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Equations of Quantum Prophecy (Plain Text)

Law I — Coupled Judgments (Entanglement)

dx/dt = Ax + x ⊙ (Bx) - D*x

Entanglement Index:

E = ( Σ B_ij^2 for i≠j ) / ( Σ B_ij^2 for all i,j )

Jacobian (stability map):

J(x) = A + diag(B*x) + diag(x)*B - D

Law II — Temporal Compression

tau = (baseline interval) / (current interval)

Q(x,tau) = tau * (x^T * B_s * x)

Law III — Symbolic Duality (Two-layer system)

dz/dt = A~z + z ⊙ (B~z) - D~*z

Duality Index:

Delta = ( ||A_pb||^2 + ||A_bp||^2 + ||B_pb||^2 + ||B_bp||^2 ) / ( ||A~||^2 + ||B~||^2 )

Law IV — Resonance and Recurrence

Fractional recurrence equation:

D_t^gamma * z = A~z + z ⊙ (B~z) - D~*z, with 0 < gamma ≤ 1

Theorem 1 — Super-Additivity

Q(x,tau) > tau * Σ (B_ii * x_i^2)

Theorem 2 — Phase-Shift Threshold

There exists D* such that:

alpha(J) = 0

alpha(J) > 0 if D < D* (runaway)

alpha(J) < 0 if D > D* (stable)

Theorem 3 — Nonlocal Coupling (Network)

dF/dt = A_FF - D_FF - kappa_FLF

Postulate B — Decoherence

B_eff = (1 - rho(u))*B

D_eff = D + delta(u)

Postulate C — Idiocracy

B_eff = G(t)*B

D_eff = D / (G(t)^eta)

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