Persistent Registration and Memory
When does a changing registration organization count as one persistent history, and what does it retain?
Exact model-level results for retained relational history (an exponentially weighted, fading-memory functional) and for when a changing organization counts as one persistent lineage rather than unrelated states.
Established
- The retained relational matrix K obeys an exact exponentially weighted history update in ACRF-4.
- Sufficient conditions exist for a changing registration organization to remain one persistent, non-decomposed lineage over a finite regime.
Relevant claims
Retained registration state is an exact fading-memory history functional
In ACRF-4, the retained relational matrix K obeys the discrete update Kₙ₊₁ = (1−ρ)Kₙ + ρK̂(xₙ₊₁); under exposure-normalized refinement this converges to an exact continuum Volterra-type fading-memory functional of the relational path, K(T) = e^(−γT)K(0) + γ∫₀ᵀ e^(−γ(T−t)) K̂(x(t)) dt.
Scope: An exact result for the canonical ACRF-4 retained-relational-matrix update. It supports, but does not by itself formally establish, reading the enlarged state (x, K) as locally Markovian where projection to x alone generally is not.
- A general spatial or continuum stable-record invariant beyond this prototype remains open.
- K should not be equated with literal physical memory in every possible implementation; its scope is tied to this model.
Last reviewed 2026-08-27
Relevant publications
Retained Relational Geometry as a Fading-Memory History Functional in ACRF-4
A Discrete-to-Continuum Theorem and Exact Equal-Area Path Dependence.
A Persistent Registration Lineage Theorem
Organizational Identity Through Change and the Boundary to Conscious Subjectivity. Defines a persistent registration lineage; does not derive consciousness.