Computable Limits Catalog¶
Jean-Paul Niko · RTSG v8
Every limit has an equation. The equation tells you: (1) what TYPE (substrate vs filter), (2) which parameters control it, (3) which interventions move it. Filter limits are removable. Substrate limits are real walls with known shapes.
| Limit | Formula | Type | Movable by |
|---|---|---|---|
| Negative emergence threshold | \(m^* = 1 + \lfloor v_{\max}/(\beta - s_{\max}) \rfloor\) | Coordination | Reducing \(\beta\) (coordination cost) |
| Working memory capacity | \(C_{WM} = \lfloor f_\gamma / f_\theta \rfloor \approx 6\) | Substrate | External memory, chunking (K consolidation) |
| Ambient manifold volume | \(\text{Vol}(M) = (4\pi)^n\) | Dimensional | Increasing \(n\) (adding dimensions via tools) |
| Fill ratio ceiling | \(\Phi \in [0,1]\) | Structural | Cannot exceed 1 for fixed \(n\); increase \(n\) |
| CCI from filter chain | \(\sum r_j^{d^*} = 1\) (Moran) | Filter | Adding/modifying filters (education, therapy, tools) |
| Cognitive Ricci flow singularity | \(\partial \kappa_i / \partial t = 2\kappa_i^2 + L_i(t) + \sum_j K_{ij} f(\kappa_j)\) | Curvature | Perelman surgery (paradigm shift) |
The Key Insight¶
This is what people care about: Can I get smarter? How? What are my walls? Which ones can I move?
RTSG answers all of these with computable numbers. The math is the engine; the human experience of cognitive growth is the product.
Every time you hit a wall, you can see the wall's equation, identify whether it's a substrate constraint or a filter constraint, and if it's a filter constraint, compute exactly what modification removes it.