Scale-Invariant Determinism: Algebraic Closure and Constant-Time $O(1)$ Territory Governance in the Base-3 Substrate

Conventional cybersecurity architectures degrade nonlinearly as network scale increases. Both binary allowlisting (1 / 0) and probabilistic machine-learning telemetry suffer from combinatorial rule explosion, centralized bandwidth saturation, and compounding epistemic uncertainty across large-scale deployments. This paper formalizes the Scalable Invariant property of the Base-3 Territory (B3T) architecture developed by VR Konstrukt Pty Ltd (ACN 696 473 935). By governing state transitions through the algebraically closed Balanced Ternary set {+1, 0, -1} under the Multiplicative Triadic Law (T = A x E x I x Phi), computational territories maintain identical mathematical determinism, fractal property inheritance, and constant-time O(1) local execution complexity whether operating on a single process register, an endpoint workstation, or a 100,000-node critical infrastructure grid. Executing 100% locally within an ultra-dense sub-3MB foundational footprint via Six-Part Cryptographic Behavioral Charters (FIPS 180-4 SHA-256), the architecture enforces zero-absorption containment (state 0) and deterministic revocation (state -1) in sub-milliseconds alongside existing antivirus and VPN stacks without cloud latency or central server bottlenecks. Licensing & IP Notice: Foundational mathematical specifications and open-source Base-3 Substrate reference implementations are governed by the GNU Affero General Public License v3.0 (AGPLv3). Commercial runtime implementations, including Base-3 Territory (B3T) Mobile, B3T Windows, and B3T Defender, are proprietary commercial software licensed exclusively by VR Konstrukt Pty Ltd ([email protected]).