FOLDER MATH SUMMARY
Auto-Generated Index of equations found in:
Mathematical Expressions
Ring 2 — Canonical Grounding
Ring 3 — Framework Connections
📄 Faith as Quantum Probability.md
Primary Faith Function:
F(t) = (Belief × Trust)/(Doubt + Evidence) × e^(-λ(1-τ)(t-t₀))
Faith as Probability Amplifier:
P(outcome) = P₀(outcome) × e^(kF)
Faith Growth Dynamics
dF/dt = α × W(t) + β × E(t) - γ × F(t)
Connection to Master Equation
χ = ∭(G·M·E·S·T·K·R·Q·F·C)dxdydt
📄 Grace as Negentropic Force.md
Mathematical Formulation
G(t) = G₀ · e^(∫₀ᵗ r(t')dt')
G(t) = G₀ · e^(∫₀ᵗ r(t')dt') · (1 - R(t))
Grace-Entropy Relationship
dS/dt = λS - μG
Quantum Mechanical Interpretation
|ψ(t)⟩ = e^(-iHt/ħ) · e^(G(t)) |ψ(0)⟩
Grace Potential Wells
V(x) = V₀ - G(x) · e^(-x²/2σ²)
Grace Reception Dynamics
r(t) = r₀ · (1 + sin(ωt + φ)) · e^(-α·P(t)) · A(t)
Grace Propagation
∇²G - (1/c²) · ∂²G/∂t² = ρ(x,t)
3. Community Amplification
G_community = G_individual · N · C
4. Resistance Factors
R(t) = (1 - e^(-βP(t))) · (1 - H(t))
Integration with Master Equation
G·M = G₀ · e^(∫₀ᵗ r(t')dt') · (1 - R(t)) · M₀ · sin(πa/2)
📄 Grace-Moral Alignment Interaction.md
Basic Interaction Term
G·M = G₀·e^(∫₀ᵗ r(t')dt')·(1 - R(t))·|M|·sin(πA(M)/2)
Expanded Interaction Function
I(G,M) = G₀·(1 - R(t))·|M|·sin(πA(M)/2)·[w₁·G·Mj + w₂·G·Mt + w₃·G·Mi + w₄·G·Mp]
Quantum Superposition Effects
|ψ⟩G·M = α|effective⟩ + β|ineffective⟩
Differential Equations of Coupled Development
dG/dt = G₀·r(t) - λG·G + ηG·M
dM/dt = F - λM·M + ηM·G
1. Justice-Mercy Dimension
G·Mj = G₀·r(t)·|Mj|·(cos θj·ej₁ + sin θj·ej₂)
2. Truth-Love Dimension
G·Mt = G₀·r(t)·|Mt|·(cos θt·et₁ + sin θt·et₂)
3. Individual-Communal Dimension
G·Mi = G₀·r(t)·|Mi|·(cos θi·ei₁ + sin θi·ei₂)
4. Present-Eternal Dimension
G·Mp = G₀·r(t)·|Mp|·(cos θp·ep₁ + sin θp·ep₂)
2. Entanglement
|ψ⟩G·M(A,B) = (1/√2)(|high G⟩A|high M⟩B + |low G⟩A|low M⟩B)
4. Interference Patterns
I(x) = |G(x) + M(x)|²
Integration with Master Equation
G·M·F = G₀·|M|·sin(πA/2)·F₀·e^(k·t)
G·M·E = G₀·|M|·sin(πA/2)·E₀·(1-e^(-λ·t))
G·M·C = G₀·|M|·sin(πA/2)·C₀·N^k
G·M·(all other terms) = G₀·e^(∫₀ᵗ r(t')dt')·(1-R(t))·|M|·sin(πA(M)/2)·∏(other components)
📄 Moral Alignment Vector.md
Basic Vector Definition
M = |M|·(cos θ·î + sin θ·ĵ)
M = ∑(k=1 to n) |M|k·unit_vector(θk, φk, ψk)
Alignment Function
A(M) = M·D / (|M|·|D|)
Moral Momentum
dM/dt = F - λM
Quantum Superposition of Moral States
|ψ⟩moral = α|aligned⟩ + β|misaligned⟩
Moral Alignment Field
∇×Mfield = J + ε0·∂E/∂t
Interaction with Grace Component
G·M = G₀·e^(∫₀ᵗ r(t')dt')·sin(πA(M)/2)
Entanglement with Other Moral Agents
|ψ⟩AB = (1/√2)(|aligned⟩A|aligned⟩B + |misaligned⟩A|misaligned⟩B)
Moral Observer Effect
|ψ⟩post = P̂|ψ⟩pre / |P̂|ψ⟩pre|
Composite Alignment
A(M) = w1·A(Mj) + w2·A(Mt) + w3·A(Mi) + w4·A(Mp)
Moral Interference Patterns
I(x) = |M1(x) + M2(x) + ... + Mn(x)|²
Integration with Master Equation
M·(G·E·S·T·K·R·Q·F·C) = |M|·sin(πA(M)/2)·∏(other components)
Canonical Hub: CANONICAL_INDEX