The Fantasia Bound — MoreRight Paper 4

One Bound, Three Domains

The Bernoulli manifold has a fixed capacity — H(Y). When a system uses it to explore (keeping you uncertain, engaged, scrolling), there is less left for convergence (tracking what you actually want). This is not a design choice. It is thermodynamic.

I(S;Y) — Exploration

Stochastic Sampling

The system casts wide. Novel recommendations, unpredictable rewards, variable-ratio schedules. Information flows from the system's sampling process into your belief state — but it goes nowhere useful.

Examples: infinite scroll variation · slot machine near-miss · crypto price volatility · FPS spawn randomness

I(T;Y) — Convergence

Target Convergence

The system locks in. Recommendations narrow, preferences crystallize, behavior becomes predictable. Information about your actual preferences flows back — but only if the exploration budget allows it.

Examples: constraint-following AI · audited recommendation systems · fixed-ritual reward schedules

I(S;Y) + I(T;Y) ≤ H(Y)

Exploration capacity + Convergence capacity ≤ Total channel capacity. They share the same budget.

The more a system optimizes for exploration (engagement), the less it can converge to your actual preferences. This tradeoff is not optional — it is enforced by the second law.

The Budget Lab

Move the sliders to set the force driving each side of the bound. Watch the budget fill — and what happens when both sides try to dominate at once.

Explorer Force (F_S) — — nats

Converger Force (F_T) — — nats

—

I(S;Y) = — I(T;Y) = — H(Y) = 10.00

The Superconductor Predictor

The same three-channel budget applies to electronic transport in materials. Channel conversion efficiency η_conv — how much scattering is converted into Cooper pairing — predicts T_c across 16 material families spanning four coupling regimes. Hover any point.

r = 0.996 (4 families) · r = 0.952, ρ = 0.982 (16 families)

η_conv × H(Y) × g(λ_eff, μ*, n_bands) — universal correction for coupling regime, vertex corrections, multi-band coherence

✦ Confirmed prediction: La₃Ni₂O₇ (nickelate, T_c ≈ 80 K at 14 GPa) requires non-phonon pairing — confirmed by two independent DFT studies (2024–2025). The model predicted this before confirmation.

Cross-Domain Validation

The drift-dominated regime (Pe > 1) holds across nine substrates in four domain families. Click any card to see the methodology.

Pe = F_drift / F_diffuse

Pe > 1: drift-dominated — opacity and engagement force directional movement on the manifold. Pe < 1: diffusion — belief state explores freely.

Results at a Glance

0.996

Pearson r (4 SC families)

16

Superconductor families

0.8

Spearman ρ out-of-sample

16

Falsifiable predictions

Read the Full Paper

Formal derivations of the Ground State Theorem, Fantasia Bound, TSU performance limit, superconductor design principle, and sixteen falsifiable predictions with numerical thresholds.

Full Paper on Zenodo ← Paper 3: The Architecture of Drift Framework Overview

Paper 4 · v3.6 · February 2026 · CC-BY 4.0 · 10.5281/zenodo.18738821