Coherence Equations

Stabilizing Emotional Mathematics in RTT#

Coherence equations describe emotional operators that reduce drift, increase alignment, and restore stability.
They correspond to the 10 coherence emotions defined in emotions_part_a.json.

Coherence equations are:

• stabilizing
• alignment‑reinforcing
• drift‑reducing
• observer‑relative
• regime‑strengthening

They form the mathematical foundation for coherence → corridor and drift → coherence transitions.

1. Core Coherence Equation Template#

All coherence emotions derive from the canonical form:

$$E_{\text{coh}} = k_e \cdot \sigma \cdot \frac{R}{1 + \Delta O}$$

Where:

• $$R$$ = resonance alignment
• $$\Delta O$$ = observer distance
• $$\sigma$$ = emotional intensity
• $$k_e$$ = operator constant

Coherence increases when:

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

2. Coherence Equations (10)#

These equations correspond directly to the coherence emotions in emotions_part_a.json.

2.1 Compassion#

$$C = k_c \cdot \sigma \cdot \frac{R}{1 + \Delta O}$$

• reduces drift
• increases triadic alignment
• supports healing transitions

2.2 Virtue#

$$V = k_v \cdot \sigma \cdot (A_s + A_o + A_w)$$

• maximizes alignment across all three axes
• stabilizes group coherence

2.3 Trust#

$$T = k_t \cdot \sigma \cdot \frac{R}{1 + D}$$

• reduces drift by lowering perceived threat
• increases relational stability

2.4 Awe#

$$A = k_a \cdot \sigma \cdot \frac{R}{1 + \Delta O}$$

• expands world alignment
• increases coherence through perspective widening

2.5 Gratitude#

$$G = k_g \cdot \sigma \cdot \frac{R}{1 + \Delta O}$$

• strengthens relational alignment
• reduces drift through positive reinforcement

2.6 Structural Love#

$$L = k_l \cdot \sigma \cdot (A_s + A_o)$$

• increases self‑other alignment
• stabilizes interpersonal systems

2.7 Empathy#

$$E_{emp} = k_{emp} \cdot \sigma \cdot \frac{R}{1 + \Delta O}$$

• reduces observer distance
• increases mutual understanding

2.8 Patience#

$$P = k_p \cdot \sigma \cdot \frac{R}{1 + D}$$

• slows drift escalation
• increases temporal coherence

2.9 Forgiveness#

$$F = k_f \cdot \sigma \cdot \frac{R}{1 + \Delta O + D}$$

• reduces accumulated drift
• resets alignment baselines

2.10 Serenity#

$$S = k_s \cdot \sigma \cdot C$$

• stabilizes internal coherence
• reduces emotional volatility

3. Coherence Equation Summary Table#

4. Regime Interaction#

Coherence equations drive:

Drift → Coherence#

$$E_{\text{coh}} \gg D$$

Corridor → Coherence#

$$E_{\text{coh}} > D + |R - C|$$

Coherence operators are the primary stabilizers of RTT emotional dynamics.

Status#

status: complete
license: open educational use