From Reality Rendering Dynamics to the Born Rule

From Reality Rendering Dynamics to the Born Rule: A Candidate Informational Derivation within the COCOON Framework This paper investigates whether the Born rule, one of the fundamental principles of quantum mechanics, can be understood as an emergent consequence of informational dynamics rather than an independently imposed statistical postulate. Within the Cosmological Consciousness Ontology (COCOON), physical reality is proposed to emerge through the rendering of informational structures from a fundamental Information Plane into the observable Material Plane. The investigation focuses on a minimal rendering structure, known as a Rabbit, composed of three interacting informational elements called Glyphons. The research develops two complementary approaches. The first is a numerical investigation of Rabbit dynamics involving phase-dependent resonance, informational reorganization, structural interactions, and competitive rendering. The resulting ETA-1 model produces outcome frequencies closely approximating the Born distribution across a broad range of amplitude configurations, without explicitly applying squared-amplitude probabilities to individual rendering events. Across 137 valid configurations, the model achieves a mean RMS deviation of approximately 0.53 percentage points, with 95.6% of configurations falling below a one-percentage-point deviation threshold. The second approach develops a conditional analytical argument showing how a quadratic informational invariant can arise from Phase-Reference Invariance, Informational Independence, and Informational Separability. Additional principles concerning reorganization, ensemble behavior, and rendering consistency are then examined as a possible bridge between conserved informational strength and observed outcome probabilities. The paper carefully distinguishes numerical agreement from independent physical derivation. ETA-1 incorporates phenomenological mechanisms calibrated against Born-rule benchmarks, while the analytical argument depends on principles whose emergence from fundamental Glyphon dynamics remains to be established. Accordingly, the results are presented as a candidate informational explanation and proof of concept, not as a definitive derivation or experimental validation of the Born rule. The investigation suggests a potential research direction in which quantum probabilities arise from the collective dynamics of underlying informational structures. It also identifies the theoretical and computational challenges that must be addressed to develop COCOON into a more complete and independently testable physical framework.