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formal statement (Lean)
229theorem E_coh_pos : 0 < E_coh := by
proof body
Term-mode proof.
230 simp only [E_coh]
231 exact zpow_pos phi_pos (-5)
232
233/-! ## Summary: The Forcing Chain -/
234
235/-- **PHI FORCING PRINCIPLE**
236
237The golden ratio φ is forced by self-similarity in a discrete J-cost ledger:
238
2391. Discrete ledger with J-symmetry (from previous levels)
2402. Self-similarity: the structure references itself at different scales
2413. Compositional constraint: r² = r + 1 (next scale = current + base)
2424. Unique positive solution: r = φ = (1 + √5)/2
243
244This is Level 4 of the forcing chain:
245Composition law → J unique → Discreteness → Ledger → **φ** → D=3 → physics -/
used by (9)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (23)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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Chain
in IndisputableMonolith.Chain
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E_coh_pos
in IndisputableMonolith.Compat.Constants
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E_coh_pos
in IndisputableMonolith.Constants
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scale
in IndisputableMonolith.Cosmology.LargeScaleStructureFromRS
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E_coh_pos
in IndisputableMonolith.Foundation.ConstantDerivations
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Composition
in IndisputableMonolith.Foundation.CostAxioms
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
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cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
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cost
in IndisputableMonolith.Foundation.ObserverForcing
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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from
in IndisputableMonolith.Foundation.PrimitiveDistinction
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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Chain
in IndisputableMonolith.Recognition
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self
in IndisputableMonolith.RecogSpec.Core
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Chain
in IndisputableMonolith.RRF.Core.Recognition
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E_coh_pos
in IndisputableMonolith.RRF.Foundation.Constants
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next
in IndisputableMonolith.RRF.Hypotheses.EightTick
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