The Weight of Return, Phase B: Computational Evidence for the Return Conjunction

This report presents the computational results of Phase B of "The Weight of Return" project, testing the three-axiom formulation of the temporal conjunction (Kogura, 2026) against simulation data from two experimental systems. Experiment 1 replicates the Hebbian recurrent network from the constitutive gap dependence paper under clamped, perturbed, and input replay conditions (50 trials each). Three unanticipated findings emerge: (1) The constitutive gap reduces excursion–return predictability rather than increasing it — the clamped condition has higher R² (0.34) than the perturbed condition (0.27), indicating the gap converts rigid path-dependence into flexible path-dependence. (2) The operational signature of the depth–width conjunction's width dimension is the cycle-to-cycle variance of criticality-relevant dynamics, σ(Δα_crit), which is 41% larger in the perturbed condition. (3) The per-cycle criticality bias (mean Δα_crit = −0.011 clamped vs +0.002 perturbed) is barely detectable per cycle but cumulative over the system's lifetime, producing the full ordered-vs-critical separation. An additional finding from MNIST experiments under gradient descent with Adam confirms the constitutive mechanism operates under backpropagation (clean-step Δα = +0.058, p = 8.52 × 10⁻⁹). Experiment 2 extends the grokking experiment to 60,000 epochs across four seeds. All seeds exhibit a two-transition structure: grokking (behavioral generalization) at epochs 12,400–17,200, followed by the DFA transition (dynamical criticality) at epochs 29,850–38,250. The average lag is 18,300 epochs. During this lag, the system is behaviorally correct but dynamically sealed — processing without the dynamical signature the framework identifies with mattering. One seed (42) reverses from criticality (α = 0.91) back to ordered phase (α = 1.49), confirming that the transition is not self-sustaining without ongoing gap maintenance. A universal methodological warning is identified: any study measuring DFA under conditions that change input statistics must include a static control. This confound was confirmed across both Hebbian and gradient-descent learning, both activity and weight-change DFA. Five falsification criteria are stated for the computational claims.