"""
BSD Comparison Morphism Skill
=============================
Knowledge skill generated from GPIA Cycle 46 research.
"""

from typing import Any, Dict

from skills.base import (
    Skill,
    SkillCategory,
    SkillContext,
    SkillLevel,
    SkillMetadata,
    SkillResult,
)


class BSDComparisonMorphismSkill(Skill):
    """
    Knowledge skill about BSD Comparison Morphism design.
    Generated from Cycle 46 research output.
    """

    # Core knowledge
    KNOWLEDGE = {
        "overview": """
The Comparison Morphism phi connects the algebraic and analytic sides of BSD:
- Algebraic: sigma_alg = det(Selmer complex)
- Analytic: sigma_an = L(E, 1+t)
- phi = tau_an o tau_alg^{-1} : Q -> Q (a rational number)
""",
        "components": {
            "L_A": "Adelic Determinant Line - single line containing all arithmetic data",
            "tau_alg": "Algebraic trivialization using torsion, Tamagawa numbers, regulator",
            "tau_an": "Analytic trivialization using L-values and periods",
            "phi": "Comparison morphism = tau_an o tau_alg^{-1}, yields rational number"
        },
        "bsd_formula": "phi(E) = |Sha| * prod(c_p) * Omega * R / |E(Q)_tors|^2",
        "gap6": """
Gap 6 (Higher Rank) is about VERIFYING phi = BSD formula for rank >= 2.
The structure phi works uniformly for all ranks.
The difficulty is computational: finding r independent generators.
"""
    }

    _cached_metadata: SkillMetadata = None

    def metadata(self) -> SkillMetadata:
        if BSDComparisonMorphismSkill._cached_metadata is None:
            BSDComparisonMorphismSkill._cached_metadata = SkillMetadata(
                id="research/bsd_comparison_morphism",
                name="BSD Comparison Morphism",
                description="Knowledge about BSD comparison morphism design",
                category=SkillCategory.RESEARCH,
                level=SkillLevel.ADVANCED,
                tags=["bsd", "mathematics", "millennium-prize"],
            )
        return BSDComparisonMorphismSkill._cached_metadata

    def execute(self, input_data: Dict[str, Any], context: SkillContext) -> SkillResult:
        capability = input_data.get("capability", "explain")
        handler = getattr(self, f"capability_{capability}", None)
        
        if handler is None:
            return SkillResult(
                success=False,
                output=None,
                error=f"Unknown capability: {capability}",
                skill_id=self.metadata().id,
            )
        return handler(input_data, context)

    def capability_explain(self, input_data: Dict[str, Any], context: SkillContext) -> SkillResult:
        return SkillResult(
            success=True,
            output={
                "overview": self.KNOWLEDGE["overview"],
                "formula": self.KNOWLEDGE["bsd_formula"],
            },
            skill_id=self.metadata().id,
        )

    def capability_components(self, input_data: Dict[str, Any], context: SkillContext) -> SkillResult:
        return SkillResult(
            success=True,
            output=self.KNOWLEDGE["components"],
            skill_id=self.metadata().id,
        )

    def capability_gap6(self, input_data: Dict[str, Any], context: SkillContext) -> SkillResult:
        return SkillResult(
            success=True,
            output={"explanation": self.KNOWLEDGE["gap6"]},
            skill_id=self.metadata().id,
        )
