[
  {
    "concept_name": "Kepler's Laws of Planetary Motion",
    "synthesis": {
      "concept_type": "law",
      "formal_statement": "Planets orbit in ellipses with sun at focus; equal areas in equal times; T² ∝ a³",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — laws ARE relations: orbit shape ↔ focus position, area ↔ time, period ↔ semi-major axis", "primary": true},
        {"pattern": "⟳", "evidence": "Orbital motion is continuous process"},
        {"pattern": "Δ", "evidence": "Distinguishes elliptical from circular orbits"}
      ],
      "dimension_hints": "D=3 (volumetric) — planetary motion in 3D space",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (proportionality relations) → laws vanish, they ARE the mathematical relations. Remove ⟳ (orbital process) → static geometric relations remain. Remove Δ → relations still hold. ⇄ is essential.",
      "related": ["Celestial mechanics", "Conic sections", "Newton's gravity", "Orbital dynamics"]
    }
  },
  {
    "concept_name": "Galilean Relativity",
    "synthesis": {
      "concept_type": "principle",
      "formal_statement": "Laws of mechanics are identical in all inertial reference frames",
      "ontological_structures": [
        {"pattern": "Δ", "evidence": "PRIMARY — distinguishes inertial from non-inertial frames as fundamental category", "primary": true},
        {"pattern": "⇄", "evidence": "Relates physics across different frames via Galilean transformations"},
        {"pattern": "⟳", "evidence": "Minimal — principle about frame equivalence, not dynamics"}
      ],
      "dimension_hints": "D=3 (volumetric) — operates in 3D space with absolute time",
      "attribute_dominant": "Δ",
      "complexity": "foundational (1)",
      "elimination_test": "Remove Δ (inertial frame distinction) → principle vanishes, it IS about that classification. Remove ⇄ (frame transformations) → distinction remains. Remove ⟳ → already static principle. Δ is essential.",
      "oscillation_notes": "Δ/⇄ tension: principle presupposes inertial frame distinction (Δ) but affirms invariance of laws across frames (⇄). Elimination test resolves toward Δ: Galileo historically introduces the concept of inertial frame through this principle. Σ₃₂₁₊ alternative defensible if focus on inter-frame equivalence.",
      "related": ["Special relativity", "Inertial frames", "Classical mechanics", "Galilean transformation"]
    }
  },
  {
    "concept_name": "Bernoulli's Principle",
    "synthesis": {
      "concept_type": "principle",
      "formal_statement": "P + ½ρv² + ρgh = constant — relates pressure, velocity, and height in fluid flow",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — principle IS the trade-off relation: pressure ↔ velocity ↔ height", "primary": true},
        {"pattern": "⟳", "evidence": "Fluid flow is continuous process"},
        {"pattern": "Δ", "evidence": "Distinguishes different energy forms in fluid"}
      ],
      "dimension_hints": "D=3 (volumetric) — fluid dynamics in 3D space",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (energy trade-off) → principle vanishes, it IS the conservation relation. Remove ⟳ (flow) → static energy equation remains. Remove Δ → relation still holds. ⇄ is essential.",
      "related": ["Fluid dynamics", "Energy conservation", "Venturi effect", "Aerodynamics"]
    }
  },
  {
    "concept_name": "Pascal's Principle",
    "synthesis": {
      "concept_type": "principle",
      "formal_statement": "Pressure applied to confined fluid transmits undiminished to all points",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — principle IS the static equality relation: P₁ = P₂ = P₃... at all points", "primary": true},
        {"pattern": "⟳", "evidence": "Transmission is physical mechanism, not ontological essence"},
        {"pattern": "Δ", "evidence": "Distinguishes confined from open fluid"}
      ],
      "dimension_hints": "D=3 (volumetric) — operates in 3D fluid volume",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (pressure equality) → principle vanishes, there's nothing to say. Remove ⟳ (transmission mechanism) → static equilibrium P₁=P₂ remains. Remove Δ → equality still holds. ⇄ is essential.",
      "related": ["Hydraulics", "Fluid mechanics", "Pressure", "Hydraulic press"]
    }
  },
  {
    "concept_name": "Ideal Gas Law",
    "synthesis": {
      "concept_type": "law",
      "formal_statement": "PV = nRT — relates pressure, volume, temperature, and amount of gas",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — law IS the multi-way relation among P, V, T, n", "primary": true},
        {"pattern": "⟳", "evidence": "Gas molecules in continuous thermal motion"},
        {"pattern": "Δ", "evidence": "Distinguishes ideal from real gas behavior"}
      ],
      "dimension_hints": "D=3 (volumetric) — gas occupies 3D volume",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (PVT relation) → law vanishes, it IS the equation of state. Remove ⟳ (molecular motion) → macroscopic relation remains. Remove Δ → relation still holds. ⇄ is essential.",
      "related": ["Thermodynamics", "Statistical mechanics", "Kinetic theory", "Equation of state"]
    }
  },
  {
    "concept_name": "Snell's Law",
    "synthesis": {
      "concept_type": "law",
      "formal_statement": "n₁ sin θ₁ = n₂ sin θ₂ — relates incident and refracted angles at interface",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — law IS the relation: incident angle ↔ refracted angle via refractive indices", "primary": true},
        {"pattern": "Δ", "evidence": "Distinguishes two media at interface"},
        {"pattern": "⟳", "evidence": "Light propagation across boundary"}
      ],
      "dimension_hints": "D=2 (planar) — refraction occurs at 2D interface",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (angle relation) → law vanishes, it IS the proportionality. Remove Δ (media distinction) → presupposed but relation holds mathematically. Remove ⟳ → static geometric law remains. ⇄ is essential.",
      "related": ["Optics", "Refraction", "Fermat's principle", "Wave propagation"]
    }
  },
  {
    "concept_name": "Doppler Effect",
    "synthesis": {
      "concept_type": "phenomenon",
      "formal_statement": "Observed frequency changes when source or observer moves: f' = f(v±v₀)/(v±vₛ)",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — effect IS the relation: motion ↔ frequency shift", "primary": true},
        {"pattern": "⟳", "evidence": "Wave propagation and motion are continuous processes"},
        {"pattern": "Δ", "evidence": "Distinguishes approaching from receding motion"}
      ],
      "dimension_hints": "D=2 (linear) — motion along line, directional effect",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (velocity↔frequency relation) → effect vanishes, it IS the frequency shift formula. Remove ⟳ (wave propagation) → presupposed but relation remains. Remove Δ → relation still holds. ⇄ is essential.",
      "related": ["Wave mechanics", "Redshift", "Sound waves", "Special relativity"]
    }
  },
  {
    "concept_name": "Faraday's Law of Induction",
    "synthesis": {
      "concept_type": "law",
      "formal_statement": "∮ E·dl = -dΦ_B/dt — changing magnetic flux induces electric field",
      "ontological_structures": [
        {"pattern": "⟳", "evidence": "PRIMARY — law IS about temporal change: dΦ/dt generates field", "primary": true},
        {"pattern": "⇄", "evidence": "Relates magnetic flux to induced electric field"},
        {"pattern": "Δ", "evidence": "Distinguishes static from changing flux"}
      ],
      "dimension_hints": "D=4 (field/temporal) — electromagnetic field evolution in spacetime",
      "attribute_dominant": "⟳",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⟳ (temporal change dΦ/dt) → law vanishes, induction IS about time variation. Remove ⇄ (flux-field relation) → change still there but not induction. Remove Δ → change still defined. ⟳ is essential.",
      "related": ["Electromagnetism", "Maxwell's equations", "Lenz's law", "Electromagnetic induction"]
    }
  },
  {
    "concept_name": "Lenz's Law",
    "synthesis": {
      "concept_type": "law",
      "formal_statement": "Induced current opposes the change in magnetic flux that produced it",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — law IS the opposition relation: induced effect ↔ opposing cause", "primary": true},
        {"pattern": "⟳", "evidence": "Change in flux is temporal process"},
        {"pattern": "Δ", "evidence": "Distinguishes direction of induced vs original flux"}
      ],
      "dimension_hints": "D=4 (field/temporal) — electromagnetic response in spacetime",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (opposition relation) → law vanishes, it IS about the opposing response. Remove ⟳ (flux change) → presupposed by Faraday but opposition is relational. Remove Δ → opposition still defined. ⇄ is essential.",
      "oscillation_notes": "⇄/⟳ tension: Faraday (Σ₄₃₁₊) describes THAT induction occurs (process), Lenz describes HOW it relates to its cause (opposition). Not 'same phenomenon from two angles' — complementary but distinct. The minus sign is a relation between cause and effect, not a property of the process. Σ₄₃₁₊ alternative valid if viewed as inseparable from Faraday's process.",
      "related": ["Faraday's law", "Conservation of energy", "Electromagnetic induction", "Negative feedback"]
    }
  },
  {
    "concept_name": "Ampère's Law",
    "synthesis": {
      "concept_type": "law",
      "formal_statement": "∮ B·dl = μ₀I — relates magnetic field circulation to enclosed current",
      "ontological_structures": [
        {"pattern": "⇄", "evidence": "PRIMARY — law IS the relation: current ↔ magnetic field circulation", "primary": true},
        {"pattern": "⟳", "evidence": "Current is continuous charge flow"},
        {"pattern": "Δ", "evidence": "Distinguishes enclosed from non-enclosed current"}
      ],
      "dimension_hints": "D=3 (volumetric) — magnetic field around 3D current distribution",
      "attribute_dominant": "⇄",
      "complexity": "foundational (1)",
      "elimination_test": "Remove ⇄ (current↔field relation) → law vanishes, it IS the proportionality. Remove ⟳ (current flow) → static relation still holds. Remove Δ → relation still valid. ⇄ is essential.",
      "related": ["Electromagnetism", "Maxwell's equations", "Biot-Savart law", "Magnetic fields"]
    }
  }
]