Books

What if mathematics could be built on structure rather than sets?

Book I launches the Panta Rhei series by constructing Category τ from nine axioms on a small, explicit signature. The result is a foundational framework that is categorical (unique up to isomorphism), rigid (no nontrivial automorphisms), and designed to be structurally decidable in...

What does “holomorphic” mean in a universe built from categorical structure?

Book II develops a full holomorphic function theory on the canonical fibered product

τ³ = τ _f τ²—a rigid, self-calibrated mathematical universe derived from the same generators and axioms introduced in Book I. Here, τ³ carries a discrete quaternionic structure and a...

How do the great “millennium themes” change when you insist on finite structure, explicit cutoffs, and spectral control?

Book III offers a τ-effective spectral reading of seven major mathematical themes—framed as eight “lenses” that keep scope and claims disciplined. Rather than presenting sweeping one-line solutions, the book builds a shared...

What if quantum mechanics, particles, atoms, and chemistry were not postulates—but consequences of geometry?

Book IV turns the Panta Rhei program toward the microcosm: quantum mechanics, the particle spectrum, atomic structure, forces, and chemical bonding. Its core thesis is bold and sharply stated: microphysics emerges from the fiber τ² in the...

What if time, gravity, thermodynamics, fluids, and cosmology were not separate theories—but different aspects of one base geometry?

Book V turns the Panta Rhei program toward the macrocosm: time, gravitation, thermodynamics, fluid dynamics, collective matter, astrophysics, and cosmology. Its core thesis mirrors Book IV—now “above” rather than “...

What if life is not an accident—but the categorical structure of τ³ recognizing itself?

Book VI extends the Panta Rhei program from physics into life, mind, and meaning. Its core thesis is explicitly structural: life is not primarily “metabolism,” “reproduction,” or “information processing” (each of which has non-living counterexamples). Instead,...

What happens when you treat relations, transformations, and coherence—not “things”—as the basic vocabulary of reality?

Book VII brings the Panta Rhei program to its philosophical culmination. Using the categorical framework developed across Books I–VI (τ, τ³, the lemniscate boundary 𝕃, and the guiding idea that global structure arises from gluing...