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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.
Verifies World Extractable Value (WEV) using quadrant classification, GF(3) triads, reafference loops, and Proof-of-Frog consensus. Provides Julia functions for learning agent simulation and validation.
Provides methodologies for quantum-enhanced AGI including Shor's/Grover's algorithms, entanglement systems, error correction codes, and Python performance optimizers. Useful for advanced quantum AI discussions.
Performs symbolic math in Python using SymPy: solves equations algebraically, computes derivatives/integrals/limits, simplifies expressions, handles matrices, physics, and generates code.
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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.
"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:
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):
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):
| 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 |
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")
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)
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
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
Principia Qualia (2016) - Michael Edward Johnson
QRI Wiki - Symmetry Theory of Valence
smoothbrains.net - Cube Flipper
LessWrong Primer on STV
| 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 |
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")
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}"
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
This skill is ERGODIC (0) - it coordinates between:
Conservation: suffering_detected + healing_applied + coordination = 0
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
general: 734 citations in bib.duckdbThis 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
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.