recognition /
Complexity /
Complexity.CircuitLedger /
explainer
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formal statement (Lean)
154 def CircuitZCapacity {n : ℕ} (c : BooleanCircuit n) : ℕ :=
proof body
Definition body.
155 CircuitBondCount c
156
157 /-- **THEOREM (Circuit Capacity Bound).**
158 A Boolean circuit of size S has Z-complexity capacity at most 2S.
159
160 The significance: a polynomial-size circuit (S = poly(n)) has
161 Z-capacity at most 2·poly(n) = poly(n). -/
used by (4)
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.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
BooleanCircuit
in IndisputableMonolith.Complexity.CircuitLedger
decl_use
CircuitBondCount
in IndisputableMonolith.Complexity.CircuitLedger
decl_use
has
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
A
in IndisputableMonolith.Masses.Anchor
decl_use
Z
in IndisputableMonolith.Masses.Anchor
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use
Z
in IndisputableMonolith.Physics.AnchorPolicyCertified
decl_use
significance
in IndisputableMonolith.Quantum.PlanckScale
decl_use
S
in IndisputableMonolith.Relativity.ILG.Action
decl_use