Add an explicit path from the loop to the center

Read the equation

The center now receives an increment G(cₜ,ℓₜ). Its dependence on the outer state creates a possible causal path, but only if changing ℓ can actually change G and the update is executed. The magnitude, stability, and persistence of resulting changes depend on the defined function G.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

ℓt+1=Fℓt,ut,  ct+1=ct.

By induction, ct=c0 for every update. Increasing the number of outer iterations does not change this conclusion. The audit ran 10,000 outer-state updates while preserving the center exactly at two.

For the center to change, the model needs a causal connection, for example ct+1=ct+Gct,ℓt. Physical spatial proximity is not itself a mathematical coupling term. If electromagnetic effects are intended, their field strengths, circuit geometry, material properties, and coupling must be specified; a diagram of information “around” a number supplies none of those quantities.

7.2 Proposition 5: repeated positive input does not always accumulate without bound

For a leaky accumulator,

An+1=ρAn+q,  A0=0,  0<ρ<1,

{c}_{t+1}={c}_{t}+G\left({c}_{t},{ℓ}_{t}\right)