soft3/tru/docs/explanation/epistemic-markets.md

Epistemic Markets Specification

The inversely coupled bonding surface (ICBS) market mechanism and market inhibition — the two components that give the cybergraph its inhibitory channel.

Source material: inversely coupled bonding surface, market inhibition


ICBS 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.


ICBS Properties

Property Description
self-scaling TVL $= C(s_{YES}, s_{NO})$ grows with trading volume
solvency total value locked always equals the cost function
early conviction prices range from 0 to $\lambda$, rewarding early discovery
geometric simplicity only square roots — tractable on-chain computation
inverse coupling buying one side directly suppresses the other

Role in the Cybergraph

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.


Market Inhibition

In a standard graph, every cyberlink contributes positively to attention flow. Market inhibition introduces a negative channel: when a prediction market on a link's validity resolves against the link, the market outcome scales down its weight.

$$w_{\text{eff}}(\ell) \;=\; w(\ell) \cdot \bigl(1 - \alpha \cdot m(\ell)\bigr)$$

where $w(\ell)$ is the original stake-weighted strength, $m(\ell) \in [0, 1]$ is the market's disbelief signal, and $\alpha$ is the inhibition coefficient.


Effective Adjacency

The effective adjacency weight combines stake, karma, and ICBS price:

$$A^{\text{eff}}_{pq} = \sum_\ell \text{stake}(\ell) \times \text{karma}(\nu(\ell)) \times f(\text{ICBS price}(\ell))$$


Neural Network Equivalence

Excitation alone produces a directed weighted graph. Adding inhibition makes the cybergraph computationally equivalent to a neural network:

Biological Cyber
excitatory synapse staked cyberlink with positive weight
inhibitory synapse market-suppressed cyberlink
neurotransmitter balance stake vs. disbelief ratio

The tri-kernel processes both signals simultaneously: diffusion spreads excitation, while market inhibition dampens unreliable paths.


Economic Dynamics

Inhibition carries a cost. A neuron that inhibits a link must stake into the ICBS market against it. If the link turns out to be valid, the inhibitor loses stake. This symmetry ensures that both belief and disbelief are costly — cheap talk in either direction is eliminated.


See cyber/truth/coupling for the full specification. 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. See cyberlinks, cybergraph, tri-kernel, attention, tru.

Homonyms

reference/epistemic-markets

Graph