truth in the cybergraph has two irreducible components. neither alone is sufficient. together they define what the network calls true
| factor | form | source | question answered |
|---|---|---|---|
| structural | binary — the cyberlink exists | one neuron's signed assertion | what is connected to what? |
| epistemic | continuous — ICBS price $\in (0,1)$ | all market participants | how much does the collective believe this connection? |
the structural layer is permanent and append-only — a link that exists cannot be deleted, only economically muted. the epistemic layer is dynamic — the market price shifts continuously as new neurons buy TRUE or FALSE positions on the edge.
why two factors
a single-factor truth model fails in one of two directions.
structural only: all cyberlinks weighted by stake alone. $\pi^*$ reflects link count and economic weight, but the graph cannot distinguish a well-supported theorem from well-funded spam. the tri-kernel converges — but possibly to a false attractor. there is no inhibitory signal.
epistemic only: markets over propositions with no underlying link structure. the market has no substrate — nothing to trade on. belief without assertion is formless.
the two-factor model resolves this: the structural link creates the question. the epistemic market discovers the answer. the cyberlink asserts "A relates to B." the ICBS market over that edge asks "does the collective believe A relates to B?" the price that emerges is the second truth factor.
the formal account
the effective weight of an edge in the tri-kernel:
$$A^{\text{eff}}_{pq} = \sum_{\substack{\ell \in L \\ \text{src}(\ell)=p,\;\text{tgt}(\ell)=q}} a(\ell)\cdot\kappa(\nu(\ell))\cdot f(m(\ell))$$
factor one: $a(\ell)$ — stake on the structural assertion (economic weight of the binary fact)
factor two: $m(\ell) \in (0,1)$ — ICBS reserve ratio (market-implied probability the link is valid), transformed by $f$
the two factors multiply. a high-stake link the market disbelieves is suppressed toward zero. a low-stake link the market strongly confirms is amplified through karma and market confidence. the truth signal is the product of conviction and collective validation.
the ternary bridge
between binary structure and continuous belief sits valence $v \in \{-1, 0, +1\}$ — the coarse epistemic signal provided at link creation. it is not a third truth factor but the seed that initializes the market. the neuron's prediction of where the ICBS market will settle, expressed in three states, before the collective has spoken.
the full truth model: binary structure → ternary seed → continuous market → focus distribution $\pi^*$. each layer requires the one below it.
see two kinds of knowledge for the full structural/epistemic analysis. see valence for the ternary seed. see inversely coupled bonding surface for the market that produces the continuous factor. see market inhibition for how the two factors combine to suppress false structure. see truth for the convergent signal both factors produce.