Asymptotic Stability, Recursive Boost Dynamics, and Precision Boundaries in a Lorentz-Inspired Growth Protocol
Executive Summary
This white paper formalizes the mathematical, computational, and architectural foundations of a nonlinear recursive protocol whose growth behavior is governed by a Lorentz-style boost function. The system is intentionally designed to operate near—but never cross—mathematical singularities and floating-point precision limits.
Core Principles
- Asymptotic Constraint: A hard clamp at
0.999prevents singularity conditions. - Recursive Feedback: Growth factors recursively amplify future state transitions.
- Precision Boundary Awareness: IEEE-754 limitations are treated as governed architectural thresholds.
- Deterministic Safety: The protocol intentionally avoids undefined runtime states.
Recursive State Equation
s_{n+1} = s_n * γ(s_n)
γ(s_n) = 1 / sqrt(1 - (g * r(s_n))^2)
r(s_n) = min( s_n / (1 + s_n), 0.999 )The recursive boost architecture creates super-exponential divergence characteristics while remaining bounded by asymptotic safety constraints.
IEEE-754 Boundary Analysis
The protocol intentionally approaches the representational boundaries of double-precision floating-point systems without crossing into NaN or overflow conditions.
Maximum finite float ≈ 1.797e308
Precision boundary ≈ 2^53Protocol Governance
By introducing explicit safety margins, bounded recursive amplification, and deterministic asymptotic controls, the architecture enables high-pressure computational systems to remain operational at near-maximum capacity without entering mathematically undefined states.
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