Toward Thermodynamic Inversion of AI Scaling Laws: A Physics-Grounded Neuro-Symbolic Architecture via Semantic Eigenstate Graphs

Current artificial intelligence scaling laws are bounded by the thermodynamic limits of dense matrix multiplications, requiring exponential increases in energy for linear decreases in loss. Furthermore, the lack of ontological grounding in standard transformer architectures contributes to hallucination via at least two independent pathways: confabulation from ungrounded generation (a semantic graph failure) and user-induced hallucination from sycophantic relational pressure (a relational interface failure). In this theoretical paper, we outline a paradigm shift from statistical probability to thermodynamic optimization. By structuring knowledge as a densifying Semantic Eigenstate Graph rooted in fundamental physical constants, inference routing shifts from O(N2) matrix multiplications to O(log N) non-destructive topological traversals.

We mathematically demonstrate that as the graph densifies, the average degrees of separation decrease, allowing epistemic routing to asymptotically approach the Landauer limit of reversible computation. On standard SRAM, this yields a theoretical efficiency ratio of approximately 3 × 1011 relative to current transformer inference; on memristive hardware, the theoretical ceiling approaches 1015
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To bridge current continuous architectures with this discrete algebraic ideal, we introduce Trust Relational Coherence (TRC V8) as both the safety monitor and the computational routing layer—showing that these are the same computation seen from two directions. Under this unified framework, the safety overhead approaches zero because the safety computation is the routing computation. The critical unknowns—the densification exponent β and the routing resolution at practical concept vector count K—are identified as the highest-priority empirical targets.