ordered sequences of cyberlinks forming directed paths through the cybergraph. chains of semantic connections that emerge from linking patterns
structure
a linkchain is an ordered tuple of cyberlinks:
$$\mathcal{C} = (\ell_1, \ell_2, \ldots, \ell_n) \quad \text{where } q_i = p_{i+1}$$
the target particle of each link becomes the source particle of the next, producing a directed walk through the graph
properties
- length $n$: the number of cyberlinks in the chain
- each link carries its own neuron signature, stake, and timestamp — a chain may involve one or many authors
- chains compose: concatenating two chains $\mathcal{C}_1 \circ \mathcal{C}_2$ yields a longer chain when the final particle of the first matches the initial particle of the second
- cycles emerge when $q_n = p_1$, forming closed loops in the cybergraph
semantics
linkchains capture multi-hop reasoning. a single cyberlink states one relation; a chain traces an argument, a derivation, or a narrative across the graph. the tri-kernel propagates attention along these paths, amplifying chains with consistent stake backing
discovery
the tru indexes linkchains during consensus, enabling queries like "all directed paths of length $k$ from particle $p$." this makes the graph traversable as a reasoning substrate
see cyberlinks, cybergraph, particle, neuron, tri-kernel
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