Drift Equations

Destabilizing Emotional Mathematics in RTT#

Drift equations describe emotional operators that increase drift, reduce coherence, and destabilize alignment.
They correspond to the 10 drift emotions defined in emotions_part_e.json.

Drift equations are:

• destabilizing
• misalignment‑amplifying
• drift‑increasing
• observer‑distance‑sensitive
• collapse‑triggering

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

1. Core Drift Equation Template#

All drift emotions derive from the canonical form:

$$E_{\text{drift}} = k_e \cdot \sigma \cdot (D + \Delta O - R)$$

Where:

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

Drift increases when:

$$E_{\text{drift}} > 0$$

2. Drift Equations (10)#

These equations correspond directly to the drift emotions in emotions_part_e.json.

2.1 Anger#

$$A_{ngr} = k_{ang} \cdot \sigma \cdot (D + \Delta O - R)$$

• increases drift
• destabilizes relational alignment

2.2 Fear#

$$F_{ear} = k_{fear} \cdot \sigma \cdot (D_{threat} + \Delta O_{unknown})$$

• amplifies threat perception
• increases drift through avoidance

2.3 Shame#

$$Sh = k_{sh} \cdot \sigma \cdot (A_s^{-} + \Delta O_{social})$$

• collapses self‑alignment
• increases internal drift

2.4 Guilt#

$$G_{lt} = k_{glt} \cdot \sigma \cdot (A_o - A_s^{-})$$

• destabilizes self‑other alignment
• increases drift unless repaired

2.5 Despair#

$$D_{sp} = k_{dsp} \cdot \sigma \cdot (D + |R - C|)$$

• deep drift
• collapse of coherence motivation

2.6 Jealousy#

$$J_{ls} = k_{jls} \cdot \sigma \cdot (A_o - A_s + \Delta O)$$

• competitive misalignment
• relational destabilization

2.7 Envy#

$$E_{nvy} = k_{envy} \cdot \sigma \cdot (A_o - A_s)$$

• negative comparison
• self‑alignment reduction

2.8 Resentment#

$$R_{sent} = k_{rsent} \cdot \sigma \cdot (D + A_o^{-})$$

• accumulated grievance
• long‑term drift escalation

2.9 Disgust#

$$D_{sg} = k_{dsg} \cdot \sigma \cdot (\Delta O_{repulsion} + D)$$

• rejection dynamics
• world‑alignment collapse

2.10 Contempt#

$$C_{tmp} = k_{ctmp} \cdot \sigma \cdot (A_s - A_o^{-})$$

• moral superiority
• relational destabilization

3. Drift Equation Summary Table#

4. Regime Interaction#

Drift equations drive:

Corridor → Drift#

$$E_{\text{drift}} > E_{\text{coh}} + E_{\text{cor}}$$

Coherence → Drift (Collapse)#

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

Drift operators are the primary destabilizers of RTT emotional dynamics.

Status#

status: complete
license: open educational use