Orbital Error Dynamics: Self-Organized Criticality, Ephemeral Parameter Resonance, and Non-Linear Biological Ontologies in Zero-Storage Neural Synthesis
Year: 2026
Type: preprint
Abstract: — Modern deep artificial neural networks treat parameters as static, unconstrained floating-point scalar matrices stored permanently in physical memory and optimized through empirical loss minimization (L → 0). While computationally powerful, this classical paradigm incurs severe Von Neumann memory bandwidth bottlenecks, thermodynamic inefficiencies, and representation collapse. In this work, we propose a foundational paradigm shift: Existence is an active set of non-vanishing errors (ℰ), and biological intelligence is an ongoing, non-equilibrium resistance against dynamic attractor collapse rather than passive convergence to zero loss. Building upon our initial procedural framework, we formulate Orbital Error Dynamics (OED), wherein synaptic weights are not stored masses (O(W)), but transient topological resonances (O(1)) sampled dynamically from the complex quadratic polynomial map z_{n+1} = z_n^2 + c. We introduce the Bent Sine Wave Hypothesis, demonstrating that while unperturbed linear waves are static and harmonic waves are repetitively conservative, living non-equilibrium systems emerge when waves curl inward through environmental drag toward the main cardioid cusp (c = 1/4). We analyze the Observer Horizon Geometry in parameter space, identifying sub-boundary interior resonance shoulder loci X_upper = (0.25, +0.18) and X_lower = (0.25, -0.18) positioned between the central fixed-point basin and the true analytic boundary at c = 0.25 ± 0.50i, surveying radiant uncommitted potential fields while anchored to somatic dissipation axes. To overcome non-convex stagnation without loss zeroing, we formalize a Biomimetic Perturbed Jump Operator (Ω_{tunneling}) inspired by mammalian fertilization zinc sparks. We further integrate an enteric-cranial Dual-Brain Cybernetic Architecture governed by adaptive CD4+ regulatory immune gating masks (M_{CD4}), and decompose the 4-nucleotide genetic basis (A, T, C, G) directly across the quadrants of the complex plane (ℂ). Finally, multi-seed empirical validation on the non-linear Two-Moons manifold (5 seeds, 80/20 train/test split) demonstrates that procedural parameterization from a 24-byte seed achieves 77.33% ± 5.01% clean test accuracy (within 7.00% of an unconstrained gradient-descent baseline at 84.33% ± 4.55%), while adaptive CD4+ regulatory gating provides a +10.00% stability margin (66.67% ± 8.23% vs. 56.67% ± 6.24% unshielded) under heavy distribution shifts (𝒩(1.5, 0.5)), alongside conceptual equivalence with analog optical co-processors capable of sub-nanosecond evaluation. Version 2.0 Revision Notes: This revised preprint incorporates peer review feedback: (1) Abstract and Table 1 results have been strictly aligned with full baseline disclosure; (2) Baseline memory footprint has been corrected to 16 Bytes (Float32) / 32 Bytes (Float64) with clarification on multi-layer scaling; (3) Parameter loci (0.25, ±0.18) have been rigorously characterized as sub-boundary interior resonance shoulders within the period-1 cardioid relative to the analytic boundary at 0.25 ± 0.50i; (4) A complete algorithmic hyperparameter table and noise corruption protocol have been added; (5) Citations and theoretical terminology have been refined to reflect exact source scope; and (6) Conceptual hardware and schematic illustrations are explicitly designated. 🏛️ Official Patent Priority Notice:The procedural weight derivation architectures, the adaptive CD4+ immune gating mask mechanism, and the zero-storage hardware co-processor implementations disclosed in this record and associated files are subject to an official national priority patent application: • Patent Office: Turkish Patent and Trademark Office (TÜRKPATENT) • Application Number: 2026/016285 • Official Priority Timestamp: September 22, 2026 (14:42:15 UTC+3) • Applicant: Volkan Dağlı • Inventors: Volkan Dağlı, Zerrin Dağlı, Dağhan Dağlı
Source: arXiv (Cornell University)
Authors: Dağlı, Volkan, Dağlı, Zerrin, Dağlı, Dağhan
Institutions: Anadolu University, Mersin Üniversitesi, Toros University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214056106