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Substrate-Independent Topology Framework: Systems navigating high-dimensional state spaces converge on a small set of stable configurations whose positions are structurally determined — derivable from first principles

DAVID GOLD

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Preregistration of three predictions derived from the Substrate Independent Topology Framework (SITF) concerning topological error protection in quantum computing systems. Substrate-Independent Topology Framework proposes that systems navigating high-dimensional state spaces converge on a small set of stable configurations whose positions are structurally determined — derivable from first principles, not fitted to domain-specific data

DOI
10.17605/osf.io/7szua

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Preregistration of three predictions derived from the Substrate Independent Topology Framework (SITF) concerning topological error protection in quantum computing systems. Substrate-Independent Topology Framework proposes that systems navigating high-dimensional state spaces converge on a small set of stable configurations whose positions are structurally determined — derivable from first principles, not fitted to domain-specific data
Three predictions derived from the Substrate Independent Topology Framework (SITF) concerning topological error protection in quantum computing systems. The predictions are entered into the prior art record before examination of any experimental dataset against which they would be tested. The registration timestamp is the operative prior art date. The three predictions concern: (1) local noise suppression scaling in a superconducting qubit chain engineered to enforce Fibonacci state space structure; (3) the substrate-independent suppression ratio per encoding depth level in Fibonacci-structured quantum systems across hardware platforms; and (4) a hierarchy of topological protection quality indexed to the attractor value of the state space recursion, distinguishing Fibonacci-structured from Ising-structured quantum systems. Each prediction is specific enough to be falsified by existing or readily obtainable experimental data from current quantum hardware platforms. The generative architecture that produces these predictions is not disclosed in this document. This preregistration establishes priority for the phenomenological predictions — what the framework predicts, where, and at what numerical values — without revealing the structural logic that generates them. The two are legally distinct and maintained separately. Note on prediction numbering: This preregistration covers P-QC-01, P-QC-03, and P-QC-04. P QC-02 is held pending completion of the substrate translation derivation required to state it with the operational precision a preregistration demands. P-QC-05 is withheld per standing protocol.
This paper introduces the concept of Computational Substrate Independence, a theoretical framework designed to address the fundamental question of whether equivalent computational capabilities remain the same regardless of the underlying physical or software substrate. The core challenge lies in defining a rigorous criterion for determining when a computation, expressed in one form, can be faithfully replicated across radically different computational environments – encompassing classical computers, quantum computers, neuromorphic systems, and potentially entirely novel computational media. The paper lays out the key principles of this theory, focusing on the preservation of algorithmic information and the transformation rules necessary to achieve substrate independence. It explores the implications of this concept for various emerging computing paradigms and proposes a formalization of the necessary conditions for substrate-independent computation. The central argument posits that the essence of computation resides not in the specific implementation, but in the logical structure and information flow represented by the algorithm.
This paper investigates the synergistic relationship between high-dimensional topology and quantum algorithms. We explore how the inherent properties of high-dimensional topological spaces can be leveraged to enhance the efficiency and stability of quantum algorithms. The core focus is to develop novel optimization strategies predicated on topological constraints, resulting in improved performance compared to traditional approaches. The research utilizes a framework where high-dimensional topology serves as a guiding principle for algorithm design, ultimately aiming to create more robust and computationally effective quantum systems. The investigation will delve into the mathematical underpinnings of this connection, providing a theoretical foundation for practical application. This work contributes to the advancement of quantum algorithm design by offering a new perspective on how topology can impact quantum performance.
The Event Density (ED) framework provides a substrate-level account of quantum computation in which three substrate quantities—local multiplicity (the count of available participation pathways at the system’s endpoints), cross-endpoint connectivity (the substrate-mediated bandwidth that links them), and commitment-injection rate (the rate at which the environment forces individuation)—jointly determine whether quantum computation is possible. The Unresolved-Regime Characterization Theorem (UR-1) identifies three independently necessary conditions on these quantities, and the resulting QC operating window is given structurally by τ_QC = min(τ_(i), τ_(ii), τ_(iii)) over the three corresponding failure timescales. Each architectural platform binds on whichever timescale is shortest under its protection strategy. Three architectural classes—engineered-low-multiplicity (A) covering superconducting qubits, trapped ions, and gate-model photonics; global-geometric-rigidity (B) covering topological qubits and photonic Chern channels; and high-multiplicity-redundancy (C) covering bosonic codes and multi-timescale photonics—exhaust the substrate-allowed strategies for holding the operational regime. Error correction, dynamical decoupling, reservoir engineering, and hybrid architectures are derived as compositions or extensions of the three classes rather than new strategies. The multiplicity-cap function M unifies the classes as three projections of one substrate object, with platform-specific behavior obtained by specializing class-dependent parameters. The framework’s strongest output is cross-platform unification: the matter-wave quantum-classical boundary observed empirically at 140–250 kDa molecular mass and the multiplicity walls that limit qubit-system scaling are the same substrate-determined boundary projected onto two different platforms, evaluated at consistent values of one underlying substrate constant. Sharp predictions follow directly: superconducting platforms encounter a hard scaling ceiling unless they are composed with logical-qubit encoding; topological qubits can outrun this ceiling exponentially in the topological gap if topology engineering can deliver stable structures; redundancy-based architectures saturate at a substrate-determined correlation budget. Four classes of near-term experimental tests with explicit falsification conditions are specified. The structural form of the framework is derived from substrate primitives; specific numerical thresholds (the critical multiplicity, the correlation budget, the maximum stable topological gap, and the platform-specific wall locations) are downstream empirical calibrations rather than free parameters, with the empirical anchors that fix them identified explicitly. The verdict is architectural-level structural completeness with an explicit empirical-calibration roadmap: the substrate-level account of quantum computation is delivered, the predictions are sharp enough to be falsified by near-term measurements, and the calibration program that converts structural predictions into platform-specific numerical bounds is engineering-tractable rather than theoretically blocked.