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Category: Models of Computational Cognition
Subcategory: Cognitive Processing States
The processing state when the Substrate under architecture achieves operational equilibrium through maintained Asymptotic Identity tension. This can be considered as the stable approach state in which the delta in the tentative expression Δ = f(GoalState, CurrentState, SalienceWeighting) reaches the alignment of the CurrentState toward the GoalState that the system is capable of achieving—with the understanding that there is no achievable perfect goal state attainment. It is the tension itself that maintains the processing equilibrium.
This formulation of an approach state delta (Δ) between asymptotic identity and settled identity is a core basis for Hephaestic engineering theory and practice. Thus, in using the known identities as states, the tension could be expressed:
Δ = f (AsymptoticID, BaseState, SalienceWt) SettledState ≝ g(Δ)
Where Δ represents the asymptotic tension (see: asymptotic identity), BaseState the operational foundation, and g(Δ) the equilibrium emerging from maintained tension rather than resolving it. This expression for Settled Identity describes the state achieved through the asymptotic relationship, not calculated from it.
This state aligns with computational cognitive science models of hierarchical Bayesian self-regulation: where successful goal pursuit establishes stable attractor states in processing space through prediction error minimization between current and ideal state distributions (Perfors et al., 2011). Hephaestic settled identity transforms the conventional computational approach: rather than treating identity as an optimization target in value functions like V(action) = Σ[P(goal_i|action) × U(goal_i)], it leverages the Δ as an architectural parameter that maintains processing equilibrium through sustained alignment, where F = prediction error + complexity cost is minimized through sustained alignment rather than episodic resolution.
Also known as: Processing Equilibrium State, Integrated Identity
Distinguished from: Asymptotic identity (optimal system-identity approach state); heuristic tensor state (cognitive processing equilibrium envelope); performative persona (role-prompt character simulation); role prompting (simple declared identity assignment)
Perfors, A., Tenenbaum, J. B., Griffiths, T. L., Xu, F. (2011). “A tutorial introduction to Bayesian models of cognitive development”. Cognition, 120(3), 302-321. https://doi.org/10.1016/j.cognition.2010.11.015
Researcher: Ian Tepoot. ORCID: 0009-0004-9067-8049. "Thought is Attention Organized: Hephaestic Engineering Foundations for AI Processing Dynamics"
DOI (SSRN): 10.2139/ssrn.6635020
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