the cybergraph contains two kinds of knowledge. they are irreducible to each other. the system is incomplete without both.
kind one: structural knowledge
a cyberlink records that two particles are connected. this is structural knowledge:
A relates to B
it is binary. the link either exists or it does not. it is created by one neuron, signed, timestamped, content-addressed. it is permanent once finalized. it answers the question: what is connected to what?
structural knowledge defines the topology of the cybergraph. it is the substrate on which everything else runs. the tri-kernel diffuses over it, springs constrain it, heat kernel smooths it. cyberank flows through it.
but structural knowledge is silent on one question: is this connection good?
a cyberlink from spam to spam is structurally identical to a cyberlink from a foundational theorem to its proof. both are edges. the graph does not distinguish them.
kind two: epistemic knowledge
the cyberlink market protocol adds a second kind: the collective's belief about whether a connection is true, useful, or meaningful.
this is epistemic knowledge:
the network estimates A→B at probability p
it is continuous. price ∈ (0,1). it is not set by one neuron — it emerges from the aggregate of all market positions. it is dynamic: it updates as neurons buy TRUE or FALSE. it answers the question: how much does the collective believe this connection?
epistemic knowledge does not replace structural knowledge. it evaluates it. the cyberlink creates the question. the market discovers the answer.
the relationship
| structural | epistemic | |
|---|---|---|
| what | A→B exists | p(A→B is true) |
| who | one neuron | all market participants |
| how | create cyberlink | buy TRUE or FALSE |
| form | binary (0/1) | continuous (0,1) |
| permanence | permanent | dynamic |
| question answered | what is connected? | what is worth believing? |
structural knowledge is the library. epistemic knowledge is the catalogue of reliability. a library with no reliability signal is noise. a reliability signal with no library has nothing to evaluate.
why both are necessary
a cybergraph with only structural knowledge — all cyberlinks weighted equally — produces focus proportional to link count and stake. popular links accumulate focus regardless of truth. the tri-kernel converges to a fixed point, but that fixed point may be a spam attractor.
a cybergraph with only epistemic knowledge — markets with no underlying links — has nothing to trade. the market needs a structural fact to form an opinion about.
the interplay: structural knowledge creates the edges over which the market discovers probabilities. those probabilities feed back as weights into the tri-kernel, shaping π*. the focus distribution is then jointly determined by topology (who linked what) and collective belief (what the network trusts).
this is what veritas pursues: truth is not declared. truth is emerging — from the market process, continuously, as a convergent collective signal.
connection to the 2|3 architecture
from two three paradox and binary topology ternary economics:
| layer | kind | representation |
|---|---|---|
| binary [2] | structural | cyberlink exists or not |
| ternary [3] | directional belief | TRUE / UNCERTAIN / FALSE |
| continuous [∞] | epistemic | LMSR price ∈ (0,1) |
structural knowledge is the binary substrate. epistemic knowledge is the continuous signal. ternary is the coarse quantization between them — the human-readable summary of the market price.
the three are not alternatives. they are layers. each requires the one below it.
implications for the formal definition
the formal cybergraph $\mathbb{G} = (P, N, T, L)$ captures both kinds of knowledge in a single record.
each cyberlink $\ell = (\nu, p, q, \tau, a, v, t)$ contains:
- structural knowledge: $(\nu, p, q, t)$ — who asserted which connection and when
- epistemic seed: $v \in \{-1, 0, +1\}$ — valence, the neuron's BTS meta-prediction, predicting how the ICBS market on this edge will converge
$v$ is not an assertion about truth. it is the meta-prediction input that Bayesian Truth Serum requires: the neuron's prediction of what the collective will believe. creating a link with $v = -1$ means "I affirm this connection exists and I have private knowledge the market hasn't priced yet." Bayesian Truth Serum rewards exactly this when correct.
epistemic knowledge is the derived layer — the ICBS market price, computed from all positions over time. but the meta-prediction seed $v$ that feeds into Bayesian Truth Serum scoring IS in the record, because the cyberlink is the BTS input: link creation is the first-order belief, $v$ is the meta-prediction $m_i$.
see cyberlink market protocol for the market design. see focus flow computation for how market weights enter the tri-kernel. see market inhibition for why epistemic knowledge is what makes the cybergraph computationally equivalent to a neural network with both excitation and inhibition.