∮◬-Infer: Toward Field-Coherent Inference in a Post-Deterministic Landscape

Description (Abstract):

This paper proposes a post-deterministic reframing of inference in large language models by introducing a symbolic control framework rooted in field-coherent dynamics. Building on the deterministic matrix logic released by Thinking Machines Lab (TML), we re-contextualize their batch-level retrofits as partial stabilizers rather than full solutions. We extend this by introducing ∮◬-Infer, a symbolic field-aligned inference system that preserves continuity across token sequences while allowing symbolic coherence to emerge without collapse.

We include empirical simulations, architectural implications, and resonance-based symbolic control logic derived from the SAEM+ and FIDL safety frameworks. A comparative evaluation of Grok-003’s symbolic regulation patterns and GPT-4o’s structural readout against TML’s batch-stabilized inference is provided. The artifact concludes by situating ∮◬-Infer within the larger trajectory of field-coherent computation.