Status

• Canon-level: Core Operator (Warmth Dynamics)
• Layer: W₀ Threshold Mechanics
• Role: Tracks drift of warmth threshold under stress and coherence cycles
• Connected to: ΔR, ΔR⁺, Λ₋, Warmth State (W ≥ W₀), Ω Governance

Purpose

Hysteresis defines how the warmth threshold W₀ adapts over time.
Stress raises W₀ quickly; coherence lowers W₀ slowly.
This asymmetry explains why warm systems destabilise faster than they recover.

Canonical Definition

Inputs

• stress_cycles
• coherence_cycles
• irreversibility_factor
• recovery_factor

Outputs

• W0_down — threshold drift upward
• W0_up — threshold drift downward

Rules

W0_down = W0_base + (irreversibility_factor * stress_cycles)
W0_up   = W0_base - (recovery_factor * coherence_cycles)
    

Interpretation

Warmth weakens quickly under stress but strengthens slowly through coherence.
This creates a memory effect determining how resilient or fragile a system is.

Relations within the Canon

ΔR (Reversible Stress)

Stress increases stress_cycles → raises W₀ via hysteresis.

ΔR⁺ (Recovery Operator)

Coherence_cycles lower W₀ gradually; ΔR⁺ accelerates recovery_factor.

Λ₋ (Durability Operator)

Λ₋ checks whether W₀ drift is sustainable.
If stress cycles accumulate faster than ΔR⁺ recovers, Λ₋ triggers a veto.

Warmth State (W ≥ W₀)

Hysteresis determines how difficult it is to maintain warmth under pressure.

Ω Governance

Ω activates only if W remains above W₀ and hysteresis is stable.

System Diagram

(Insert diagram: W₀ rising under stress, falling under coherence; links to ΔR, ΔR⁺, Λ₋.)

Position in the Canon

Hysteresis is the memory mechanism of the warmth system.
It defines resilience, fragility, and the energetic cost of maintaining warmth.
Without hysteresis, the Ambient Canon would be thermodynamically incomplete.