From Lossy Symbolic Observations to Task-Relevant Latent Structures

CMT proposes a research program on the geometry and dynamics of cognitive states and on their potential relation to consciousness. This paper extracts from it the formalizable subproblem of lossy symbolic observation and latent task structure, establishes criteria for exact and approximate recovery, a gain bound for complementary observations, and a decomposition of prediction loss, and gives quantitative results for active dynamic recovery: on irreversible dissipative trajectories, the minimax risk of all strategies with at most two binary reads is 1/8, strictly below the 1/6 of unidirectional sweep strategies; the first-order rate of local recovery error is determined by the projection of the task gradient onto observation-fiber directions, and when that projection vanishes the second-order rate is given by fiber bending. Controlled experiments show the following. The gain from complementary symbolic constraints reaches the theoretical baseline. Auxiliary supervision of intermediate states improves within-length state readability; the mean within-length probabilistic prediction rises slightly while directions disagree across seeds, and no out-of-length extrapolation law emerges. In budget-constrained communication, the relative merit of message formats depends on the budget and the use. Hidden-residual handover between instances of the same LLM architecture improves by 7.5 percentage points over length-matched counterfactual residuals, remains 13.2 percentage points below full-text reception, and is only 0.9 percentage points above the best per-family constant answer; the strengthened counterfactual joint criterion is not met. The results obtained do not directly establish the dynamical hypothesis of consciousness but build a restricted theoretical foundation for subsequent research; the hypotheses about cognition and experience, and the conceptual premises of consciousness explanation, are retained respectively as research directions to be tested and as philosophical discussion.