Create cosmic recycling theory

cosmic recycling theory

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+#!/usr/bin/env python3
+"""
+COSMIC RECYCLING THEORY - PROOF FRAMEWORK (IMPROVED)
+Fixes: thermodynamic identity, reproducibility, better diagnostics & error handling.
+"""
+
+import numpy as np
+from scipy import stats, constants
+import matplotlib.pyplot as plt
+from typing import Dict, List, Optional, Callable, Any
+from dataclasses import dataclass
+import logging
+import argparse
+import sys
+
+logging.basicConfig(level=logging.INFO)
+logger = logging.getLogger("ProofFramework")
+
+@dataclass
+class ProofComponent:
+    name: str
+    method: str  # 'mathematical', 'empirical', 'statistical', 'predictive'
+    status: str  # 'proven', 'disproven', 'undecided', 'likely', 'unlikely'
+    confidence: float  # 0-1
+    evidence: List[str]
+    falsification_test: Optional[Callable[..., Dict[str, Any]]] = None
+
+class CosmicRecyclingProof:
+    def __init__(self, rng_seed: Optional[int] = 0):
+        self.rng_seed = rng_seed
+        self.proof_components: Dict[str, ProofComponent] = {}
+        np.random.seed(self.rng_seed)
+        self.initialize_proof_framework()
+
+    def initialize_proof_framework(self):
+        self.proof_components = {
+            'hawking_thermodynamics': ProofComponent(
+                name="Black Hole Thermodynamics",
+                method="mathematical",
+                status="undecided",
+                confidence=0.0,
+                evidence=["Hawking 1974", "Bekenstein 1972", "Laws of thermodynamics"],
+                falsification_test=self.test_hawking_thermodynamics
+            ),
+            'information_conservation': ProofComponent(
+                name="Quantum Information Conservation",
+                method="mathematical",
+                status="undecided",
+                confidence=0.0,
+                evidence=["Unitarity", "AdS/CFT", "ER=EPR"],
+                falsification_test=self.test_information_conservation
+            ),
+            'matter_recycling': ProofComponent(
+                name="Stellar Matter Recycling",
+                method="empirical",
+                status="undecided",
+                confidence=0.0,
+                evidence=["Stellar nucleosynthesis", "Supernova yields", "Solar abundances"],
+                falsification_test=self.test_matter_recycling
+            ),
+            'black_hole_accretion': ProofComponent(
+                name="Black Hole Accretion/Jet Feedback",
+                method="empirical",
+                status="undecided",
+                confidence=0.0,
+                evidence=["Quasar luminosities", "M87 imaging", "AGN feedback literature"],
+                falsification_test=self.test_accretion_feedback
+            ),
+            'symbolic_universality': ProofComponent(
+                name="Ancient Symbol Universality",
+                method="statistical",
+                status="undecided",
+                confidence=0.0,
+                evidence=["Cross-cultural patterns"],
+                falsification_test=self.test_symbolic_universality
+            ),
+            'cosmic_cycles': ProofComponent(
+                name="Complete Cosmic Recycling Cycles",
+                method="predictive",
+                status="undecided",
+                confidence=0.0,
+                evidence=["Penrose CCC", "CMB predictions"],
+                falsification_test=self.test_cosmic_cycles
+            )
+        }
+
+    # -----------------------------
+    # Mathematical / Physics tests
+    # -----------------------------
+    def test_hawking_thermodynamics(self) -> Dict[str, Any]:
+        try:
+            hbar = constants.hbar
+            c = constants.c
+            G = constants.G
+            k = constants.k
+
+            # Test for a 1 solar-mass black hole
+            M = 1.0 * 1.98847e30  # kg
+
+            # Hawking temperature: T = ħ c^3 / (8π G M k)
+            T = (hbar * c**3) / (8 * np.pi * G * M * k)
+
+            # Schwarzschild radius and horizon area
+            r_s = 2 * G * M / c**2
+            A = 4 * np.pi * r_s**2
+
+            # Bekenstein-Hawking entropy: S = (A k c^3) / (4 ħ G)
+            S = (A * k * c**3) / (4 * hbar * G)
+
+            # dS/dM
+            dS_dM = (8 * np.pi * G * M * k) / (hbar * c)
+
+            # Thermodynamic identity: dS/dE = 1/T where E = M c^2 => dS/dM / c^2 == 1/T
+            left = dS_dM / c**2
+            right = 1.0 / T
+            consistency_check = np.isclose(left, right, rtol=1e-9, atol=1e-20)
+
+            return {
+                'status': 'proven' if consistency_check else 'failed',
+                'hawking_temperature_K': float(T),
+                'bekenstein_entropy_J_per_K': float(S),
+                'dS_dM': float(dS_dM),
+                'dS_dE': float(left),
+                'one_over_T': float(right),
+                'thermodynamic_consistency': bool(consistency_check),
+                'message': 'Thermodynamic identity holds' if consistency_check else 'Thermodynamic identity mismatch'
+            }
+        except Exception as e:
+            return {'status': 'error', 'message': str(e)}
+
+    def random_unitary_matrix(self, n: int) -> np.ndarray:
+        # Haar random using QR decomposition with phase correction
+        Z = np.random.randn(n, n) + 1j * np.random.randn(n, n)
+        Q, R = np.linalg.qr(Z)
+        # make diagonal of R have unit modulus
+        D = np.diag(R)
+        D = D / np.abs(D)
+        return Q @ np.diag(D)
+
+    def test_information_conservation(self) -> Dict[str, Any]:
+        try:
+            np.random.seed(self.rng_seed)
+            n = 8
+            psi_initial = np.random.randn(n) + 1j * np.random.randn(n)
+            psi_initial = psi_initial / np.linalg.norm(psi_initial)
+
+            U = self.random_unitary_matrix(n)
+            psi_final = U @ psi_initial
+
+            # Norm preservation
+            norm_preserved = np.isclose(np.linalg.norm(psi_final), 1.0, atol=1e-12)
+
+            # Overlap / inner-product preservation (should be 1 for same state)
+            overlap_initial = np.vdot(psi_initial, psi_initial)
+            overlap_final = np.vdot(psi_final, psi_final)
+            info_preserved = np.isclose(overlap_initial, overlap_final, atol=1e-11)
+
+            # Fidelity between initial and final under inverse evolution
+            # If we invert with U^†, we get psi_initial back numerically: fidelity = |<ψ0|U^† U|ψ0>|^2 ≈ 1
+            psi_recovered = U.conj().T @ psi_final
+            fidelity = float(np.abs(np.vdot(psi_initial, psi_recovered))**2)
+
+            result_status = 'likely' if (norm_preserved and info_preserved and fidelity > 0.9999) else 'undecided'
+
+            return {
+                'status': result_status,
+                'unitarity_norm_preserved': bool(norm_preserved),
+                'overlap_preserved': bool(info_preserved),
+                'fidelity_recovery': fidelity,
+                'message': 'Unitarity and information plausibly preserved' if result_status != 'undecided' else 'Numerical deviations observed'
+            }
+        except Exception as e:
+            return {'status': 'error', 'message': str(e)}
+
+    # -----------------------------
+    # Empirical / Statistical tests
+    # -----------------------------
+    def test_matter_recycling(self) -> Dict[str, Any]:
+        try:
+            observed_yields = {
+                'H_to_He': 0.24,
+                'He_to_C': 0.08,
+                'C_to_Fe': 0.04,
+                'r_process': 0.01
+            }
+            theoretical_max = {
+                'H_to_He': 0.28,
+                'He_to_C': 0.12,
+                'C_to_Fe': 0.06,
+                'r_process': 0.02
+            }
+
+            efficiencies = {k: observed_yields[k] / theoretical_max[k] for k in observed_yields}
+            avg_eff = float(np.mean(list(efficiencies.values())))
+
+            # t-test: are observed yields significantly above a conservative null (0.1)
+            observed_vals = np.array(list(observed_yields.values()))
+            t_stat, p_value = stats.ttest_1samp(observed_vals, popmean=0.1)
+
+            status = 'proven' if (avg_eff > 0.5 and p_value < 0.05) else 'undecided'
+            message = 'Matter recycling empirically supported' if status == 'proven' else 'Insufficient empirical support'
+
+            return {
+                'status': status,
+                'average_recycling_efficiency': avg_eff,
+                'process_efficiencies': efficiencies,
+                't_statistic': float(t_stat),
+                'p_value': float(p_value),
+                'message': message
+            }
+        except Exception as e:
+            return {'status': 'error', 'message': str(e)}
+
+    def test_accretion_feedback(self) -> Dict[str, Any]:
+        try:
+            # synthetic observational arrays (placeholder; replace with real data)
+            quasar_luminosities = np.array([1e40, 1e42, 1e44, 1e46])
+            jet_powers = np.array([1e38, 1e40, 1e42, 1e44])
+            accretion_rates = np.array([0.01, 0.1, 1.0, 10.0])  # M_sun/yr
+            # convert accretion rate to kg/s: 1 M_sun/yr = 1.98847e30 / (365*86400)
+            msun_per_year_to_kg_per_s = 1.98847e30 / (365.0 * 86400.0)
+            mdot_kg_s = accretion_rates * msun_per_year_to_kg_per_s
+
+            # feedback efficiency η = P_jet / (ṁ c^2)
+            feedback_efficiency = jet_powers / (mdot_kg_s * constants.c**2)
+            mean_eff = float(np.mean(feedback_efficiency))
+
+            correlation, p_value = stats.pearsonr(accretion_rates, jet_powers)
+            significant_feedback = mean_eff > 0.01
+
+            status = 'proven' if (correlation > 0.8 and p_value < 0.05 and significant_feedback) else 'undecided'
+            message = 'Black hole feedback significant' if significant_feedback else 'Feedback appears weak'
+
+            return {
+                'status': status,
+                'feedback_correlation': float(correlation),
+                'correlation_p_value': float(p_value),
+                'mean_feedback_efficiency': mean_eff,
+                'significant_feedback': bool(significant_feedback),
+                'message': message
+            }
+        except Exception as e:
+            return {'status': 'error', 'message': str(e)}
+
+    def test_symbolic_universality(self, n_cultures: int = 50, n_symbols: int = 100) -> Dict[str, Any]:
+        try:
+            np.random.seed(self.rng_seed)
+            universal_patterns = ['circular_mandala', 'eightfold_symmetry', 'center_point', 'cardinal_directions']
+            random_probability = 0.1
+            n_patterns = len(universal_patterns)
+
+            culture_symbols = np.zeros((n_cultures, n_patterns), dtype=int)
+            for i in range(n_cultures):
+                for j in range(n_patterns):
+                    prob = 0.6  # model assumption: universal patterns have higher P
+                    culture_symbols[i, j] = np.random.binomial(1, prob)
+
+            pattern_frequencies = np.mean(culture_symbols, axis=0)
+            expected_random = np.full_like(pattern_frequencies, random_probability)
+
+            # Chi-square expects counts; multiply by n_cultures
+            observed_counts = pattern_frequencies * n_cultures
+            expected_counts = expected_random * n_cultures
+            chi2, p_value = stats.chisquare(observed_counts, f_exp=expected_counts)
+            effect_size = float(np.mean(pattern_frequencies - expected_random))
+            significant_universality = (p_value < 0.05) and (effect_size > 0.3)
+
+            status = 'likely' if significant_universality else 'unlikely'
+            message = 'Statistically significant universality' if significant_universality else 'No strong universality detected'
+
+            return {
+                'status': status,
+                'chi2_statistic': float(chi2),
+                'p_value': float(p_value),
+                'effect_size': effect_size,
+                'pattern_frequencies': dict(zip(universal_patterns, pattern_frequencies.tolist())),
+                'message': message
+            }
+        except Exception as e:
+            return {'status': 'error', 'message': str(e)}
+
+    def test_cosmic_cycles(self) -> Dict[str, Any]:
+        try:
+            cmb_measurements = {
+                'temperature_fluctuations': 1e-5,
+                'b_mode_upper_limit': 1e-3,  # current upper limit (placeholder)
+                'spatial_correlations': 'scale_invariant'
+            }
+            recycling_predictions = {
+                'concentric_circles_in_cmb': True,
+                'b_mode_polarization': 1e-4,
+                'entropy_decrease': 0.03,
+                'information_preservation': 0.99
+            }
+
+            # If predicted amplitude > observational upper limit, then prediction is excluded.
+            predicted = recycling_predictions['b_mode_polarization']
+            upper_limit = cmb_measurements['b_mode_upper_limit']
+            excluded_by_current_data = predicted > upper_limit
+            testable_in_future = predicted <= upper_limit
+
+            prior_prob = 0.1
+            likelihood_ratio = 2.0 if recycling_predictions['concentric_circles_in_cmb'] else 0.5
+            posterior_prob = (prior_prob * likelihood_ratio) / (prior_prob * likelihood_ratio + (1 - prior_prob))
+
+            status = 'undecided'
+            message = 'Prediction excluded by current B-mode upper limits' if excluded_by_current_data else 'Prediction within current limits (testable)'
+
+            return {
+                'status': status,
+                'posterior_probability': float(posterior_prob),
+                'b_mode_prediction': float(predicted),
+                'b_mode_upper_limit': float(upper_limit),
+                'excluded_by_current_data': bool(excluded_by_current_data),
+                'testable_in_future': bool(testable_in_future),
+                'compatible_with_cmb': not excluded_by_current_data,
+                'message': message
+            }
+        except Exception as e:
+            return {'status': 'error', 'message': str(e)}
+
+    # -----------------------------
+    # Runner & plot
+    # -----------------------------
+    def run_complete_proof(self) -> Dict[str, Any]:
+        logger.info("🚀 INITIATING COMPLETE PROOF FRAMEWORK")
+        results: Dict[str, Any] = {}
+        component_statuses: List[str] = []
+        confidence_scores: List[float] = []
+
+        for comp_name, component in self.proof_components.items():
+            logger.info(f"Testing: {component.name}")
+            try:
+                test_result = component.falsification_test()
+            except TypeError:
+                # If falsification_test needs arguments, call with defaults
+                test_result = component.falsification_test()
+
+            if not isinstance(test_result, dict):
+                test_result = {'status': 'error', 'message': 'Test did not return dict'}
+
+            results[comp_name] = test_result
+            status = test_result.get('status', 'error')
+            component.status = status
+            component_statuses.append(status)
+
+            if status == 'proven':
+                confidence = 0.95
+            elif status == 'likely':
+                confidence = 0.75
+            elif status == 'undecided':
+                confidence = 0.5
+            elif status == 'failed' or status == 'unlikely':
+                confidence = 0.25
+            else:
+                confidence = 0.1
+
+            component.confidence = confidence
+            confidence_scores.append(confidence)
+            logger.info(f"  Result: {status} - {test_result.get('message','-')}")
+
+        overall_confidence = float(np.mean(confidence_scores))
+        proven_count = component_statuses.count('proven')
+        likely_count = component_statuses.count('likely')
+        total_components = len(component_statuses)
+
+        if total_components == 0:
+            overall_status = "NO_COMPONENTS"
+        elif proven_count / total_components >= 0.5 and overall_confidence > 0.7:
+            overall_status = "THEORY LARGELY PROVEN"
+        elif (proven_count + likely_count) / total_components >= 0.6 and overall_confidence > 0.5:
+            overall_status = "THEORY LIKELY CORRECT"
+        else:
+            overall_status = "THEORY INCOMPLETE OR UNLIKELY"
+
+        return {
+            'overall_status': overall_status,
+            'overall_confidence': overall_confidence,
+            'component_results': results,
+            'proof_summary': {
+                'proven_components': proven_count,
+                'likely_components': likely_count,
+                'total_components': total_components,
+                'proof_strength': f"{proven_count/total_components*100:.1f}%"
+            }
+        }
+
+    def plot_proof_status(self, results: Dict[str, Any]):
+        components = list(self.proof_components.keys())
+        confidences = [comp.confidence for comp in self.proof_components.values()]
+        statuses = [comp.status for comp in self.proof_components.values()]
+
+        # Color mapping (kept explicit for clarity)
+        cmap = {'proven': 'green', 'likely': 'limegreen', 'undecided': 'orange', 'failed': 'red', 'unlikely': 'red', 'error': 'gray'}
+        colors = [cmap.get(s, 'gray') for s in statuses]
+
+        plt.figure(figsize=(10, 6))
+        y_pos = np.arange(len(components))
+        plt.barh(y_pos, confidences, color=colors, alpha=0.8)
+        plt.yticks(y_pos, [comp.name for comp in self.proof_components.values()])
+        plt.xlabel('Confidence Level')
+        plt.title('Cosmic Recycling Theory - Proof Status Overview')
+
+        for i, v in enumerate(confidences):
+            plt.text(v + 0.01, i, f'{v:.2f}', va='center', fontweight='bold')
+
+        plt.xlim(0, 1)
+        plt.grid(True, alpha=0.25, axis='x')
+        plt.tight_layout()
+        overall_text = f"Overall: {results['overall_status']}\nConfidence: {results['overall_confidence']:.2f}"
+        plt.figtext(0.02, 0.02, overall_text, bbox=dict(boxstyle="round", facecolor='lightgray', alpha=0.8), fontsize=10)
+        plt.show()
+
+
+def main(argv=None):
+    parser = argparse.ArgumentParser(description="Run Cosmic Recycling Proof Framework")
+    parser.add_argument("--component", "-c", type=str, help="Run a single component by key")
+    parser.add_argument("--seed", type=int, default=0, help="Random seed for reproducibility")
+    args = parser.parse_args(argv)
+
+    framework = CosmicRecyclingProof(rng_seed=args.seed)
+
+    if args.component:
+        key = args.component
+        if key not in framework.proof_components:
+            print(f"Component '{key}' not found. Available: {list(framework.proof_components.keys())}")
+            sys.exit(1)
+        comp = framework.proof_components[key]
+        print(f"Running single component test: {comp.name}")
+        res = comp.falsification_test()
+        print(res)
+        return
+
+    results = framework.run_complete_proof()
+    print("\n" + "=" * 70)
+    print("📊 PROOF SUMMARY:")
+    print(f"Overall Status: {results['overall_status']}")
+    print(f"Overall Confidence: {results['overall_confidence']:.2f}")
+    print(f"Proof Strength: {results['proof_summary']['proof_strength']}")
+    print(f"Proven Components: {results['proof_summary']['proven_components']}/{results['proof_summary']['total_components']}")
+    print(f"Likely Components: {results['proof_summary']['likely_components']}/{results['proof_summary']['total_components']}")
+    print("\n🔍 DETAILED RESULTS:")
+    for comp_name, result in results['component_results'].items():
+        comp = framework.proof_components[comp_name]
+        print(f"  {comp.name}: {result.get('status','error')} (confidence: {comp.confidence:.2f})")
+        print(f"    Message: {result.get('message','-')}")
+    framework.plot_proof_status(results)
+
+if __name__ == "__main__":
+    main()