The paper argues that reasoning—particularly long chain-of-thought reasoning—is not a linear symbolic procedure but a structured, metastable configuration analogous to a macromolecule. Such configurations are stabilized by internal logical bonds and evolve dynamically. This process is formalized as active geodesic inference, in which inference trajectories and the semantic geometry they traverse co-evolve.
Reasoning is modeled as the evolution of coupled semantic fields—scalar, vector, and entropy—over a high-dimensional semantic manifold. A Hamiltonian governs this system, balancing coherence, exploratory motion, and entropy production.
Under coarse-graining, RSVP dynamics reduce to an effective five-dimensional Ising model. The coupled dimensions correspond to semantic activation, directional flow, entropy suppression, reflective coherence, and exploratory openness. Stable reasoning states emerge when these dimensions synchronize, forming macromolecular-like reasoning structures.
Distinct reasoning trajectories can yield the same final output while differing internally in structure, stability, and energetic profile. These semantic isomers explain why averaging or mixing reasoning paths—such as during distillation—often degrades performance despite preserving outputs.
Transformer attention is interpreted as a Boltzmann distribution over interaction energies. Strong logical dependencies correspond to low-energy bonds, while exploratory reasoning steps correspond to shallow energy wells that permit reconfiguration.
Inference trajectories are modeled as geodesics on a semantic manifold whose geometry is dynamically reshaped by the system itself. Attention induces curvature, exploration introduces controlled noise, and reflection enforces long-range consistency. The process is history-sensitive, irreversible, and monotonically entropic.
Spherepop is introduced as a computational realization of RSVP dynamics. It enforces reasoning through nested, irreversible scopes that preserve history and constrain execution paths. Within this framework, semantic isomers appear as distinct execution histories that are observationally equivalent at the output level.
Intelligence is defined as the capacity of a system to sustain low-action, coherent geodesic trajectories through its configuration space while actively maintaining those trajectories under perturbation. Intelligence is thus a dynamical, history-indexed property rather than a static measure of correctness or optimization.
Learning and evolution are reinterpreted as geodesic persistence across different timescales. The framework yields empirical predictions, including the claim that wider geodesics correlate with robustness, that exploratory noise increases local entropy while stabilizing global structure, and that intelligence exhibits scale-dependent irreversibility. Proposed evaluation metrics include geodesic width, trajectory degeneracy, action stability, and entropy commitment ratios.
Shannon information theory measures uncertainty, whereas intelligence in this framework measures coherence under uncertainty. Kolmogorov complexity emphasizes minimal description length, while active geodesic inference emphasizes persistence of viable execution histories. Compared with the Free Energy Principle and active inference, RSVP treats semantic geometry as dynamically generated rather than fixed. In contrast to Integrated Information Theory, the emphasis is on dynamical synchronization rather than static causal structure.
The paper presents a no-free-lunch theorem for chain-of-thought distillation, demonstrating that faithful compression of reasoning histories without re-execution is impossible. Intelligence is further formalized through theorem–corollary structures linking geodesic stability, semantic isomerism, robustness, and non-distillability.
The paper advances the claim that intelligence is best understood as the active stabilization of coherent semantic structure under energetic and entropic constraints, rather than as symbol manipulation, sequence prediction, or static optimization. Together, the RSVP framework and the Spherepop calculus provide a unified mathematical and computational foundation for reasoning as a field-mediated, history-sensitive, and geometrically constrained process.