Juncai Zhou

From Reactive Agents to a Cross-Universe Civilization: Emergent Communication, Institutions, Science, and Invention in a Deterministic Multi-Agent Simulation (v16.0)

This record accompanies the v16.0 release of a deterministic multi-agent simulation in which a small society of artificial agents develops symbolic communication, social institutions, written records, mathematics, proof, law, experimental science, energy technology, automation, a...

The Hybrid Group ⊕_γ over ℝ and 𝔽_p: Face Operations, Transport Rigidity, Gradient-free Learning, and a Fully-Resident Software Protection Loader

This work develops a self-contained algebraic framework based on the hybrid group operator a ⊕_γ b = a + b + γ ab, defined simultaneously on real vector spaces and prime fields. We establish the face-operation calculus (M, A, D, E faces), prove the dual-derivative power theorem w...

The Hyperoperation Continuum: Existence, Uniform Construction, and Complete Classification of Continuous Extensions

We address the continuous extension problem for the hyperoperation hierarchy: given a base g>0, extend the discrete height index of exponentiation, tetration, pentation, hexation, and beyond to a real parameter. A single strip construction S_F[s](x)=F^{\lfloor x\rfloor}(s(\{x\}))...

The Hyperoperation Continuum: Existence, Uniform Construction, and Complete Classification of Continuous Extensions

We address the continuous extension problem for the hyperoperation hierarchy: given a base g>0, extend the discrete height index of exponentiation, tetration, pentation, hexation, and beyond to a real parameter. A single strip construction S_F[s](x)=F^{\lfloor x\rfloor}(s(\{x\}))...

Dual-Derivative Power Theorem: Group Homomorphic Structure on Hybrid Characteristic Abelian Groups

We define the hybrid characteristic Abelian group H_D(γ,p) = R^D × F_p^D with a unified nonlinear operator: a ⊕_γ b = a + b + γ·(a⊙b) acting simultaneously on real (characteristic 0) and finite field (characteristic p) components. We introduce the dual-derivative power operator D...