Rhiannon seven-stage self-extension sum

Read the equation

Apply each of seven stage operators twice to x and sum the resulting outputs. This expression is a sum of self-composed stage transforms, not the sequential composition S_7∘…∘S_1. Its left side R(S) also leaves the input x implicit.

Its role in the build

The Rhiannon Equation

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read R(S) as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• The source does not define the operators, addition on their outputs, or why this sum realizes self-extension. The smaller atlas version has an unclear lower index and is retained as a separate source variant.

Original context

The Rhiannon Equation: Apply each of seven stage operators twice to x and sum the resulting outputs. This expression is a sum of self-composed stage transforms, not the sequential composition S_7∘…∘S_1. Its left side R(S) also leaves the input x implicit.

R(S) = Σ_{k=1}^7 S_k(S_k(x)),  k = 1…7

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