{
  "ai.module": "collatz_transformers_rtt",
  "ai.version": "1.0",
  "ai.purpose": "RTT-aligned structural map of the paper 'Transformers Know More Than They Can Tell — Learning the Collatz Sequence'.",
  "ai.source.pdf": "https://arxiv.org/pdf/2511.10811",
  "ai.keywords": [
    "Collatz",
    "loop-length regime",
    "residue classes",
    "control-flow inference",
    "representation geometry",
    "transformer limitations"
  ],

  "ai.module.summary": "This module exposes the hidden regime structure, tensions, and transitions underlying the transformer behavior described in the paper. It preserves all claims from the authors while adding RTT operator grammar for agentic reasoning.",

  "ai.regimes": {
    "binary_residue_regime": {
      "description": "Model learns equivalence classes modulo 2^p rather than the Collatz function.",
      "evidence": "Paper reports near-perfect accuracy on 2^p classes and systematic errors when loop depth is misestimated."
    },
    "loop_length_regime": {
      "description": "Model infers temporal depth (loop length) rather than arithmetic behavior.",
      "evidence": "Authors note correct arithmetic but incorrect loop-length estimation in >90% of failures."
    },
    "base_geometry_regime": {
      "description": "Model performance varies sharply by base due to representational geometry alignment.",
      "evidence": "Bases 24/32 yield ~99% accuracy; bases 3/11 collapse to ~25–37%."
    }
  },

  "ai.tensions": {
    "arithmetic_vs_control_flow": {
      "description": "Transformers are spatial pattern machines forced to approximate temporal branching.",
      "paper_alignment": "Authors mention difficulty in 'figuring the control structure'."
    },
    "correct_local_vs_wrong_global": {
      "description": "Model performs correct arithmetic but misestimates loop depth.",
      "paper_alignment": "Reported as dominant failure mode."
    },
    "rigidity_vs_brittleness": {
      "description": "Low hallucination due to structural rigidity; brittle errors due to regime lock.",
      "paper_alignment": "Hallucination 'almost never happens'."
    }
  },

  "ai.transitions": {
    "regime_ladder": {
      "description": "Model learns shallow 2^p classes first, then deeper ones.",
      "paper_alignment": "Authors observe predictable sequence of class acquisition."
    },
    "geometry_thresholds": {
      "description": "Base encoding determines when transitions between loop-depth classes become learnable.",
      "paper_alignment": "High-base encodings accelerate learning."
    },
    "structured_failure_transition": {
      "description": "When loop-length inference fails, model snaps into wrong 2^p attractor.",
      "paper_alignment": "Errors are structured, not random."
    }
  },

  "ai.operators": {
    "temporal_depth": {
      "type": "operator",
      "role": "Maps input to inferred loop length; core hidden variable learned by the model."
    },
    "residue_partition": {
      "type": "operator",
      "role": "Partitions inputs into 2^p classes; primary attractor structure."
    },
    "representation_alignment": {
      "type": "operator",
      "role": "Measures geometric compatibility between base encoding and model lattice."
    }
  },

  "ai.audience": "Researchers, AI alignment practitioners, and authors of the referenced paper.",
  "ai.contact.github": "https://github.com/TriadicFrameworks",
  "ai.license": "Open educational use permitted"
}