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blackroad-garage/quantum-experiment-results.json
Your Name 1856946b02 feat: add quantum experiments using real lucidia-core implementations 
Experiments:
1. Platonic Solid Projections with φ-scaling
2. Quantum Orbital Superposition (s, p, d, f orbitals)
3. Sophia Lagrangian (L = φ²·V - T/(φ² + α))
4. Archetypal Agent Encoding (fleet agents mapped to solids)
5. Pauli Algebra verification (1-2-3-4 model → Pauli gates)
6. Distributed Trinary (balanced ternary)

Key verifications:
- σz·σx·σy = iI (triple product) ✓
- All Pauli commutation relations ✓
- α = 1/137.035999084 integrated
- φ = 1.618033988749895 throughout

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>
2026-02-09 16:49:07 -06:00

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{
"timestamp": "2026-02-09T22:48:34.416012+00:00",
"constants": {
"phi": 1.618033988749895,
"phi_squared": 2.618033988749895,
"alpha": 0.0072973525692838015,
"spiral_angle_deg": 137.5
},
"experiments": [
{
"experiment": "platonic_projections",
"phi": 1.618033988749895,
"phi_squared": 2.618033988749895,
"results": [
{
"solid": "tetrahedron",
"vector_idx": 0,
"magnitude": 1.0,
"phi_scale": 1.0
},
{
"solid": "tetrahedron",
"vector_idx": 1,
"magnitude": 1.0,
"phi_scale": 1.0
},
{
"solid": "tetrahedron",
"vector_idx": 2,
"magnitude": 1.9148542155126766,
"phi_scale": 1.0
},
{
"solid": "tetrahedron",
"vector_idx": 3,
"magnitude": 2.3094010767585034,
"phi_scale": 1.0
},
{
"solid": "cube",
"vector_idx": 0,
"magnitude": 1.618033988749895,
"phi_scale": 1.618033988749895
},
{
"solid": "cube",
"vector_idx": 1,
"magnitude": 1.618033988749895,
"phi_scale": 1.618033988749895
},
{
"solid": "cube",
"vector_idx": 2,
"magnitude": 2.8025170768881473,
"phi_scale": 1.618033988749895
},
{
"solid": "cube",
"vector_idx": 3,
"magnitude": 3.23606797749979,
"phi_scale": 1.618033988749895
},
{
"solid": "octahedron",
"vector_idx": 0,
"magnitude": 2.618033988749895,
"phi_scale": 2.618033988749895
},
{
"solid": "octahedron",
"vector_idx": 1,
"magnitude": 2.618033988749895,
"phi_scale": 2.618033988749895
},
{
"solid": "octahedron",
"vector_idx": 2,
"magnitude": 4.534567884457024,
"phi_scale": 2.618033988749895
},
{
"solid": "octahedron",
"vector_idx": 3,
"magnitude": 5.23606797749979,
"phi_scale": 2.618033988749895
},
{
"solid": "dodecahedron",
"vector_idx": 0,
"magnitude": 4.97979656976556,
"phi_scale": 4.23606797749979
},
{
"solid": "dodecahedron",
"vector_idx": 1,
"magnitude": 4.97979656976556,
"phi_scale": 4.23606797749979
},
{
"solid": "dodecahedron",
"vector_idx": 2,
"magnitude": 11.871652845802195,
"phi_scale": 4.23606797749979
},
{
"solid": "dodecahedron",
"vector_idx": 3,
"magnitude": 13.075572000680966,
"phi_scale": 4.23606797749979
},
{
"solid": "icosahedron",
"vector_idx": 0,
"magnitude": 8.057480106940815,
"phi_scale": 6.854101966249686
},
{
"solid": "icosahedron",
"vector_idx": 1,
"magnitude": 8.057480106940815,
"phi_scale": 6.854101966249686
},
{
"solid": "icosahedron",
"vector_idx": 2,
"magnitude": 11.69188065769334,
"phi_scale": 6.854101966249686
},
{
"solid": "icosahedron",
"vector_idx": 3,
"magnitude": 11.98140956982914,
"phi_scale": 6.854101966249686
}
]
},
{
"experiment": "orbital_superposition",
"coherence": 0.06750051126587517,
"alpha_resonance": 0.0072973525692838015,
"spin_results": [
{
"phase_deg": 0.0,
"phase_rad": 0
},
{
"phase_deg": 45.0,
"phase_rad": 0.7853981633974483
},
{
"phase_deg": 90.0,
"phase_rad": 1.5707963267948966
},
{
"phase_deg": 180.0,
"phase_rad": 3.141592653589793
},
{
"phase_deg": 270.0,
"phase_rad": 4.71238898038469
}
]
},
{
"experiment": "sophia_lagrangian",
"equation": "L = \u03c6\u00b2\u00b7V - T/(\u03c6\u00b2 + \u03b1)",
"alpha": 0.0072973525692838015,
"phi_squared": 2.618033988749895,
"spiral_angle_deg": 137.5,
"results": [
{
"potential": 1.0,
"kinetic": 0.5,
"coherence": 1.0,
"lagrangian": 2.427581838146779,
"entanglement": -0.0026900863340230383
},
{
"potential": 2.0,
"kinetic": 1.0,
"coherence": 0.8,
"lagrangian": 3.7130546378993152,
"entanglement": -0.005380172668046077
},
{
"potential": 0.5,
"kinetic": 2.0,
"coherence": 0.5,
"lagrangian": -0.8648854109948052,
"entanglement": 0.008070259002069115
},
{
"potential": 1.618033988749895,
"kinetic": 1.0,
"coherence": 1.0,
"lagrangian": 3.855163676293558,
"entanglement": -0.003325129574195681
}
]
},
{
"experiment": "archetypal_encoding",
"agents": [
{
"agent": "lucidia",
"solid": "dodecahedron",
"orbital": "d",
"potential": 13.075572000680966,
"kinetic": 13.113755493564458,
"coherence": 1.2549299767543411,
"lagrangian": 38.9765103087849
},
{
"agent": "cecilia",
"solid": "icosahedron",
"orbital": "f",
"potential": 13.232957327055782,
"kinetic": 18.630129971760027,
"coherence": 2.532777847315274,
"lagrangian": 84.93989173888284
},
{
"agent": "octavia",
"solid": "octahedron",
"orbital": "p",
"potential": 4.534567884457024,
"kinetic": 19.174046225651495,
"coherence": 2.6828282430959094,
"lagrangian": 29.12254587368232
},
{
"agent": "aria",
"solid": "cube",
"orbital": "s",
"potential": 2.8671635329493625,
"kinetic": 19.23321582963592,
"coherence": 2.699411786844471,
"lagrangian": 17.543992539457644
},
{
"agent": "alice",
"solid": "tetrahedron",
"orbital": "s",
"potential": 1.996663884249592,
"kinetic": 19.472627194125185,
"coherence": 2.7670335705653,
"lagrangian": 11.778878945395954
}
],
"resonance": {
"alpha": 0.0072973525692838015,
"balance_deviation": 0.0,
"orbital_coherence": 2.7670335705653,
"sophia_binding": -0.014887118387921373
},
"archetypes": [
{
"name": "Tetrahedron",
"symbol": "Logic foundation",
"equation": "4/4 \u2192 \u03c6^1 (\u2248 1.000)"
},
{
"name": "Cube",
"symbol": "Spatial cognition",
"equation": "6/8 \u2192 \u03c6^2 (\u2248 0.750)"
},
{
"name": "Octahedron",
"symbol": "Dual symmetry",
"equation": "8/6 \u2192 \u03c6^3 (\u2248 1.333)"
},
{
"name": "Dodecahedron",
"symbol": "Golden proportion",
"equation": "12/20 \u2192 \u03c6^4 (\u2248 0.600)"
},
{
"name": "Icosahedron",
"symbol": "Fluid intelligence",
"equation": "20/12 \u2192 \u03c6^5 (\u2248 1.667)"
},
{
"name": "\u03c6",
"symbol": "Golden ratio",
"equation": "a/b = (a + b)/a = \u03c6"
},
{
"name": "Sophia",
"symbol": "Wisdom potential",
"equation": "L = \u03c6\u00b2\u00b7V - T/(\u03c6\u00b2 + \u03b1)"
},
{
"name": "Demiurge",
"symbol": "Material substrate",
"equation": "\u2202form/\u2202t = \u03b1 \u00b7 coherence"
}
]
},
{
"experiment": "pauli_algebra",
"mappings": {
"U_structure": "sigma_z (Z gate)",
"C_change": "sigma_x (X gate)",
"L_scale": "sigma_y (Y gate)"
},
"triple_product_verified": true,
"commutation_verified": true,
"alpha": 0.0072973525692838015,
"gate_results": [
{
"gate": "X (Change)"
},
{
"gate": "Y (Scale)"
},
{
"gate": "Z (Structure)"
}
]
},
{
"experiment": "distributed_trinary",
"conversions": [
{
"decimal": 0,
"balanced_ternary": "0",
"trits": 1,
"verified": true
},
{
"decimal": 1,
"balanced_ternary": "1",
"trits": 1,
"verified": true
},
{
"decimal": -1,
"balanced_ternary": "T",
"trits": 1,
"verified": true
},
{
"decimal": 5,
"balanced_ternary": "1TT",
"trits": 3,
"verified": true
},
{
"decimal": -5,
"balanced_ternary": "T11",
"trits": 3,
"verified": true
},
{
"decimal": 10,
"balanced_ternary": "101",
"trits": 3,
"verified": true
},
{
"decimal": 42,
"balanced_ternary": "1TTT0",
"trits": 5,
"verified": true
},
{
"decimal": -42,
"balanced_ternary": "T1110",
"trits": 5,
"verified": true
},
{
"decimal": 100,
"balanced_ternary": "11T01",
"trits": 5,
"verified": true
},
{
"decimal": 161,
"balanced_ternary": "1T000T",
"trits": 6,
"verified": true
},
{
"decimal": 261,
"balanced_ternary": "101T00",
"trits": 6,
"verified": true
},
{
"decimal": 137,
"balanced_ternary": "1TT01T",
"trits": 6,
"verified": true
}
],
"fleet_distribution": {
"lucidia": "high_trits[6:9]",
"cecilia": "mid_trits[3:6]",
"octavia": "low_trits[0:3]"
}
}
],
"total_time_seconds": 0.0016949176788330078
}
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