Size-Invariant Performance in Cognitive Damping Systems: Definitive Empirical Proof of Internal Temporal Coherence (τ-Invariance) and Absolute O(1) Scalability
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2025
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| author | Al-Mayahi, Abdulsalam |
| author_facet | Al-Mayahi, Abdulsalam |
| contents | <p>We present a definitive empirical validation of the Union Dipole Theory (UDT) through implementation of the Union Dipole Computing Engine (UDCE), a meta-cognitive control system founded on Internal Temporal Coherence (τ-Invariance). Using a large-scale τ-Blocks architecture tested across system sizes B = 10 to 10⁵, we show that the global control efficacy remains strictly constant (mean = 72.0637 %, σ = 0.0004 %), establishing the first reproducible evidence of O(1) performance scalability in a nonlinear dynamical network.</p> <p>The wall-clock computational cost grows linearly with B, yet the performance level remains invariant, proving that control efficacy depends on the internally regulated time-field τ rather than external dimensionality. Comparative benchmarking against a tuned PID controller reveals a 7.55-fold improvement under equal decision complexity. Analytical derivation confirms that the decoupling between external complexity O(B) and internal performance O(1) arises from a conservation of effective computational energy per τ-cycle. These results constitute the first operational framework for the hypothesised Union Dipole Particle (UDP) and provide experimental support for UDT’s claim that internal time—not external spacetime—governs the scalability of physical and computational processes.</p> <p>Note. The computational framework described herein is protected under a filed UK Patent Application.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17340532 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Size-Invariant Performance in Cognitive Damping Systems: Definitive Empirical Proof of Internal Temporal Coherence (τ-Invariance) and Absolute O(1) Scalability Al-Mayahi, Abdulsalam <p>We present a definitive empirical validation of the Union Dipole Theory (UDT) through implementation of the Union Dipole Computing Engine (UDCE), a meta-cognitive control system founded on Internal Temporal Coherence (τ-Invariance). Using a large-scale τ-Blocks architecture tested across system sizes B = 10 to 10⁵, we show that the global control efficacy remains strictly constant (mean = 72.0637 %, σ = 0.0004 %), establishing the first reproducible evidence of O(1) performance scalability in a nonlinear dynamical network.</p> <p>The wall-clock computational cost grows linearly with B, yet the performance level remains invariant, proving that control efficacy depends on the internally regulated time-field τ rather than external dimensionality. Comparative benchmarking against a tuned PID controller reveals a 7.55-fold improvement under equal decision complexity. Analytical derivation confirms that the decoupling between external complexity O(B) and internal performance O(1) arises from a conservation of effective computational energy per τ-cycle. These results constitute the first operational framework for the hypothesised Union Dipole Particle (UDP) and provide experimental support for UDT’s claim that internal time—not external spacetime—governs the scalability of physical and computational processes.</p> <p>Note. The computational framework described herein is protected under a filed UK Patent Application.</p> |
| title | Size-Invariant Performance in Cognitive Damping Systems: Definitive Empirical Proof of Internal Temporal Coherence (τ-Invariance) and Absolute O(1) Scalability |
| url | https://doi.org/10.5281/zenodo.17340532 |