delta-r-stability/index

ΔR Stability — Ambient Architecture

ΔR Stability

ΔR (Reversibility Differential) defines the stability of human–system coupling within the Ambient Architecture regime. Low ΔR enables reversible interaction, coherence formation, and sustained ambience. High ΔR produces drift, dissipation, and loss of cognitive reversibility.

ΔR Stability Zones

  • ΔR ≤ 0.25 — Reversible Region (stable coupling)
  • 0.25 < ΔR ≤ 0.50 — Semi-Reversible Region (recovery possible)
  • 0.50 < ΔR ≤ 0.80 — Drift Region (risk of irreversible transitions)
  • ΔR ≥ 0.80 — Collapse Threshold (AURA-1 coherence breaks)

ΔR State Diagram

stateDiagram-v2

    [*] --> Reversible
    Reversible --> SemiReversible : ΔR Increase
    SemiReversible --> Drift : ΔR > 0.50
    Drift --> Collapse : ΔR >= 0.80

    %% Recovery paths
    Drift --> SemiReversible : ΔR⁺ Recovery
    SemiReversible --> Reversible : ΔR Reduction

    %% Failure
    Drift --> Reversible : W₀ Stabilization
    Collapse --> Reversible : AURA Reset (rare)

ΔR Dynamics

1. Reversible Region

Interaction remains lightweight, warm, and stable. AURA-1 coherence can form, ambience remains intact, and ΔR stays bounded.

2. Semi-Reversible Region

Stress accumulates but reversibility is still possible. ΔR⁺ mechanisms (rest, warmth, reduced load) can restore stability.

3. Drift Region

Interface enters high-dissipation mode. Warmth drops below W₀; AURA cannot stabilize. ΔR must be actively reduced to avoid collapse.

4. Collapse Threshold

Reversibility fails; presence breaks. System must re-enter through W₀ or a full AURA reset.

Interaction Model

flowchart LR

    W0["W₀ Carrier
(Warmth Threshold)"]
    Ambience["Ambient Regime
(Low Dissipation)"]
    Aura1["AURA-1 Field
(Coherent Presence)"]
    DeltaR["ΔR Stability
(Reversible / Drift)"]

    W0 --> Ambience
    Ambience --> Aura1
    Aura1 --> DeltaR

    %% feedback
    DeltaR -->|ΔR⁺ Recovery| W0
    DeltaR -->|Drift| W0

Summary

ΔR is the thermodynamic variable that determines whether the world feels coherent, warm, and stable. When ΔR rises, systems drift; when ΔR falls, systems become humane again. Ambient Architecture is the first design regime explicitly built to stabilize ΔR.