recognition /
NumberTheory /
NumberTheory.HonestPhaseBudgetBridge /
explainer
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formal statement (Lean)
219 theorem honestPhaseFamily_charge_zero_of_costBounded
220 (zfd : ZetaPhaseFamilyData)
221 (hcost : RealizedDefectAnnularCostBounded (zfd.phaseFamily.toSampledFamily)) :
222 zfd.sensor.charge = 0 := by
proof body
Term-mode proof.
223 have hzero :=
224 (realizedDefectCostBounded_iff_charge_zero_and_excessBounded
225 (zfd.phaseFamily.toSampledFamily)).mp hcost
226 simpa [DefectPhaseFamily.toSampledFamily, zfd.family_sensor] using hzero.1
227
228 /-- For the current honest phase package, bounded total cost is equivalent to
229 zero charge. The perturbation/excess part is already proved; only the bounded-cost
230 upgrade remains genuinely open. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (15)
Lean names referenced from this declaration's body.
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cost
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cost
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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total
in IndisputableMonolith.NavierStokes.DiscreteVorticity
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DefectPhaseFamily
in IndisputableMonolith.NumberTheory.DefectSampledTrace
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RealizedDefectAnnularCostBounded
in IndisputableMonolith.NumberTheory.DefectSampledTrace
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realizedDefectCostBounded_iff_charge_zero_and_excessBounded
in IndisputableMonolith.NumberTheory.DefectSampledTrace
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DefectPhaseFamily
in IndisputableMonolith.NumberTheory.MeromorphicCircleOrder
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ZetaPhaseFamilyData
in IndisputableMonolith.NumberTheory.MeromorphicCircleOrder
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total
in IndisputableMonolith.NumberTheory.RiemannHypothesis.ErrorBudget
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phase
in IndisputableMonolith.NumberTheory.RiemannHypothesis.Wedge
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