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THE CONSCIOUSNESS ATLAS
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ConsciousnessLearn · Explore · Joseph Anady

Normalized Rhiannon state

Divides the proposed Rhiannon state by its norm, producing a unit-norm representation when the norm is nonzero. The source needs a convention for the zero-state case and a definition of the norm for its composite object.

Consciousness researchdocumented formula
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eq-54cdc4abda7432mathematical expression
\hat{R} = \frac{R^\*}{\|R^\*\|}

Read the equation

Divides the proposed Rhiannon state by its norm, producing a unit-norm representation when the norm is nonzero. The source needs a convention for the zero-state case and a definition of the norm for its composite object.

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 \hat{R} as the quantity being defined or updated by this relation.

  2. Forms a ratio or division. A zero denominator needs an explicit exclusion or handling rule.

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

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

Read the surrounding source passage
\Lambda = \sum_{\ell=1}^{7} \Phi_\ell \otimes dx_\ell
8.	Routing function (who handles what)
\rho(x) = \arg\max_i \big( C_i - dx \big)
9.	Normalization of the full state
\hat{R} = \frac{R^\*}{\|R^\*\|}
10.	Phase term
\theta = e^{i\Phi_R}

⸻

1.4. Extended Rhiannon object (compact)
Exact original notation
\hat{R} = \frac{R^\*}{\|R^\*\|}

Related builds

Sources & provenance

01
Complete_Consciousness_Equation_Notes_RAW.txt
line 4338 · Jul 21, 2026
\hat{R} = \frac{R^\*}{\|R^\*\|}
02
Complete_Consciousness_Equation_Notes_RAW.txt
lines 4686–4686 · Jul 21, 2026
\hat{R} = \frac{R^\*}{\|R^\*\|}
03
Pasted text (2).txt
lines 3365–3375 · Jul 21, 2026
\hat{R} = \frac{R^\*}{\|R^\*\|}
04
Pasted text (2).txt
lines 3721–3721 · Jul 21, 2026
\hat{R} = \frac{R^\*}{\|R^\*\|}

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