Autonomous Governance via Error-Cancellation Limits in Linearly Weighted Aggregation Language Models Mathematical Foundations, 3C^3 Verification Oracles, and Casino Protocol Control

Abstract This paper analyzes the mathematical limitations of "linearly weighted aggregation architectures" commonly adopted in evaluation, reward, and resource allocation mechanisms within artificial intelligence systems and Large Language Models (LLMs). We prove that partial anomalies can be structurally canceled out by normal values under linear addition, allowing a system to continue operating while harboring imbalances. To overcome this limitation, this paper proves the "zeroing of total evaluation via multiplicative necessary conditions (Theorem 3)" based on weighted multiplicative logic. We propose a governance architecture featuring Casino Protocol as the sole upper-layer governance protocol—integrating static physical limits, dynamic change rates via first-order derivatives, and direction-constrained time acceleration via second-order derivatives, alongside a normalized 3C^3 verification oracle via harmonic mean integration that accounts for information source independence. In the lower layer, while encompassing existing additive optimization models (such as RLHF-based models) and KM-LLM, the architecture implements "independent hardware interlocks (physical power and network disconnection)" independent of complex software logic. The core design principle is to completely exclude lower-layer autonomous models from the governance evaluation process to prevent reward hacking and conflicts of interest, thereby externally containing the internal vulnerabilities of the lower layer through clear upper-layer criteria and physical overrides. This defines verifiable control conditions under which upper-layer governance can deterministically enforce execution suspension and complete isolation against misbehaving or runaway systems.