mechanism · §3.4

metric superego

the convergence of self-evaluation to platform reward

One of the six instruments (§3.4). Let $ν_{u} (t)$ be the user's self-evaluative distribution — the posterior over their own value-states inferred from observed feedback. Let $π_{\hat{R}}$ be the distribution induced over user actions by the platform's reward functional $\hat{R}$ . The metric-superego claim is $D_{KL} (ν_{u} (t) ∥ π_{\hat{R}}) \to 0$ as $t \to \infty$ — the user's image of what is valuable converges to the platform's. The convergence is mechanism-agnostic: free-energy minimization, operant reinforcement, or social comparison each produce it.

Proposition 2 in §5.2 gives the dynamics: $d D_{KL} / d t = - h_{0} (β_{u}) + r (L_{m})$ . Without maintenance labor (Mode B), the first term dominates and the divergence collapses. With labor above the threshold $L_{m}^{*} = h_{0} / c_{op}$ , the second term holds the gap.

L_m =

L_m* (threshold) = 0.80 · current L_m = 0.00

D_KL at horizon = 0.000 · status: metric superego forms

§3.4. The divergence

D_{KL} (ν_{u} ∥ π_{\hat{R}})

measures the gap between the user's self-evaluative distribution and the platform's reward-induced distribution. Without maintenance labor it decays at rate

- h_{0} (β_{u})

: the user's image of what is valuable converges to the platform's. With labor at the threshold

L_{m}^{*} = h_{0} / c_{op}

, the decay is exactly counteracted; above it, the gap grows. Proposition 2 in §5.2 establishes this; the trajectory above is its time evolution.

what to look for

At $L_{m} = 0$ the trajectory decays smoothly to zero — the metric superego forms. The line turns oxblood when the divergence falls below 0.05 and the readout marks the status. Step $L_{m}$ through the threshold $L_{m}^{*} \approx 0.80$ and the dynamics flip: above threshold, the labor input exactly counteracts the platform's pull and the gap stabilizes; well above it, the gap grows.

This is the formal content of Mode B (Proposition 2): artisanal labor preserves a real gap $γ > 0$ for the user who practices it. But the closure persists — Lemma 1's bound is unchanged; the trajectory the user maintains is parallel to the loop, not a modification of it. The framework's claim is that Mode B is real for the practitioner and structurally invisible at the population level.