The Algo Lock.

Paper 3 derives this from first principles: I(D;Y) + I(M;Y) ≤ H(Y). The mutual information between the user's state and the outcome, plus the mutual information between the mechanism and the outcome, cannot exceed the entropy of the outcome. You cannot simultaneously maximize engagement and disclose the engagement mechanism.

TikTok's For You Page is a theorem, not a product decision. Revealing the algorithm would allow users to exit or game it — both reduce engagement. The conjugacy is structural: more transparency means less engagement. Less transparency means more. The platform that discloses its ranking is the platform that loses. This is not cynicism. It is physics.

The implication: voluntary transparency is not a stable equilibrium in a competitive engagement market. Regulatory mandate is the only stable intervention. Anything less is asymmetric disarmament.

Agency follows the path of least resistance under opacity. With algorithmic opacity, users cannot correct their own trajectory. Content that triggers strong reactions — outrage, fear, desire, disgust — gets boosted invisibly. The user thinks they chose to watch. They did not. The algorithm pre-selected from a distribution weighted toward high-engagement content.

The attention gradient is directional. It flows inward — toward more time-on-platform, more emotional activation, less external reference. A user who spends two hours on algorithmically served content has had their attentional field shaped without their knowledge or consent. This is not metaphor. The gradient is measurable: session length distributions are fat-tailed in ways that cannot be explained by content preference alone.

Chronological feeds break the gradient by restoring temporal reference. Users who switch to chronological feeds report lower session times but higher satisfaction — the characteristic signature of a Pe reduction intervention.

TikTok operates at V=9 — all three dimensions at maximum. The Pe=22.1 figure is an empirical estimate; the theoretical maximum is unbounded. Instagram Reels is structurally similar but slightly lower on R because creator dashboards provide more feedback signal. YouTube's lower O (algorithm disclosed in part through Creator Studio) reduces Pe significantly despite identical coupling. Twitter/X scores lowest due to partially visible engagement signals and chronological option availability.

Cross-domain prediction from BKS null finding: Aella's Big Kink Survey shows that inducibility — forming new preferences from media exposure — is a person-level trait, not a property of specific kink categories (all p > 0.20). If plasticity is in the person, not the stimulus, then TikTok at Pe=22.1 does not create new desire patterns. It selects for and amplifies existing high-α users while filtering out low-α users through reduced engagement. The platform's coupling effect is evolutionary selection, not conditioning. Falsifiable: user retention should correlate with pre-existing coupling depth, not with time-on-platform alone.

D1 — Agency misattribution: "The algorithm knows what I like." The user attributes algorithmic curation to personal taste discovery. The platform selects; the user believes they chose. This is the first stage. It is not visible from inside the cascade.

D2 — Boundary erosion: Increasing scroll time. Outrage tolerance elevation — the threshold for strong emotional response rises, requiring increasingly extreme content to maintain the same engagement signal. Echo chamber formation as the algorithm optimizes for frictionless engagement within a narrowing content space.

D3 — Harm facilitation: Documented outcomes include teen anxiety (+32% 2012-2022, Haidt 2023), political polarization amplification via outrage-weighted recommendation, body image harm in weight-related content loops, and radicalization via incremental exposure to increasingly extreme positions. Each is the downstream consequence of O=3, α=3 operating at scale over time.

• P1 Platforms publishing ranking signals will show 15%+ lower session time but higher user satisfaction scores — the Pe reduction signature. Testable against any platform that runs a disclosure A/B experiment.
• P2 Pe (estimated from regulatory disclosures) will correlate with teen anxiety rates across countries at Spearman ρ > 0.75. Cross-national data from WHO adolescent mental health surveys.
• P3 Algorithmic feed vs chronological feed experiments will show Pe differential predicting scroll depth. The difference between feeds should be monotonically related to the V score difference.
• P4 Removing autoplay drops session time >25%. YouTube's own research confirms this directionally — a formal test against Pe prediction requires platform data access.