OAI/NumberTheory/CubicMoment/Theta/CubicThetaArithmeticGradientL2.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

The actual arithmetic differential is globally square integrable. The result uses the finite arithmetic cusp/core cover and the literal hyperbolic energy density, without assuming energy-graph membership.

  1. lemma OAI.CubicFirstMoment.cubicThetaArithmeticQuotientEnergy_cusp_integrable line 15
  2. theorem OAI.CubicFirstMoment.cubicThetaArithmeticQuotientEnergy_integrable line 26
  3. lemma OAI.CubicFirstMoment.cubicThetaArithmeticGradient_continuous line 38
  4. lemma OAI.CubicFirstMoment.cubicThetaArithmeticGradientRepresentative_measurable line 50
  5. lemma OAI.CubicFirstMoment.cubicThetaArithmeticGradientRepresentative_norm_sq line 54
  6. lemma OAI.CubicFirstMoment.cubicThetaArithmeticGradientRepresentative_memLp line 62
  7. def OAI.CubicFirstMoment.cubicThetaArithmeticGradientL2 line 70
  8. lemma OAI.CubicFirstMoment.cubicThetaArithmeticGradientL2_coe line 73