FOLDER MATH SUMMARY
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03_Core_Papers
Ring 2 — Canonical Grounding
Ring 3 — Framework Connections
📄 P 01 THE PHYSICS OF COHERENCE.md
The Phase Transition
χ ∝ |T - Tc|^β for T < Tc (ordered phase)
χ → 0 for T > Tc (disordered phase)
📄 P 02 The Variable Substitution.md
The Equations (Unchanged)
χ ∝ |T - Tc|^β for T < Tc
χ → 0 for T > Tc
χ ∝ |P - Pc|^β for P > Pc
χ → 0 for P < Pc
The Constraint Removal Function
P(t) = P₀ · ∏ᵢ [1 - αᵢ · H(t - tᵢ)]
📄 P 03 The Nine Domains of Social Coherence.md
Computing χ
zᵢ(t) = [xᵢ(t) - μᵢ] / σᵢ
χ(t) = (1/9) · Σᵢ zᵢ(t)
📄 P 05 Implications and Falsifiability.md
The Question of Reversibility
dχ/dt = -λχ + G(t) - Σᵢ δ(t - tᵢ)·Δχᵢ
📄 THE MATHEMATICAL FRAMEWORK FOR SOCIAL COHERENCE.md
Definition of χ (The Coherence Variable)
χ = ⟨Ψ|Ψ₀⟩
χ(t) = (1/N) Σᵢ wᵢ · zᵢ(t)
The Nine Measurement Domains (Fruits of the Spirit Mapping)
zᵢ(t) = [xᵢ(t) - μᵢ(baseline)] / σᵢ(baseline)
The Phase Transition Model
χ ∝ |T - Tc|^β for T < Tc
χ = 0 for T > Tc
χ ∝ |P - Pc|^β for P > Pc (constraints maintained)
χ → 0 for P < Pc (constraints removed)
P(t) = P₀ · ∏ᵢ [1 - Hᵢ(t - tᵢ)]
The Master Equation (Dynamics)
dχ/dt = -λχ + G(t) - Σᵢ δ(t - tᵢ)·Δχᵢ
χ(t) = χ₀ · e^(-λt) · ∏ᵢ[1 - Δχᵢ · H(t - tᵢ)] + ∫₀ᵗ G(τ) · e^(-λ(t-τ)) dτ
The Cross-Domain Correlation (The Key Test)
Rᵢⱼ = Corr(zᵢ(t), zⱼ(t))
R̄ = (2/N(N-1)) Σᵢ<ⱼ Rᵢⱼ
The Structural Break Test (Identifying Tc)
P = (5/100)^9 ≈ 2 × 10⁻¹²
The Control Group Prediction (Amish)
χ_America(t) → 0 as t → 2025
The Physical Isomorphism (Validation)
M(T)/M(0) = (1 - T/Tc)^β
χ(t)/χ(1950) = f(t; tc, β')
Canonical Hub: CANONICAL_INDEX