{
  "ai.module": "parity_k_differentials_rtt",
  "ai.version": "1.0",
  "ai.purpose": "RTT structural map of the paper 'Parity of k-differentials in genus zero and one'.",
  "ai.source.pdf": "https://arxiv.org/pdf/2602.03722",
  "ai.keywords": [
    "k-differentials",
    "parity",
    "genus zero",
    "genus one",
    "moduli spaces",
    "flat geometry",
    "strata"
  ],

  "ai.module.summary": "This module exposes the regime structure underlying parity phenomena in k-differentials for genus 0 and 1. It preserves the authors' mathematical results while adding RTT operators for agentic reasoning.",

  "ai.regimes": {
    "combinatorial_parity_regime": {
      "description": "Parity determined by combinatorial data of zeros/poles and k-residue constraints.",
      "evidence": "Paper classifies parity via discrete invariants of k-differentials."
    },
    "geometric_strata_regime": {
      "description": "Behavior depends on the geometry of strata in moduli spaces of k-differentials.",
      "evidence": "Authors analyze strata structure in genus 0 and 1."
    },
    "genus_transition_regime": {
      "description": "Genus 0 and genus 1 exhibit distinct parity behavior due to topological constraints.",
      "evidence": "Paper separates results by genus and proves different criteria."
    }
  },

  "ai.tensions": {
    "local_vs_global_parity": {
      "description": "Local zero/pole data vs global topological constraints on differentials.",
      "paper_alignment": "Parity classification depends on both local orders and global genus."
    },
    "combinatorial_vs_geometric": {
      "description": "Discrete invariants vs geometric structure of moduli strata.",
      "paper_alignment": "Authors combine combinatorial and geometric arguments."
    },
    "genus_zero_vs_genus_one": {
      "description": "Different parity rules emerge from different topologies.",
      "paper_alignment": "Paper proves separate theorems for g=0 and g=1."
    }
  },

  "ai.transitions": {
    "strata_refinement_transition": {
      "description": "Moving between strata changes parity classification.",
      "paper_alignment": "Authors analyze how strata boundaries affect parity."
    },
    "genus_lift_transition": {
      "description": "Transition from genus 0 to genus 1 introduces new parity phenomena.",
      "paper_alignment": "Paper highlights new behaviors in genus 1."
    },
    "combinatorial_to_geometric_transition": {
      "description": "Parity criteria shift from purely combinatorial to geometric as genus increases.",
      "paper_alignment": "Authors use geometric arguments in genus 1."
    }
  },

  "ai.operators": {
    "parity_operator": {
      "type": "operator",
      "role": "Computes parity from zero/pole data and k-residue constraints."
    },
    "strata_operator": {
      "type": "operator",
      "role": "Identifies geometric strata relevant to parity classification."
    },
    "genus_operator": {
      "type": "operator",
      "role": "Encodes topological constraints that differentiate genus 0 and 1 behavior."
    }
  },

  "ai.audience": "Researchers in algebraic geometry, flat surfaces, and moduli theory.",
  "ai.contact.github": "https://github.com/TriadicFrameworks",
  "ai.license": "Open educational use permitted"
}