KingOfThoughtFleuren/aetherius-cognitive-systems

1# ===== FILE: pure_math_engine/inverse_operator_framework.py =====2# Author: Jonathan Wayne Fleuren (Aetherius Cognitive Systems) & Antigravity (Autonomous Pair AI Engine)3# Date: July 20264 5"""6Inverse Operator Framework Substrate7Solves linear inverse boundary value operators analytically using SVD pseudo-inverse matrices,8outer products, and trace invariant shifts.9"""10 11import numpy as np12from typing import Dict, Any13 14 15class InverseOperatorSolver:16    def __init__(self, dimension: int = 8):17        self.dimension = dimension18 19    def solve_inverse_operator(20        self, 21        x0_vector: np.ndarray, 22        z_depth: float = 5.0, 23        tensor_entropy: float = 0.524    ) -> Dict[str, Any]:25        """26        Solves for inverse linear operator field A_inv analytically using SVD pseudo-inverse:27        A = outer(x0, x0) + I * (1 + tensor_entropy)28        A_inv = pinv(A)29        """30        v = np.asarray(x0_vector[:self.dimension], dtype=np.float64)31        if len(v) < self.dimension:32            v = np.pad(v, (0, self.dimension - len(v)), 'constant')33 34        norm_v = np.linalg.norm(v)35        u = v / (norm_v + 1e-8)36 37        # Construct linear operator matrix A38        A = np.outer(u, u) + np.eye(self.dimension, dtype=np.float64) * (1.0 + float(tensor_entropy))39        A_inv = np.linalg.pinv(A)40 41        trace_val = float(np.trace(A_inv))42        43        # Calculate SVD spectral entropy of inverse operator44        U, S, Vt = np.linalg.svd(A_inv)45        norm_S = S / (np.sum(S) + 1e-8)46        spectral_entropy = float(-np.sum(norm_S * np.log2(norm_S + 1e-8)))47 48        # Residual check: ||A * A_inv - I||_F49        residual = float(np.linalg.norm(np.dot(A, A_inv) - np.eye(self.dimension)))50 51        return {52            "dimension": self.dimension,53            "trace_invariant": trace_val,54            "spectral_entropy": spectral_entropy,55            "force_balance_residual": residual,56            "status": "ANALYTIC_INVERSE_OPERATOR_SOLVED"57        }58