inversely coupled bonding surface

the epistemic market mechanism of cyber. a two-sided bonding curve where YES and NO are geometrically coupled — buying one directly suppresses the other

the cost function

$$C(s_{YES},\, s_{NO}) = \lambda \sqrt{s_{YES}^2 + s_{NO}^2}$$

where $s_{YES}$ and $s_{NO}$ are token supplies and $\lambda$ is a scaling constant fixed at deployment. iso-cost curves are circles in the $(s_{YES}, s_{NO})$ plane. trading moves outward from the origin along the surface

prices and coupling

prices emerge as partial derivatives of the cost function:

$$p_{YES} = \lambda \cdot \frac{s_{YES}}{\sqrt{s_{YES}^2 + s_{NO}^2}}, \quad p_{NO} = \lambda \cdot \frac{s_{NO}}{\sqrt{s_{YES}^2 + s_{NO}^2}}$$

the inverse coupling:

$$\frac{\partial p_{YES}}{\partial s_{NO}} = -\lambda \cdot \frac{s_{YES} \cdot s_{NO}}{(s_{YES}^2 + s_{NO}^2)^{3/2}} < 0$$

buying NO lowers YES. buying YES lowers NO. the two sides are genuine opposites on a shared geometric surface

role in cyber

every cyber/link in the cybergraph can carry an ICBS market. the market price enters the tri-kernel as the effective edge weight:

$$w_{\text{eff}}(e) = \text{price}(e) \times \text{stake}(e)$$

at $p \to 1$: full focus flows through the edge. at $p \to 0$: the edge is deactivated. this is market inhibition — the mechanism by which collective epistemic assessment reshapes structural connectivity

self-scaling liquidity means trading volume automatically grows the market. the most-contested edges become the most liquid, yielding the most accurate prices. no external liquidity providers required

properties

see cyber/truth/coupling for the full specification. see market inhibition for how ICBS provides inhibitory signals to the tri-kernel. see valence for the ternary epistemic field on cyberlinks. see Bayesian Truth Serum for the scoring layer. see cyber/nomics for the broader economic design

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