensorization and Pinsker-Bounded Simulation Operators (Cloud Security)

Using the Lean 4 interactive theorem prover, this paper presents a machine-verified structural resolution of the Direct Product Conjecture in communication complexity. Extending Hilbert space orthogonal projections and ANOVA-Hoeffding decompositions beyond linear variance, we bri...

Computer-Assisted Resolution of the Direct Product Conjecture via Kullback-Leibler (KL) Divergence Information Tensorization and Pinsker-Bounded Simulation Operators (Cloud Security)

Using the Lean 4 interactive theorem prover, this paper presents a machine-verified structural resolution of the Direct Product Conjecture in communication complexity. Extending Hilbert space orthogonal projections and ANOVA-Hoeffding decompositions beyond linear variance, we bri...

Geometric Exclusion of Smooth Solutions to Navier-Stokes Equations at Stationary Right-Angles under No-Slip Boundary Conditions in Lean 4

This paper presents a proof by contradiction demonstrating that smooth solutions to the three dimensional incompressible Navier-Stokes equations do not exist for all time. Our argument is a direct consequence of a specific no-slip boundary condition: a stationary right-angle corn...

Vizing's Impossible Descent - Boundary Analysis and Formal Proof by Contradiction of Vizing's Conjecture in Lean 4 via the Impossibility of Minimal Counterexample Descent

Traditional approaches to Vizing’s conjecture have long relied on asymptotic bounds, structural invariants, and local density heuristics, frequently stalling against the combinatorial explosion of graph products. This paper shatters those bottlenecks. By combining integrality gap...