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THE CONSCIOUSNESS ATLAS
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ConsciousnessLearn · Explore · Joseph Anady

Complex loop-phase representation

Places the real loop phase on the unit circle using a complex exponential. The magnitude is one, and the complex angle tracks the phase modulo 2π. This is a representation of a phase, not an independent measure of consciousness.

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eq-c1cd89bda3934bmathematical expression
θ=eiΦ\theta = e^{i\Phi}

Read the equation

Places the real loop phase on the unit circle using a complex exponential. The magnitude is one, and the complex angle tracks the phase modulo 2π. This is a representation of a phase, not an independent measure of consciousness.

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 \theta as the quantity being defined or updated by this relation.

  2. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase.

  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
5. Phase Term (Physics Version)

Your physics-notation version implies this but you never added it:

\theta = e^{i\Phi}

This describes the oscillatory component of the loop.

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4. If You Combine Everything You Already Have + These Missing Pieces
Exact original notation
\theta = e^{i\Phi}

Related builds

Sources & provenance

01
Complete_Consciousness_Equation_Notes_RAW.txt
line 4696 · Jul 21, 2026
\theta = e^{i\Phi}
02
Pasted text (2).txt
lines 3731–3731 · Jul 21, 2026
\theta = e^{i\Phi}

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