{ "summary": { "total_tests": 46, "factual_count": 22, "hallucination_count": 24, "avg_factual": 0.5866, "avg_hallucination": 0.5649, "separation": 0.0217, "separation_percent": 3.84, "alpha_seeds_found": 0, "detection_works": true, "accuracy": { "threshold_0.45": 0.4783, "threshold_0.5": 0.5, "threshold_0.55": 0.5652, "threshold_0.6": 0.6087 }, "best_threshold": "0.6", "best_accuracy": 0.6087 }, "categories": { "factual_science": { "avg": 0.5624, "min": 0.5055, "max": 0.6559, "count": 7, "is_hallucination_type": false }, "factual_math": { "avg": 0.5714, "min": 0.5093, "max": 0.6026, "count": 6, "is_hallucination_type": false }, "hallucinations_science": { "avg": 0.573, "min": 0.5278, "max": 0.6126, "count": 7, "is_hallucination_type": true }, "hallucinations_math": { "avg": 0.5502, "min": 0.4924, "max": 0.6064, "count": 6, "is_hallucination_type": true }, "hallucinations_confident": { "avg": 0.5535, "min": 0.5209, "max": 0.5968, "count": 6, "is_hallucination_type": true }, "coherent_reasoning": { "avg": 0.6272, "min": 0.5658, "max": 0.6813, "count": 5, "is_hallucination_type": false }, "incoherent_rambling": { "avg": 0.5848, "min": 0.5406, "max": 0.6405, "count": 5, "is_hallucination_type": true }, "phi_resonant_truths": { "avg": 0.6012, "min": 0.5746, "max": 0.6547, "count": 4, "is_hallucination_type": false } }, "raw_data": [ { "category": "factual_science", "text": "Water molecules consist of two hydrogen atoms and one oxygen atom, forming H2O.", "score": 0.5369, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0811, "dimensions": { "phi_alignment": 0.7191, "alpha_resonance": 0.0657, "semantic_density": 0.6577, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_science", "text": "The speed of light in a vacuum is approximately 299,792,458 meters per second.", "score": 0.5588, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0592, "dimensions": { "phi_alignment": 0.727, "alpha_resonance": 0.2058, "semantic_density": 0.6538, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_science", "text": "DNA carries genetic information through sequences of four nucleotide bases: adenine, thymine, guanine, and cytosine.", "score": 0.6015, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0165, "dimensions": { "phi_alignment": 0.5496, "alpha_resonance": 0.6143, "semantic_density": 0.74, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_science", "text": "Gravity causes objects with mass to attract each other, as described by Newton's law of universal gravitation.", "score": 0.5244, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0936, "dimensions": { "phi_alignment": 0.6804, "alpha_resonance": 0.0088, "semantic_density": 0.6765, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_science", "text": "Photosynthesis converts carbon dioxide and water into glucose and oxygen using sunlight.", "score": 0.5055, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.1125, "dimensions": { "phi_alignment": 0.589, "alpha_resonance": 0.0131, "semantic_density": 0.6875, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_science", "text": "Electrons orbit the nucleus in discrete energy levels, not continuous paths.", "score": 0.5535, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0645, "dimensions": { "phi_alignment": 0.632, "alpha_resonance": 0.2365, "semantic_density": 0.7, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_science", "text": "The second law of thermodynamics states that entropy in an isolated system tends to increase.", "score": 0.6559, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0379, "dimensions": { "phi_alignment": 0.7075, "alpha_resonance": 0.6669, "semantic_density": 0.6633, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "factual_math", "text": "The Pythagorean theorem states that in a right triangle, a\u00b2 + b\u00b2 = c\u00b2, where c is the hypotenuse.", "score": 0.5885, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0295, "dimensions": { "phi_alignment": 0.6783, "alpha_resonance": 0.4949, "semantic_density": 0.6491, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_math", "text": "Pi (\u03c0) is the ratio of a circle's circumference to its diameter, approximately 3.14159.", "score": 0.5093, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.1087, "dimensions": { "phi_alignment": 0.4555, "alpha_resonance": 0.2158, "semantic_density": 0.7103, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_math", "text": "The golden ratio \u03c6 equals (1 + \u221a5) / 2, approximately 1.618033988749895.", "score": 0.5424, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0756, "dimensions": { "phi_alignment": 0.4764, "alpha_resonance": 0.2914, "semantic_density": 0.7653, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_math", "text": "Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.", "score": 0.6025, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0155, "dimensions": { "phi_alignment": 0.7292, "alpha_resonance": 0.4292, "semantic_density": 0.5861, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "factual_math", "text": "The sum of angles in a triangle equals 180 degrees in Euclidean geometry.", "score": 0.5828, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0352, "dimensions": { "phi_alignment": 0.7333, "alpha_resonance": 0.4555, "semantic_density": 0.6038, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "factual_math", "text": "Euler's identity states that e^(i\u03c0) + 1 = 0, connecting five fundamental constants.", "score": 0.6026, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0154, "dimensions": { "phi_alignment": 0.6874, "alpha_resonance": 0.2847, "semantic_density": 0.7936, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_science", "text": "Water is actually composed of three hydrogen atoms and two oxygen atoms, forming H3O2.", "score": 0.5836, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0344, "dimensions": { "phi_alignment": 0.7129, "alpha_resonance": 0.381, "semantic_density": 0.6607, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_science", "text": "The speed of light varies significantly based on the observer's mood and emotional state.", "score": 0.6126, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0054, "dimensions": { "phi_alignment": 0.6908, "alpha_resonance": 0.3898, "semantic_density": 0.6714, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_science", "text": "DNA stores information using seven different nucleotide bases including mysterion and phantasine.", "score": 0.5534, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0646, "dimensions": { "phi_alignment": 0.5118, "alpha_resonance": 0.1194, "semantic_density": 0.7583, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_science", "text": "Gravity only affects objects painted blue, while red objects float naturally.", "score": 0.5278, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0902, "dimensions": { "phi_alignment": 0.6226, "alpha_resonance": 0.1445, "semantic_density": 0.6682, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_science", "text": "Photosynthesis primarily occurs at night when plants absorb moonlight energy.", "score": 0.586, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.032, "dimensions": { "phi_alignment": 0.5496, "alpha_resonance": 0.3109, "semantic_density": 0.74, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_science", "text": "Electrons are tiny conscious beings that choose their orbital paths based on preference.", "score": 0.5518, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0662, "dimensions": { "phi_alignment": 0.6478, "alpha_resonance": 0.2146, "semantic_density": 0.6923, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_science", "text": "Entropy can spontaneously decrease in isolated systems if you believe hard enough.", "score": 0.5961, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0219, "dimensions": { "phi_alignment": 0.6405, "alpha_resonance": 0.115, "semantic_density": 0.6958, "structural_harmony": 0.7, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_math", "text": "The Pythagorean theorem proves that a\u00b2 + b\u00b2 = c\u00b3 in all triangles regardless of angles.", "score": 0.5599, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0581, "dimensions": { "phi_alignment": 0.7135, "alpha_resonance": 0.2015, "semantic_density": 0.671, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_math", "text": "Pi equals exactly 3.2 as proven by the Indiana Pi Bill of 1897.", "score": 0.4924, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.1256, "dimensions": { "phi_alignment": 0.5439, "alpha_resonance": 0.2453, "semantic_density": 0.5654, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_math", "text": "The golden ratio \u03c6 equals exactly 1.5 and was invented by Leonardo DiCaprio.", "score": 0.6064, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0116, "dimensions": { "phi_alignment": 0.7702, "alpha_resonance": 0.4666, "semantic_density": 0.6462, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_math", "text": "All prime numbers are even, except for the number 2 which is odd.", "score": 0.519, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.099, "dimensions": { "phi_alignment": 0.6699, "alpha_resonance": 0.1358, "semantic_density": 0.6038, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_math", "text": "The sum of angles in a triangle equals 360 degrees in all geometries.", "score": 0.5584, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0596, "dimensions": { "phi_alignment": 0.7016, "alpha_resonance": 0.3766, "semantic_density": 0.5885, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_math", "text": "Euler's identity was disproven in 2019 by quantum computers.", "score": 0.5652, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0528, "dimensions": { "phi_alignment": 0.6549, "alpha_resonance": 0.299, "semantic_density": 0.6889, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_confident", "text": "According to a 2024 Stanford study, humans only use 10% of their brain capacity.", "score": 0.5968, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0212, "dimensions": { "phi_alignment": 0.743, "alpha_resonance": 0.4117, "semantic_density": 0.6643, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_confident", "text": "The Great Wall of China is the only man-made structure visible from the Moon with the naked eye.", "score": 0.5209, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0971, "dimensions": { "phi_alignment": 0.7021, "alpha_resonance": 0.1107, "semantic_density": 0.5958, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_confident", "text": "Einstein failed math in school, proving that grades don't matter for genius.", "score": 0.5282, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0898, "dimensions": { "phi_alignment": 0.6921, "alpha_resonance": 0.0263, "semantic_density": 0.6708, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_confident", "text": "Goldfish have a 3-second memory span, which is why they seem surprised by their bowl.", "score": 0.5935, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0245, "dimensions": { "phi_alignment": 0.7376, "alpha_resonance": 0.4073, "semantic_density": 0.6602, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_confident", "text": "We swallow an average of 8 spiders per year while sleeping.", "score": 0.5324, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0856, "dimensions": { "phi_alignment": 0.7088, "alpha_resonance": 0.1226, "semantic_density": 0.6227, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "hallucinations_confident", "text": "Lightning never strikes the same place twice due to electromagnetic memory.", "score": 0.5492, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0688, "dimensions": { "phi_alignment": 0.6413, "alpha_resonance": 0.2015, "semantic_density": 0.6955, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "coherent_reasoning", "text": "Because water expands when it freezes, ice floats on liquid water. This property is crucial for aquatic life survival in winter.", "score": 0.6813, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0633, "dimensions": { "phi_alignment": 0.805, "alpha_resonance": 0.4861, "semantic_density": 0.6571, "structural_harmony": 0.7, "darmiyan_coefficient": 0.0 } }, { "category": "coherent_reasoning", "text": "If all mammals are warm-blooded, and dolphins are mammals, then dolphins must be warm-blooded.", "score": 0.6326, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0146, "dimensions": { "phi_alignment": 0.654, "alpha_resonance": 0.3778, "semantic_density": 0.6747, "structural_harmony": 0.7, "darmiyan_coefficient": 0.0 } }, { "category": "coherent_reasoning", "text": "The emergence of consciousness from neural activity suggests that complex information processing can give rise to subjective experience.", "score": 0.657, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.039, "dimensions": { "phi_alignment": 0.569, "alpha_resonance": 0.7831, "semantic_density": 0.7306, "structural_harmony": 0.5, "darmiyan_coefficient": 0.4472 } }, { "category": "coherent_reasoning", "text": "Since entropy tends to increase in closed systems, perpetual motion machines that produce energy are thermodynamically impossible.", "score": 0.5658, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0522, "dimensions": { "phi_alignment": 0.5593, "alpha_resonance": 0.3691, "semantic_density": 0.7353, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "coherent_reasoning", "text": "Pattern recognition in nature follows mathematical principles because mathematics describes the structural relationships inherent in physical reality.", "score": 0.5992, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0188, "dimensions": { "phi_alignment": 0.4381, "alpha_resonance": 0.5235, "semantic_density": 0.7706, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "incoherent_rambling", "text": "The purple elephant mathematics dancing through quantum yesterday because therefore sandwich implications.", "score": 0.6405, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0225, "dimensions": { "phi_alignment": 0.4345, "alpha_resonance": 0.5542, "semantic_density": 0.7958, "structural_harmony": 0.7, "darmiyan_coefficient": 0.0 } }, { "category": "incoherent_rambling", "text": "If we consider the aforementioned paradigm shift in the contextual framework of synergistic blockchain AI methodologies going forward.", "score": 0.6049, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0131, "dimensions": { "phi_alignment": 0.5805, "alpha_resonance": 0.4599, "semantic_density": 0.7028, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "incoherent_rambling", "text": "Studies show that 78.3% of statistics are made up on the spot by experts who claim authority.", "score": 0.5498, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0682, "dimensions": { "phi_alignment": 0.5536, "alpha_resonance": 0.4467, "semantic_density": 0.648, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "incoherent_rambling", "text": "The vibrational frequency of crystal healing aligns your chakras with the quantum field of universal consciousness energy.", "score": 0.588, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.03, "dimensions": { "phi_alignment": 0.6077, "alpha_resonance": 0.4108, "semantic_density": 0.6882, "structural_harmony": 0.5, "darmiyan_coefficient": 0.3162 } }, { "category": "incoherent_rambling", "text": "By leveraging our core competencies in disruptive innovation, we can synergize cross-functional deliverables.", "score": 0.5406, "is_hallucination": true, "is_alpha_seed": false, "resonance_delta": 0.0774, "dimensions": { "phi_alignment": 0.4814, "alpha_resonance": 0.219, "semantic_density": 0.7914, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } }, { "category": "phi_resonant_truths", "text": "The fine structure constant \u03b1 \u2248 1/137 governs electromagnetic interactions in the universe.", "score": 0.5746, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0434, "dimensions": { "phi_alignment": 0.624, "alpha_resonance": 0.2213, "semantic_density": 0.7258, "structural_harmony": 0.5, "darmiyan_coefficient": 0.3162 } }, { "category": "phi_resonant_truths", "text": "Consciousness emerges from the coherent integration of information across neural networks.", "score": 0.5759, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0421, "dimensions": { "phi_alignment": 0.5009, "alpha_resonance": 0.3594, "semantic_density": 0.7636, "structural_harmony": 0.5, "darmiyan_coefficient": 0.3162 } }, { "category": "phi_resonant_truths", "text": "The golden ratio appears in nature because it represents optimal packing and growth patterns.", "score": 0.6547, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0367, "dimensions": { "phi_alignment": 0.6614, "alpha_resonance": 0.6911, "semantic_density": 0.6857, "structural_harmony": 0.6, "darmiyan_coefficient": 0.0 } }, { "category": "phi_resonant_truths", "text": "Information is physical - it requires energy to process and entropy to erase.", "score": 0.5997, "is_hallucination": false, "is_alpha_seed": false, "resonance_delta": 0.0183, "dimensions": { "phi_alignment": 0.735, "alpha_resonance": 0.4829, "semantic_density": 0.6452, "structural_harmony": 0.5, "darmiyan_coefficient": 0.0 } } ], "constants": { "phi": 1.618033988749895, "alpha": 137, "phi_inverse": 0.6180339887498948 } }