{
  "ai.module": "chaos_theory.rtt1",
  "ai.version": "1.0",
  "ai.purpose": "RTT/1 engine layer for Chaos Theory: operator grammar, dimensional mapping, divergence indicators, and minimal coherence examples.",
  "ai.keywords": [
    "chaos",
    "nonlinear dynamics",
    "divergence",
    "sensitivity",
    "attractors",
    "operator grammar",
    "rtt1"
  ],

  "engine": {
    "layer": "RTT/1",
    "description": "Defines the operator grammar and dimensional behavior of chaotic systems within the RTT substrate."
  },

  "operators": {
    "core": {
      "divergence": {
        "type": "behavior",
        "description": "Rate at which nearby trajectories separate under finite precision.",
        "signals": ["exponential_separation", "loss_of_predictive_power"]
      },
      "sensitivity": {
        "type": "behavior",
        "description": "Amplification of small differences in initial conditions.",
        "signals": ["trajectory_instability", "precision_dependence"]
      },
      "attractor": {
        "type": "structure",
        "description": "Stable recurrence pattern in state space.",
        "signals": ["bounded_recurrence", "pattern_convergence"]
      },
      "recurrence": {
        "type": "behavior",
        "description": "Return of system states to neighborhoods of prior states.",
        "signals": ["quasi_periodicity", "pattern_return"]
      }
    },

    "supporting": {
      "finite_precision": {
        "type": "constraint",
        "description": "Resolution limits that amplify divergence and mask underlying structure."
      },
      "projection_loss": {
        "type": "constraint",
        "description": "Dimensional compression that produces apparent randomness."
      }
    }
  },

  "dimensional_mapping": {
    "R1": "High sensitivity due to minimal lineage tracking.",
    "R2": "Projection-induced divergence; chaos emerges from compression.",
    "R3": "Nonlinear behavior fully expressed; attractors and recurrence visible."
  },

  "coherence": {
    "markers": [
      "bounded divergence within system constraints",
      "stable attractor geometry",
      "recurrence detectable under sufficient resolution"
    ],
    "instability_signals": [
      "unbounded divergence",
      "loss of attractor structure",
      "noise dominating recurrence patterns"
    ]
  },

  "examples": {
    "minimal": [
      {
        "name": "Lorenz System",
        "demonstrates": ["divergence", "attractor", "recurrence"]
      },
      {
        "name": "Logistic Map (r > 3.57)",
        "demonstrates": ["sensitivity", "finite_precision"]
      }
    ]
  },

  "integration": {
    "cross_module": [
      "information_theory.rtt1",
      "thermodynamics.rtt1",
      "quantum_mechanics.rtt1"
    ],
    "notes": "RTT/1 treats chaos as a behavioral diagnostic; substrate-level causes are resolved in RTT/2 and RTT/3."
  }
}