Structural Emotional Equations

Regime‑Level Emotional Mathematics in RTT#

Structural emotional equations describe operators that act at the regime level, not the moment level.
They determine how emotional systems:

• restore coherence
• amplify drift
• collapse under instability
• reinforce alignment
• increase or decrease observer distance

These equations correspond to the six structural emotions defined in emotions_part_f.json.

Structural equations are:

• regime‑shaping
• system‑wide
• alignment‑triad‑driven
• drift‑sensitive
• collapse‑predictive

They form the mathematical foundation for deep drift, coherence restoration, and regime collapse.

1. Core Structural Equation Forms#

Structural operators modify regime‑level variables:

1.1 Coherence Restoration (Relief)#

$$E_{\text{relief}} = k_{rel} \cdot \sigma \cdot (C' - C)$$

1.2 Alignment Reinforcement (Joy)#

$$A_{\text{joy}} = k_{joy} \cdot \sigma \cdot (A_s + A_o + A_w)$$

1.3 Drift Amplification (Drift Anxiety)#

$$D_{\text{anx}} = k_{danx} \cdot \sigma \cdot D$$

1.4 Collapse Dynamics (Collapse Fear)#

$$C_{\text{fear}} = k_{cfear} \cdot \sigma \cdot (D + \Delta O + |R - C|)$$

1.5 Isolation Dynamics#

$$Iso = k_{iso} \cdot \sigma \cdot (\Delta O + A_s^{-})$$

1.6 Distrust Dynamics#

$$D_{tr} = k_{dtr} \cdot \sigma \cdot (A_o^{-} + \Delta O)$$

2. Structural Equations (6)#

These equations correspond directly to the structural emotions in emotions_part_f.json.

2.1 Coherence Relief#

$$E_{\text{relief}} = k_{rel} \cdot \sigma \cdot (C' - C)$$

• restores coherence
• reduces drift
• stabilizes system after turbulence

2.2 Alignment Joy#

$$A_{\text{joy}} = k_{joy} \cdot \sigma \cdot (A_s + A_o + A_w)$$

• reinforces triadic alignment
• strengthens coherence
• increases system‑wide stability

2.3 Drift Anxiety#

$$D_{\text{anx}} = k_{danx} \cdot \sigma \cdot D$$

• amplifies drift
• increases instability
• accelerates regime collapse

2.4 Collapse Fear#

$$C_{\text{fear}} = k_{cfear} \cdot \sigma \cdot (D + \Delta O + |R - C|)$$

• triggers collapse conditions
• destabilizes coherence
• increases drift sensitivity

2.5 Isolation#

$$Iso = k_{iso} \cdot \sigma \cdot (\Delta O + A_s^{-})$$

• increases observer distance
• collapses relational alignment
• deepens drift

2.6 Distrust#

$$D_{tr} = k_{dtr} \cdot \sigma \cdot (A_o^{-} + \Delta O)$$

• destabilizes relational systems
• increases drift
• reduces interpretability

3. Structural Equation Summary Table#

4. Regime Interaction#

Structural equations drive:

Deep Drift#

$$D_{\text{anx}} > D$$

Collapse#

$$C_{\text{fear}} \gg E_{\text{coh}}$$

Coherence Restoration#

$$E_{\text{relief}} > D$$

Alignment Reinforcement#

$$A_{\text{joy}} \gg 0$$

Structural operators are the highest‑order emotional forces in RTT.

Status#

status: complete
license: open educational use