import numpy as np # ============================================================ # CRYSTAL FILTER CLASS # ============================================================ class CrystalFilter: """One of 10 crystal filters for processing observations.""" def __init__(self, crystal_id, crystal_type): self.crystal_id = crystal_id self.crystal_type = crystal_type self.weights = np.random.rand(10) # Internal weights self.output_history = [] self.checksum_value = 0.5 def process(self, system_input, theta, intelligence): """Process system input through this crystal filter.""" # Scale input by alignment and intelligence scaling = (1 - intelligence) * (theta / np.pi) # Apply crystal-specific transformation if self.crystal_type == "Cubic": output = self._cubic_transform(system_input, scaling) elif self.crystal_type == "Hexagonal": output = self._hexagonal_transform(system_input, scaling) elif self.crystal_type == "Tetrahedral": output = self._tetrahedral_transform(system_input, scaling) elif self.crystal_type == "Quasicrystal": output = self._quasicrystal_transform(system_input, scaling) elif self.crystal_type == "Graphene": output = self._graphene_transform(system_input, scaling) elif self.crystal_type == "BCC": output = self._bcc_transform(system_input, scaling) elif self.crystal_type == "FCC": output = self._fcc_transform(system_input, scaling) elif self.crystal_type == "Perovskite": output = self._perovskite_transform(system_input, scaling) elif self.crystal_type == "Cayley": output = self._cayley_transform(system_input, scaling) elif self.crystal_type == "Fractal": output = self._fractal_transform(system_input, scaling) else: output = system_input * scaling self.output_history.append(output) return output def _cubic_transform(self, x, s): """Grid-based hashing - systematic analysis.""" return np.floor(x * 10) / 10 * (1 - s) def _hexagonal_transform(self, x, s): """Voronoi clustering - local grouping.""" return np.sin(x * 6 + s) * np.cos(x * 6 - s) def _tetrahedral_transform(self, x, s): """Symmetry detection - rotational checks.""" return (x**3 - x) * (1 - s) def _quasicrystal_transform(self, x, s): """Pattern recognition - aperiodic structures.""" return np.sin(x * 8.5) * np.cos(x * 5.2) * np.exp(-s) def _graphene_transform(self, x, s): """Sequential logic - edge traversal.""" return np.cumsum(np.sin(x + s)) def _bcc_transform(self, x, s): """Hierarchical reasoning - tree structures.""" return np.sort(np.abs(x)) * (1 + s) def _fcc_transform(self, x, s): """Mirror validation - inverse paths.""" return (x + np.flip(x)) / 2 * np.exp(-s) def _perovskite_transform(self, x, s): """Domain constraints - specialized filtering.""" return x * (1 + s) * np.tanh(x) def _cayley_transform(self, x, s): """Symbolic manipulation - algebraic.""" return x**2 - s * x + s**2 def _fractal_transform(self, x, s): """Multi-scale analysis - recursive.""" output = x for _ in range(3): output = output * np.sin(output + s) return output def get_checksum(self): """Return current checksum value for this crystal.""" if len(self.output_history) > 0: self.checksum_value = np.mean(self.output_history) return self.checksum_value def reset(self): """Reset the crystal filter.""" self.output_history = [] self.checksum_value = 0.5 # ============================================================ # OBSERVER VARIABLE CLASS # ============================================================ class ObserverVariable: """ Complete Observer Variable for Measurement Mathematics. Combines: - 10 crystal filters (Cubic, Hexagonal, Tetrahedral, Quasicrystal, Graphene, BCC, FCC, Perovskite, Cayley, Fractal) - π/e checksum anchoring - Will strength dynamics - Intelligence tracking - Collapse rate computation """ def __init__(self, n_crystals=10): # Crystal types in order crystal_types = [ "Cubic", "Hexagonal", "Tetrahedral", "Quasicrystal", "Graphene", "BCC", "FCC", "Perovskite", "Cayley", "Fractal" ] # === Stationary components (fixed at init) === self.Omega_0 = 1.0 # Base will strength self.I_0 = 0.5 # Base intelligence (0-1) self.theta_life = 0.1 # Life zone threshold self.n_crystals = min(n_crystals, len(crystal_types)) # === Probabilistic components (variable state) === self.Omega = self.Omega_0 # Current will strength self.I = self.I_0 # Current intelligence self.H = 1.0 # Current semantic entropy self.theta = np.pi / 2 # Alignment angle (π/2 = neutral) # === Crystal filter bank === self.crystals = [ CrystalFilter(i, crystal_types[i % len(crystal_types)]) for i in range(self.n_crystals) ] self.weights = np.ones(self.n_crystals) / self.n_crystals # === π/e checksum baselines === self.C_pi_baseline = 0.5 self.C_e_baseline = 0.5 self.observation_history = [] # === Exhaustion parameters === self.epsilon = 0.01 # Exhaustion rate self.energy_spent = 0.0 # Accumulated energy expenditure # === Collapse parameters === self.Delta_max = 1.0 self.alpha_base = 1.0 # === Performance tracking === self.success_count = 0 self.total_measurements = 0 # -------------------------------------------------------- # Observer Function (Crystal Filter Bank) # -------------------------------------------------------- def compute_observer_function(self, system_input): """Compute observer function via crystal filter bank.""" outputs = [] for i, crystal in enumerate(self.crystals): phi = crystal.process(system_input, self.theta, self.I) outputs.append(phi * self.weights[i]) result = np.sum(outputs, axis=0) self.observation_history.append(result) return result # -------------------------------------------------------- # π/e Checksum Computation # -------------------------------------------------------- def compute_pi_checksum(self, F_o, T=10.0): """C_π(O) = ∫ F_o(t) · cos(πt) dt""" t = np.linspace(0, T, 1000) F_o_array = np.atleast_1d(F_o) # Create function from scalar or array if len(F_o_array) == 1: integrand = F_o_array[0] * np.cos(np.pi * t / T) else: # Interpolate to match time points x_pts = np.linspace(0, 1, len(F_o_array)) f_interp = np.interp(np.linspace(0, 1, 1000), x_pts, F_o_array) integrand = f_interp * np.cos(np.pi * t / T) return np.trapezoid(integrand, t) def compute_e_checksum(self, F_o, T=10.0): """C_e(O) = ∫ F_o(t) · exp(-e·t) dt""" t = np.linspace(0, T, 1000) F_o_array = np.atleast_1d(F_o) if len(F_o_array) == 1: integrand = F_o_array[0] * np.exp(-np.e * t / T) else: x_pts = np.linspace(0, 1, len(F_o_array)) f_interp = np.interp(np.linspace(0, 1, 1000), x_pts, F_o_array) integrand = f_interp * np.exp(-np.e * t / T) return np.trapezoid(integrand, t) # -------------------------------------------------------- # Collapse Potential and Rate # -------------------------------------------------------- def compute_collapse_potential(self): """ Δ_c(θ, I) = Δ_max · sin²(θ/2) · (1 - I) Measures how much collapse the observer triggers. High intelligence + aligned → low collapse potential Low intelligence + misaligned → high collapse potential """ return self.Delta_max * np.sin(self.theta / 2)**2 * (1 - self.I) def compute_crystal_coherence(self): """Product of coherence factors from all crystal filters.""" coherence_prod = 1.0 for crystal in self.crystals: C_pi_i = crystal.get_checksum() coherence_factor = np.exp(-0.1 * abs(C_pi_i - self.C_pi_baseline)) coherence_prod *= coherence_factor return coherence_prod def compute_collapse_rate(self): """ α_measure = α_base · Δ_c · (Ω/(Ω+ε)) · Πφ_i Rate at which observer causes collapse. """ Delta_c = self.compute_collapse_potential() will_util = self.Omega / (self.Omega + self.epsilon) coherence = self.compute_crystal_coherence() return self.alpha_base * Delta_c * will_util * coherence # -------------------------------------------------------- # Truth Extraction # -------------------------------------------------------- def compute_understanding_level(self): """ u_i(O) = exp(-β · d_crystal) / Z How well the observer understands each truth domain. """ beta = 1.0 distances = [] for i, crystal in enumerate(self.crystals): d = abs(crystal.get_checksum() - self.C_pi_baseline) distances.append(np.exp(-beta * d)) Z = np.sum(distances) + 1e-10 return distances / Z def extract_truth(self, system_input): """Extract truth from system using sensor array.""" understanding = self.compute_understanding_level() # High understanding (>0.5) → known answer, no collapse # Low understanding (<0.5) → collapse required results = [] for i, (crystal, u) in enumerate(zip(self.crystals, understanding)): if u > 0.5: # Known - use original value results.append(("known", system_input)) else: # Unknown - collapsed value collapsed = self.force_collapse(system_input) results.append(("collapsed", collapsed)) return results def force_collapse(self, state): """Force collapse to single deterministic outcome.""" if isinstance(state, (int, float)): return state elif hasattr(state, '__len__'): return np.mean(np.atleast_1d(state)) else: return state def summarize_outcome(self, outcome): """Convert an outcome to a scalar summary for evaluation and display.""" if isinstance(outcome, (int, float, np.integer, np.floating)): return float(outcome) if hasattr(outcome, '__len__'): return float(np.mean(np.atleast_1d(outcome))) return float(outcome) # -------------------------------------------------------- # Observer State Update # -------------------------------------------------------- def update_will(self, success): """dΩ/dt = η·S - ε·E_spent""" eta = 0.1 self.Omega += eta * success - self.epsilon * self.energy_spent self.Omega = max(0.1, self.Omega) # Floor at 0.1 self.energy_spent += 0.01 def update_crystal_weights(self, divergence_per_crystal): """Adapt crystal weights based on divergence.""" kappa = 0.1 delta_good = 0.01 delta_bad = 0.01 for i, div in enumerate(divergence_per_crystal): if div < 0.1: # Good alignment self.weights[i] += kappa * delta_good else: # Bad alignment self.weights[i] -= kappa * delta_bad # Normalize self.weights = np.maximum(self.weights, 0.01) self.weights = self.weights / np.sum(self.weights) def update_intelligence(self, success): """Gradually improve intelligence based on success.""" if success > 0.8: self.I = min(1.0, self.I + 0.01) elif success < 0.3: self.I = max(0.0, self.I - 0.01) # -------------------------------------------------------- # Main Measurement Function # -------------------------------------------------------- def measure(self, system_input, ground_truth=None): """ Perform complete measurement and return results. Args: system_input: The system state to observe ground_truth: Optional ground truth for evaluation Returns: Dictionary with measurement results """ self.total_measurements += 1 # Step 1: Compute observer function F_o = self.compute_observer_function(system_input) # Step 2: Compute checksums C_pi = self.compute_pi_checksum(F_o) C_e = self.compute_e_checksum(F_o) # Step 3: Compute collapse alpha = self.compute_collapse_rate() measurement_outcome = self.collapse(system_input, alpha) measurement_value = self.summarize_outcome(measurement_outcome) # Step 4: Compute divergence per crystal divergence_per_crystal = [] for crystal in self.crystals: divergence = abs(crystal.get_checksum() - self.C_pi_baseline) divergence_per_crystal.append(divergence) # Step 5: Compute success signal if ground_truth is not None: if isinstance(ground_truth, (int, float)): success = 1.0 if abs(measurement_value - ground_truth) < 0.1 else 0.0 else: ground_truth_value = self.summarize_outcome(ground_truth) success = 1.0 if abs(measurement_value - ground_truth_value) < 0.1 else 0.0 else: # Use checksum alignment as proxy total_divergence = sum(divergence_per_crystal) success = np.exp(-total_divergence / self.n_crystals) # Step 6: Update observer state self.update_will(success) self.update_crystal_weights(divergence_per_crystal) self.update_intelligence(success) # Track success self.success_count += success # Step 7: Extract truth understanding = self.compute_understanding_level() truth_results = self.extract_truth(system_input) return { 'outcome': measurement_value, 'raw_outcome': measurement_outcome, 'checksums': { 'C_pi': C_pi, 'C_e': C_e }, 'divergence': sum(divergence_per_crystal) / self.n_crystals, 'collapse_rate': alpha, 'collapse_potential': self.compute_collapse_potential(), 'will_strength': self.Omega, 'intelligence': self.I, 'entropy': self.H, 'alignment_angle': self.theta, 'crystal_weights': self.weights.copy(), 'success': success, 'understanding': understanding, 'truth_results': truth_results } def collapse(self, system_input, alpha): """Collapse system based on computed alpha.""" if alpha < 0.1: # Low alpha: wave pattern preserved (no collapse) return system_input else: # High alpha: particle pattern (forced collapse) return self.force_collapse(system_input) # -------------------------------------------------------- # Status and Reset # -------------------------------------------------------- def get_status(self): """Get current observer status.""" return { 'will_strength': self.Omega, 'intelligence': self.I, 'entropy': self.H, 'alignment': self.theta, 'success_rate': self.success_count / max(1, self.total_measurements), 'energy_spent': self.energy_spent } def reset(self): """Reset observer to initial state.""" self.Omega = self.Omega_0 self.I = self.I_0 self.H = 1.0 self.theta = np.pi / 2 self.energy_spent = 0.0 self.success_count = 0 self.total_measurements = 0 self.observation_history = [] self.weights = np.ones(self.n_crystals) / self.n_crystals for crystal in self.crystals: crystal.reset() def __repr__(self): return f"ObserverVariable(Ω={self.Omega:.3f}, I={self.I:.3f}, crystals={self.n_crystals})" # ============================================================ # DEMONSTRATION # ============================================================ if __name__ == "__main__": # Create observer obs = ObserverVariable() print("Created:", obs) print("\n" + "="*60) print("OBSERVER STATUS") print("="*60) print(obs.get_status()) # Run several measurements print("\n" + "="*60) print("RUNNING MEASUREMENTS") print("="*60) #np.random.seed(42) for i in range(5): # Simulate system input system_input = np.random.rand(10) * 10 ground_truth = np.mean(system_input) result = obs.measure(system_input, ground_truth) print(f"\n--- Measurement {i+1} ---") print(f" Outcome: {result['outcome']:.4f}") print(f" Collapse Rate: {result['collapse_rate']:.4f}") print(f" Will Strength: {result['will_strength']:.4f}") print(f" Intelligence: {result['intelligence']:.4f}") print(f" Success: {result['success']:.4f}") print("\n" + "="*60) print("FINAL STATUS") print("="*60) status = obs.get_status() for key, value in status.items(): print(f" {key}: {value:.4f}") print("\n" + "="*60) print("CRYSTAL WEIGHTS") print("="*60) crystal_names = ["Cubic", "Hexagonal", "Tetrahedral", "Quasicrystal", "Graphene", "BCC", "FCC", "Perovskite", "Cayley", "Fractal"] for i, (name, w) in enumerate(zip(crystal_names[:obs.n_crystals], obs.weights)): print(f" {name:12s}: {w:.4f}")