Path-Dependent Knowledge Substrates (PDKS)
Framework + Mathematical Proof
A mathematical framework proving search authority is an engineered convergent property. Contraction mappings, adversarial robustness, multi-agent competition, and economic stability.
Authority Is Not Emergent. It's Engineered
Part 1 of the PDKS series. In AI-mediated information economies, authority doesn't just happen. It converges, or fails to. Based on structural properties you can formally specify.
The Math of Authority Convergence: Contraction Mappings and Fixed Points
Part 2 of the PDKS series. Authority convergence isn't a hope. It's a provable property. Here's the contraction mapping that guarantees it, and what breaks the guarantee.
Projection Without Mutation: How to Personalize Without Destroying Truth
Part 3 of the PDKS series. Every personalization system faces a tension: adapt to the user or preserve the truth. The projection operator formalism resolves it.
Adversarial Robustness in Authority Systems: Perturbation Bounds and Spectral Stability
Part 4 of the PDKS series. When competitors, bots, or algorithm changes try to destabilize your authority, how much damage can they actually do? The math gives a bound.
Multi-Agent Authority Competition: When Substrates Fight for Dominance
Part 5 of the PDKS series. In any niche, multiple domains compete for authority. Replicator dynamics from evolutionary game theory reveal when equilibria exist, and when winner-take-all is inevitable.
Economic Stability Through Semantic Architecture
Part 6 of the PDKS series. Authority convergence isn't an academic exercise. It directly bounds revenue volatility. Here's why the contraction gap is a financial metric.