all_phiInv_instances_equal
All five model definitions of 1/φ quantities across domains in Recognition Science are identical by construction. A physicist modeling decay rates or inequality ceilings would cite this to verify uniform application of the phi-inverse attractor. The proof is a term-mode construction that supplies four reflexivity steps because each quantity reduces definitionally to phiInv.
claimLet $1/φ$ denote the reciprocal of the golden ratio. Then the senolytic target ratio, the Gini coefficient ceiling, the counter-cyclical policy balance, the stem-cell reserve decay per rung, and the circadian amplitude decay are all equal to $1/φ$.
background
The CrossDomain.PhiInverseInvariants module states the C22 structural claim that $1/φ ≈ 0.618$ is the canonical attractor for negative-rung quantities such as decay rates, dampings, and target ratios. Each listed quantity is introduced by a noncomputable definition that sets it equal to phiInv. An upstream definition in Economics.InequalityCeilingFromSigma likewise sets the Gini ceiling to $φ^{-1}$, and the module records the supporting identities $1/φ < 1$, $1/φ > 0$, and $1/φ = φ - 1$.
proof idea
The proof is a term-mode construction that directly supplies the four reflexivity proofs. Because senolyticTargetRatio, giniCeiling, policyBalance, stemCellDecay, and circadianDecay are each defined to be exactly phiInv, the conjunction of equalities holds definitionally with no additional lemmas required.
why it matters in Recognition Science
The theorem confirms uniform application of the $1/φ$ value and thereby supports the phiInverseInvariantsCert definition that collects positivity, boundedness, and Fibonacci identities. It instantiates the cross-domain convergence asserted in C22 for wave 64 and aligns with the Recognition Science forcing chain that fixes phi as the self-similar fixed point.
formal statement (Lean)
98theorem all_phiInv_instances_equal :
99 senolyticTargetRatio = giniCeiling ∧
100 giniCeiling = policyBalance ∧
101 policyBalance = stemCellDecay ∧
102 stemCellDecay = circadianDecay := ⟨rfl, rfl, rfl, rfl⟩
proof body
Term-mode proof.
103
104/-- All five are bounded in (0, 1). -/