Corridor Equations

Transitional Emotional Mathematics in RTT#

Corridor equations describe emotional operators that sit between coherence and drift.
They are directional, context‑dependent, and regime‑sensitive.

Corridor emotions can:

• move a system toward coherence
• move a system toward drift
• maintain a transitional state

They correspond to the 10 corridor emotions defined in emotions_part_c.json.

1. Core Corridor Equation Template#

All corridor emotions derive from the canonical form:

$$E_{\text{cor}} = k_e \cdot \sigma \cdot \theta \cdot (R - D)$$

Where:

• $$R$$ = resonance alignment
• $$D$$ = drift
• $$\theta$$ = context factor
• $$\sigma$$ = emotional intensity
• $$k_e$$ = operator constant

Corridor direction:

• $$E_{\text{cor}} > 0$$ → coherence‑leaning
• $$E_{\text{cor}} < 0$$ → drift‑leaning

2. Corridor Equations (10)#

These equations correspond directly to the corridor emotions in emotions_part_c.json.

2.1 Curiosity#

$$Q = k_q \cdot \sigma \cdot \theta \cdot (R - D)$$

• coherence if aligned
• drift if misaligned

2.2 Anticipation#

$$A_{nt} = k_{ant} \cdot \sigma \cdot \theta \cdot (R_{future} - D)$$

• future‑oriented alignment
• drift if expectations break

2.3 Surprise#

$$S_{pr} = k_{spr} \cdot \sigma \cdot |\Delta O|$$

• neutral baseline
• direction determined by interpretation

2.4 Interest#

$$I = k_i \cdot \sigma \cdot \theta \cdot (R - D/2)$$

• coherence if regulated
• drift if overstimulated

2.5 Desire#

$$D_{sr} = k_{dsr} \cdot \sigma \cdot (A_s - A_o)$$

• self‑aligned desire → coherence
• other‑misaligned desire → drift

2.6 Vulnerability#

$$V_{ln} = k_{vln} \cdot \sigma \cdot (A_o - A_s)$$

• supported → coherence
• unsupported → drift

2.7 Excitement#

$$E_x = k_{ex} \cdot \sigma \cdot \theta \cdot (R - D/3)$$

• coherence if regulated
• drift if overstimulated

2.8 Nostalgia#

$$N = k_n \cdot \sigma \cdot (R_{past} - R_{present})$$

• integration → coherence
• longing → drift

2.9 Ambition#

$$A_{mb} = k_{amb} \cdot \sigma \cdot (A_s - A_o + A_w)$$

• aligned ambition → coherence
• competitive ambition → drift

2.10 Confusion#

$$C_{nf} = k_{cnf} \cdot \sigma \cdot (D + |R - C|)$$

• increases drift
• destabilizes alignment

3. Corridor Equation Summary Table#

4. Regime Interaction#

Corridor equations drive:

Coherence → Corridor#

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

Corridor → Coherence#

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

Corridor → Drift#

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

Corridor operators are the primary directional forces of RTT emotional dynamics.

Status#

status: complete
license: open educational use