Inhaltsangabe: :: Library Catalog

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1. Verfasser:	Stone, Travis Raymond-Charlie
Format:	Recurso digital
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Veröffentlicht:	Zenodo 2026
Online-Zugang:	https://doi.org/10.5281/zenodo.19491090
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Geometric GPS for Quantum Momentum. Maps Hilbert space onto a 3D manifold using Alpha/Beta duality to track data trajectory and velocity deterministically.   Title: Recursive Phase-Space Manifolds (RPSM): A Deterministic Protocol for N=100 Qubit Kinematic Tracking and Data Sovereignty Author: Travis Raymond-Charlie Stone Affiliation: Stone Software Solutions Abstract This paper introduces the Recursive Phase-Space Manifold (RPSM), a post-Von Neumann data architecture that utilizes the Stone Equation to map high-dimensional Hilbert space coordinates onto a stable 3-axis matrix. Moving beyond the probabilistic limitations of gate-based quantum systems, RPSM establishes a N=100 Qubit-Analogue framework capable of tracking Geometric Trajectory and Velocity within a decentralized, "Server-Zero" runtime. This provides a deterministic bridge between theoretical quantum mechanics and the practical requirements of data sovereignty.   Section 1: Introduction to the N=100 Paradigm The primary challenge of quantum computing is dimensionality. A standard n=100 qubit system possesses a state space of 2100 complex amplitudes, rendering classical tracking impossible. The Stone-Shift: RPSM avoids exponential dimensionality growth by projecting N qubit analogues into N parallel geometric indices. By scaling to n=100, the RPSM engine creates a continuous, high-fidelity "Sheet of Datum." This allows a classical distributed system to verify the stability, health, and trajectory of complex information manifolds in real-time. Section 2: Structural Integrity and the Unitive Range RPSM utilizes a symmetric dual-list dictionary structure that replaces binary logic with a 4-Point Unitive Range. For each index k∈{1…100}: <ul> <li>Alpha State (αk ): Represents positive, Divergent field potential.</li> <li>Beta State (βk ): Represents negative, Convergent field potential.</li> </ul> This pairing ensures that Growth (α) and Stability (β) are balanced. In a decentralized network, this Unitive DualityallowsNode B to verify the "health" of a data signature from Node A by visually analyzing the resulting manifold for "Symmetry Turbulence." Section 3: The QCAD Operator and Kinematic Tracking The mapping of the unitive pairs into the 3D matrix is governed by the QCAD Recursive Operator (Q^ ). Optimized for n=100, Q^  uses super-exponential scaling factor (e±k) to establish a recursive spectrum of potential: Q^ =k=1∑100 (e+k⋅αk +e−k⋅βk ) By indexing variability (I) within a primary array, the RPSM engine tracks the kinematics of the n=100 manifold: 3.1 Trajectory (T) The geometric path of the 100-point system across the 3-axis matrix. This collapses complex data into an observable Topological Signature. 3.2 Modulation Velocity (V) The derivative of potential change relative to the index position: V=ΔIΔΦ Predicting the "momentum" of the data manifold provides advanced warning of stability changes (e.g., market volatility, network interference, or data corruption). Section 4: Utility and Decentralized Sovereignty The RPSM architecture provides original utility in decentralized, "Server-Zero" environments. <ul> <li>Symmetric Verification: Instead of transmitting raw, private data, a node transmits the Manifold Signature.Because the RPSM logic is deterministic, the recipient can verify the shape of the manifold and confirm data integrity without ever seeing the raw input.</li> <li>Error Diagnosis via Geometric Turbulence: At n=100, a single error in one qubit analogue manifests as visible Geometric Turbulence (a tear or spike in the "Sheet of Datum"). This allows for immediate visual debugging of complex distributed networks.</li> </ul> Section 5: Conclusion RPSM provides a mathematically rigorous, deterministic framework for simulating N=100 quantum states on classical systems. By treating information as a kinematic manifold rather than a probabilistic vector, the Stone Manifold Engine offers a robust protocol for the next generation of sovereign, symmetric, and decentralized data infrastructure.   The core QCAD operator is defined by a recursive summation that modulates a dynamic field function across multiple layers of feedback. At its center is P(x,t), representing the probabilistic or dynamic field function of a given state in space and time. This function is subjected to a summation from an initial state up to Lmax , which represents the maximum recursion depthor the total number of feedback layers in the system. Within this summation, the field is scaled by two opposing exponential forces: <ul> <li>The term e+k introduces divergence, signifying expansion, instability, or growth within the system.</li> <li>The term e−k introduces convergence, signifying stability, compression, or decay.</li> </ul> By combining these elements, the equation describes a recursive exponential system rather than a standard differential one, where the final state is an accumulation of balanced expansion and contraction across a defined depth of feedback loops.   Founder: Travis Raymond-Charlie Stone Stone Software Solutions LLC

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