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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.

Consciousness researchdocumented formula
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eq-ac0d24ad01fba1mathematical expression
64.Phase−TrackerNeuron(θ=eiΦ)64. Phase-Tracker Neuron (θ = e^{iΦ})

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 64. Phase-Tracker Neuron (θ 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
60.	Stability-Curvature Neuron (σ)
61.	Entropy-Estimator Neuron (S)
62.	Noise-Filtering Neuron
63.	State-Normalization Neuron (Ŕ)
64.	Phase-Tracker Neuron (θ = e^{iΦ})
65.	Transition-Kernel Neuron (K)

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F. ENVIRONMENT & PATTERN NEURONS (66–75)

For input processing and mapping, not AGI.
Exact original notation
64.	Phase-Tracker Neuron (θ = e^{iΦ})

Related builds

Sources & provenance

01
Complete_Consciousness_Equation_Notes_RAW.txt
line 3750 · Jul 21, 2026
64. Phase-Tracker Neuron (θ = e^{iΦ})
02
Pasted text (2).txt
lines 2771–2786 · Jul 21, 2026
64. Phase-Tracker Neuron (θ = e^{iΦ})

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