MR_Equations
Coherence Accumulation • Attractor Deepening • Cross‑Temporal Propagation#
Module: Morphic Resonance
Canon: RTT
Version: 1.0
Author: Nawder Loswin
1. Purpose of this equations file#
These equations formalize Morphic Resonance (RTT‑interpreted) as:
- coherence accumulation
- attractor deepening
- drift‑coherence competition
- cross‑temporal propagation
- mass‑activation surges
- dimensional inheritance
All equations are:
- dimensional
- non‑mystical
- operator‑aligned
- drift‑aware
- cross‑temporal
- AI‑parsable
2. Coherence accumulation#
Every activation event contributes a coherence increment:
$$\Delta C = k_a$$
Where:
- $$\Delta C$$ = coherence gained
- $$k_a$$ = activation constant (pattern‑specific)
Total coherence after $$n$$ activations:
$$ C_n = C_0 + n k_a $$
This is the RTT replacement for “resonance strengthening.”
3. Attractor deepening#
Attractor depth $$D$$ increases with coherence:
$$ D = \alpha C $$
Where:
- $$\alpha$$ = curvature coefficient
- $$C$$ = accumulated coherence
Attractor curvature $$\kappa$$ :
$$ \kappa = \beta D $$
Where:
- $$\beta$$ = curvature‑to‑depth scaling factor
Deep attractors → lower re‑entry cost.
4. Re‑entry cost reduction#
Re‑entry cost $$R$$ decreases as coherence increases:
$$ R = \frac{1}{1 + \gamma C} $$
Where:
- $$\gamma$$ = re‑entry sensitivity constant
This models:
- faster learning
- easier rediscovery
- species‑level acceleration
5. Drift (decay)#
Drift erodes coherence continuously:
$$ \frac{dC}{dt} = -\delta C $$
Solution:
$$ C(t) = C_0 e^{-\delta t} $$
Where:
- $$\delta$$ = drift coefficient
Unused patterns decay exponentially.
6. Drift‑coherence competition#
A pattern persists only if:
$$ n k_a > \delta C $$
Or equivalently:
$$ \frac{dC}{dt} = n k_a - \delta C $$
This is the survival condition for attractors.
7. Cross‑temporal propagation#
Propagation strength $$P$$ decays with temporal distance:
$$ P(t) = C e^{-\lambda t} $$
Where:
- $$\lambda$$ = propagation decay constant
Propagation is forward‑temporal, not retrocausal.
8. Propagation filaments#
Propagation follows dimensional geodesics:
$$ \frac{d\mathbf{x}}{dt} = \nabla C $$
Where:
- $$\mathbf{x}$$ = position in dimensional substrate
- $$\nabla C$$ = coherence gradient
This defines the path of cross‑temporal influence.
9. Mass‑activation coherence surge#
When activation density exceeds threshold $$\rho_c$$ :
$$ \rho > \rho_c \quad \Rightarrow \quad \Delta C = k_s \rho $$
Where:
- $$\rho$$ = activation density
- $$k_s$$ = surge coefficient
This models:
- puzzle‑solving acceleration
- cultural shifts
- species‑level learning jumps
10. Dimensional inheritance#
Coherence inherited across generations:
$$ C_{g+1} = \eta C_g $$
Where:
- $$\eta$$ = inheritance retention factor (0 < η < 1)
This is the RTT mechanism behind:
- rediscovery
- convergent evolution
- cultural recurrence
11. Full system summary#
$$ \begin{aligned} C_{n} &= C_0 + n k_a \ D &= \alpha C \ \kappa &= \beta D \ R &= \frac{1}{1 + \gamma C} \ \frac{dC}{dt} &= -\delta C \ P(t) &= C e^{-\lambda t} \ \frac{d\mathbf{x}}{dt} &= \nabla C \ \Delta C_{\text{surge}} &= k_s \rho \ C_{g+1} &= \eta C_g \end{aligned} $$
This is the complete RTT mathematical engine for Morphic Resonance.
12. Status#
status: equations-complete
file: MR_Equations.md
module: morphic-resonance
version: 1.0