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Foundation /
Foundation.StillnessGenerative /
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formal statement (Lean)
332 theorem one_plus_phi_eq_phi_sq : 1 + PhiForcing.φ = PhiForcing.φ ^ 2 := by
proof body
Term-mode proof.
333 linarith [PhiForcing.phi_equation]
334
335 /-- **Ledger Composition Populates**: If the ledger has entries at
336 scales φ^n and φ^{n+1}, additive ledger composition (from T6
337 closure) creates an entry at scale φ^{n+2}.
338
339 This is the POPULATION theorem — not a cost bound, but a structural
340 consequence of closure. The composed entry EXISTS. -/
depends on (18)
Lean names referenced from this declaration's body.
phi_equation
in IndisputableMonolith.Algebra.PhiRing
decl_use
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
scale
in IndisputableMonolith.Cosmology.LargeScaleStructureFromRS
decl_use
has
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
Composition
in IndisputableMonolith.Foundation.CostAxioms
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
decl_use
cost
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
phi_equation
in IndisputableMonolith.Foundation.PhiForcing
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
from
in IndisputableMonolith.Foundation.PrimitiveDistinction
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use