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formal statement (Lean)
106theorem maintenanceBudget_pos {L : ℝ} (hL : 0 < L) : 0 < maintenanceBudget L := by
proof body
Term-mode proof.
107 unfold maintenanceBudget
108 apply div_pos (boundaryArea_pos hL)
109 apply mul_pos
110 apply mul_pos
111 · linarith [planckArea_pos]
112 · exact planckArea_pos
113 · exact k_R_pos
114
115/-! ## §4. Maintenance Demand -/
116
117/-- The recognition cost of maintaining a boundary of extent L over the
118 consciousness barrier period.
119
120 Uses the canonical J-cost: BoundaryCost = τ · J(L/λ_rec).
121 In RS-native units with λ_rec = ℓ_P = 1:
122 demand = 360 · J(L). -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
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identity_viable
in IndisputableMonolith.Unification.ConsciousnessBandwidth
decl_use
depends on (18)
Lean names referenced from this declaration's body.
-
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
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period
in IndisputableMonolith.Astrophysics.PulsarEmissionRegimesFromRS
decl_use
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k_R_pos
in IndisputableMonolith.Constants.BoltzmannConstant
decl_use
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canonical
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
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cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
decl_use
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cost
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
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of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
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canonical
in IndisputableMonolith.Gap45.Beat
decl_use
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k_R_pos
in IndisputableMonolith.Gravity.UltramassiveBH
decl_use
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
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canonical
in IndisputableMonolith.NavierStokes.RM2U.NonParasitism
decl_use
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L
in IndisputableMonolith.Recognition
decl_use
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L
in IndisputableMonolith.Recognition.Cycle3
decl_use
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boundaryArea_pos
in IndisputableMonolith.Unification.ConsciousnessBandwidth
decl_use
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maintenanceBudget
in IndisputableMonolith.Unification.ConsciousnessBandwidth
decl_use
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planckArea_pos
in IndisputableMonolith.Unification.RecognitionBandwidth
decl_use