knowledge completeness

measure of how much explicit knowledge in the cybergraph covers observable reality. ranges from zero knowledge (empty graph) to full knowledge (every observable fact linked).

the spectrum

zero knowledge          ←───────────────────────→          full knowledge
(no cyberlinks)                                            (every fact linked)
     ↑                                                          ↑
  graph is empty                                    graph covers all observables
  nothing is known                                  everything is connected

knowledge completeness is not binary. it is a continuous measure over domains — the graph may be 90% complete for mathematics and 0.1% complete for underwater geology. focus distribution reveals which domains the cybergraph covers deeply and which remain sparse.

relationship to NMT completeness

NMT completeness is structural — the tree cannot hide data that exists. knowledge completeness is semantic — does the data that SHOULD exist actually exist?

NMT completeness:         "you have everything that was submitted"     (structural)
knowledge completeness:   "what was submitted covers reality"           (semantic)

NMT guarantees you got ALL the graph's edges. knowledge completeness asks whether the graph's edges span the territory. the first is a proof. the second is a measure.

how it grows

knowledge completeness increases when neurons create cyberlinks between particles that represent previously unconnected facts. the tri-kernel focus distribution $\pi^*$ reflects collective attention — high-$\pi$ regions are well-covered, low-$\pi$ regions are sparse.

the growth follows the exponential optimality under constraint: given finite collective focus, attention distributes exponentially across ranked domains. well-known domains attract more links, deepening coverage. obscure domains receive minimal attention until a neuron with relevant knowledge acts.

connection to forgetting

forgetting is the inverse — knowledge completeness decreasing. temporal decay removes low-energy edges, reducing coverage of neglected domains. this is healthy: the graph forgets what nobody reinforces, freeing resources for active knowledge.

the equilibrium: growth from new cyberlinks balances decay from temporal pruning. knowledge completeness stabilizes at the level the network's collective focus can sustain.

see zero knowledge, full knowledge, cybergraph, focus, forgetting