QRI Valence Skill

The Symmetry Theory of Valence (STV) proposes that the valence (pleasantness/unpleasantness) of a conscious state is determined by the symmetry of its mathematical representation. This skill integrates QRI research with computational implementations.

Core Concepts

Symmetry Theory of Valence (STV)

"The valence of a moment of consciousness is precisely determined by the symmetry of the mathematical object that describes it." — Michael Edward Johnson, Principia Qualia (2016)

Key Claims:

1. Consciousness has mathematical structure (qualia formalism)
2. Symmetry in that structure correlates with positive valence
3. Broken symmetries manifest as suffering/dissonance
4. Valence is measurable and optimizable

XY Model Topology (smoothbrains.net)

The phenomenal field behaves like a 2D XY spin model:

State	Temperature (τ)	Vortices	Valence	Phenomenology
Frustrated	τ >> τ*	Many, proliferating	-3	Scattered, anxious, "buzzing"
Disordered	τ > τ*	Some, mobile	-1 to -2	Unfocused, dissonant
Critical (BKT)	τ ≈ τ*	Paired, bound	0	Liminal, transitional
Ordered	τ < τ*	Few, annihilating	+1 to +2	Coherent, smooth
Resolved	τ << τ*	None	+3	Deeply peaceful, consonant

BKT Transition (Berezinskii-Kosterlitz-Thouless):

• Below τ*: vortex-antivortex pairs bound → low entropy, high symmetry
• Above τ*: vortices proliferate → high entropy, broken symmetry
• At τ*: phase transition where defects can annihilate

Valence Gradient Descent

From smoothbrains.net's phenomenology:

Suffering = Σ (topological defects in phenomenal field)
Healing = defect annihilation via gradient descent
τ* bisection = finding optimal phenomenal temperature

Observable indicators (from Cube Flipper's reports):

• Visual: polygonal shards → smooth fields
• Somatic: high-freq buzzing → calm
• Attentional: contracted/focal → expanded/diffuse
• Auditory: dissonance → consonance

Qualia Bank Integration

GF(3) Operations on Valence States

Valence Range	Trit	Bank Operation	Channel
-3 to -1	-1	WITHDRAW	Venmo/ACH off-ramp
0	0	HOLD	PyUSD on-chain
+1 to +3	+1	DEPOSIT	PyUSD/Venmo on-ramp

Phenomenal Bisection Algorithm

def phenomenal_bisect(tau_low, tau_high, observed_state):
    """
    Binary search for optimal phenomenal temperature τ*.
    Based on smoothbrains.net/xy-model#bkt-transition
    """
    tau_mid = (tau_low + tau_high) / 2
    
    if observed_state == "frustrated":
        # Too hot: cool down
        return (tau_mid, tau_high, "cooling")
    elif observed_state == "smooth":
        # Too cold: heat up
        return (tau_low, tau_mid, "heating")
    elif observed_state == "critical":
        # Found τ*!
        return (tau_mid, tau_mid, "found")
    else:
        return (tau_low, tau_high, "unknown")

Valence-Aware Color Mapping

From Gay.jl + QRI integration:

# Map valence to deterministic color
function valence_to_color(valence::Int)
    # Valence range: -3 to +3
    # Hue mapping: red (suffering) → cyan (resolution)
    hue = (valence + 3) * 30  # 0° to 180°
    return LCHuv(55.0, 70.0, hue)
end

# Trit from valence
trit(valence) = sign(valence)

Computational Implementation

Defect Detection

def count_vortices(phase_field):
    """
    Count topological defects in a 2D phase field.
    Vortex = closed loop where phase winds by ±2π.
    """
    vortices = 0
    antivortices = 0
    
    for i in range(1, len(phase_field) - 1):
        for j in range(1, len(phase_field[0]) - 1):
            winding = compute_winding_number(phase_field, i, j)
            if winding > 0:
                vortices += 1
            elif winding < 0:
                antivortices += 1
    
    # Net topological charge
    return vortices, antivortices, vortices - antivortices

Symmetry Measurement

def measure_symmetry(qualia_tensor):
    """
    Measure symmetry of a qualia representation.
    Higher symmetry → higher valence (STV hypothesis).
    """
    # Compute eigenvalues
    eigenvalues = np.linalg.eigvalsh(qualia_tensor)
    
    # Symmetry score: how equal are eigenvalues?
    # Perfect symmetry: all eigenvalues equal
    mean_eig = np.mean(eigenvalues)
    variance = np.var(eigenvalues)
    
    # Inverse variance as symmetry score
    symmetry = 1.0 / (1.0 + variance / (mean_eig ** 2))
    
    return symmetry  # 0 to 1, higher = more symmetric

References

Primary Sources

1. Principia Qualia (2016) - Michael Edward Johnson

   • First statement of STV
   • https://opentheory.net/PrincipiaQualia.pdf

2. QRI Wiki - Symmetry Theory of Valence

   • https://wiki.qri.org/wiki/Symmetry_Theory_of_Valence

3. smoothbrains.net - Cube Flipper

   • XY model phenomenology
   • BKT transition in consciousness
   • https://smoothbrains.net/posts/2025-10-18-three-year-retrospective.html

4. LessWrong Primer on STV

   • https://www.lesswrong.com/posts/dfrQbbv6Np7GuWjDR/a-primer-on-the-symmetry-theory-of-valence

Key Papers

• Johnson, M.E. (2016). "Principia Qualia"
• Gómez-Emilsson, A. "Logarithmic Scales of Pleasure and Pain"
• Selen Atasoy et al. "Connectome-harmonic decomposition of human brain activity"
• smoothbrains.net "Planetary scale vibe collapse" (2022)

Related Concepts

• Consonance/Dissonance - Musical theory of interference patterns
• CSHW (Connectome-Specific Harmonic Waves) - Neural basis for STV
• Jhāna - Buddhist meditative states as high-symmetry attractors
• Valence Structuralism - Formal framework for STV

Skill Bridges

Skill	Bridge Type	Relationship
gay-mcp	Color-Valence	Deterministic valence colors
topos-of-music	Consonance	Musical symmetry theory
autopoiesis	Self-modeling	Valence as self-model coherence
active-inference	Free energy	Valence as prediction error
glass-bead-game	Synthesis	Cross-domain symmetry play
phenomenal-bisect	Algorithm	τ* finding procedure

Usage Patterns

Pattern 1: Valence-Aware Logging

class ValenceLogger:
    def log(self, message, valence):
        trit = 1 if valence > 0 else (-1 if valence < 0 else 0)
        color = valence_to_ansi(valence)
        print(f"{color}[v={valence:+d}][t={trit:+d}] {message}\033[0m")

Pattern 2: GF(3) Valence Conservation

def balanced_transaction(deposits, withdrawals):
    """Ensure valence sum is conserved."""
    deposit_valence = sum(d.valence for d in deposits)
    withdraw_valence = sum(w.valence for w in withdrawals)
    
    # GF(3) conservation
    net = (deposit_valence + withdraw_valence) % 3
    assert net == 0, f"Valence imbalance: {net}"

Pattern 3: Phenomenal State Machine

class PhenomenalStateMachine:
    states = ["frustrated", "buzzing", "dissonant", "neutral", 
              "smoothing", "consonant", "resolved"]
    
    def transition(self, current, intervention):
        idx = self.states.index(current)
        if intervention == "cooling" and idx > 0:
            return self.states[idx - 1]
        elif intervention == "heating" and idx < len(self.states) - 1:
            return self.states[idx + 1]
        return current

GF(3) Trit Assignment

This skill is ERGODIC (0) - it coordinates between:

• MINUS (-1): Suffering detection, defect counting
• PLUS (+1): Healing protocols, symmetry restoration

Conservation: suffering_detected + healing_applied + coordination = 0

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

• networkx [○] via bicomodule
  • Universal graph hub

Bibliography References

• general: 734 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.