{
  "ai.module": "andrews_dhar_partitions_rtt",
  "ai.version": "1.0",
  "ai.purpose": "RTT structural map of the paper 'A Problem of Andrews and Dhar on Partitions'.",
  "ai.source.pdf": "https://arxiv.org/pdf/2606.05117",
  "ai.keywords": [
    "integer partitions",
    "Andrews–Dhar problem",
    "restricted partitions",
    "generating functions",
    "q-series",
    "asymptotics",
    "combinatorial identities"
  ],

  "ai.module.summary": "This module exposes the regime structure behind the Andrews–Dhar partition problem, connecting restricted partition conditions, generating-function identities, and asymptotic behavior. It preserves the authors' results while adding RTT operators for agentic reasoning.",

  "ai.regimes": {
    "restricted_partition_regime": {
      "description": "Partitions are constrained by Andrews–Dhar-type conditions on parts and gaps.",
      "evidence": "Paper formulates the problem via specific restrictions on allowed partitions."
    },
    "generating_function_regime": {
      "description": "Restricted partitions are encoded by q-series and product/sum generating functions.",
      "evidence": "Authors derive generating functions for the constrained partition families."
    },
    "identity_regime": {
      "description": "New identities relate Andrews–Dhar partitions to classical partition families.",
      "evidence": "Paper proves equivalences and transformations between generating functions."
    },
    "asymptotic_regime": {
      "description": "Growth rates and asymptotics of the restricted partition counts are analyzed.",
      "evidence": "Authors obtain asymptotic formulas or bounds for large n."
    }
  },

  "ai.tensions": {
    "local_constraints_vs_global_counts": {
      "description": "Local restrictions on parts vs global enumeration of partitions.",
      "paper_alignment": "Problem asks how specific local rules affect total counts."
    },
    "combinatorial_vs_analytic_q_series": {
      "description": "Combinatorial interpretations vs analytic manipulation of q-series.",
      "paper_alignment": "Proofs move between combinatorial bijections and q-series identities."
    },
    "exact_identities_vs_asymptotics": {
      "description": "Exact generating-function identities vs asymptotic growth behavior.",
      "paper_alignment": "Paper balances closed forms with asymptotic analysis."
    }
  },

  "ai.transitions": {
    "constraints_to_generating_function_transition": {
      "description": "Translate Andrews–Dhar restrictions into q-series/product formulas.",
      "paper_alignment": "Initial derivation of generating functions."
    },
    "generating_function_to_identity_transition": {
      "description": "Manipulate q-series to reveal identities and equivalences.",
      "paper_alignment": "Main identity proofs and transformations."
    },
    "identity_to_asymptotic_transition": {
      "description": "Use identities to access asymptotic behavior of coefficients.",
      "paper_alignment": "Asymptotic results derived from analytic forms."
    }
  },

  "ai.operators": {
    "restricted_partition_operator": {
      "type": "operator",
      "role": "Generates partitions satisfying Andrews–Dhar constraints."
    },
    "q_series_operator": {
      "type": "operator",
      "role": "Builds and manipulates generating functions for restricted partitions."
    },
    "identity_operator": {
      "type": "operator",
      "role": "Transforms q-series to reveal partition identities."
    },
    "asymptotic_operator": {
      "type": "operator",
      "role": "Extracts asymptotic growth from generating functions."
    }
  },

  "ai.audience": "Researchers in partition theory, q-series, and analytic/combinatorial number theory.",
  "ai.contact.github": "https://github.com/TriadicFrameworks",
  "ai.license": "Open educational use permitted"
}