Unified Theory of Observer--Attention--Knowledge Graph\\ in Computational Universe:\\ Cognitive Dynamics and Discrete Geometric Structure\\ Under Finite Resources

In previous works on the ``computational universe'' series U_{comp} = (X,T,C,I), we separately constructed discrete complexity geometry, discrete information geometry, control manifold (M,G) induced by unified time scale, and task information manifold (S_Q,g_Q), giving on joint manifold E_Q = M \times S_Q joint variational principle for time--information--complexity. These structures characterize ``geometry of computational universe itself'' at ontological level, but have not yet explicitly introduced mathematical object of ``internal observer'': how does observer with finite resources select attention, construct knowledge graph, and gradually accumulate information on complexity--information geometry? This paper, within framework of computational universe and its continuous geometric limit, gives unified axiomatic and geometric description of ``observer--attention--knowledge graph.'' We first formalize observer as class of state machine with finite memory $ O = (M_{int},\Sigma_{obs},\Sigma_{act},P,U), where M_{int} is internal memory state space, \Sigma_{obs} is observation symbol space, \Sigma_{act} is action space, P is attention--observation policy, U is internal update operator. Based on this structure we define time-dependent attention operator A_t : X \to [0,1], or equivalently visible subset X_t^{att} \subset X, proving: attention operator defines on complexity--information geometry of computational universe a family of time-dependent ``reachable sections,'' thereby imposing constraints on observer's worldline. Second, we formalize knowledge graph as G_t = (V_t,E_t,w_t,\Phi_t), where V_t is finite node set, E_t \subset V_t\times V_t are relation edges, w_t are weights, \Phi_t:V_t\toS_Q is embedding mapping into task information manifold. We construct knowledge graph Laplace operator \Delta_t, proving that in suitable limit, spectrum of \Delta_t approximates Laplace--Beltrami operator on (S_Q,g_Q), thereby viewing finite-node knowledge graph as ``discrete skeleton'' on information manifold. Then we introduce observer's extended worldline on joint manifold z(t) = (\theta(t),\phi(t),m(t),G_t,A_t), where (\theta(t),\phi(t))\inE_Q is control--information state, m(t)\in M_{int} is internal memory, G_t and A_t are knowledge graph and attention at time t$. On basis of time--information--complexity joint action, we add observer internal cost and knowledge graph reconstruction cost, obtaining extended observation--computation action, deriving its Euler--Lagrange type conditions, giving variational characterization of ``under finite complexity budget and finite memory, how observer selects attention and updates knowledge graph.'' Finally, we prove two representative results: enumerate \item Under local Lipschitz and finite capacity assumptions, information entropy increment observable by observer in any finite time is subject to double upper bound of complexity budget and attention bandwidth, giving class of ``observer version time--information inequality''; \item Spectral dimension of knowledge graph tends in long-time limit toward local information dimension of task information manifold, showing that ``knowledge graph of rational observer almost necessarily approximates skeleton of true information geometry in infinite time limit.'' enumerate This paper lays structural foundation at single-observer level for subsequent construction of ``multi-observer--consensus geometry--causal network'' theory, viewing observer as geometric object internal to computational universe rather than external ``measurer.''