🎼 Echo Strength Index (ESI)

Quantifying Echo Intensity • Recurrence • Substrate Spread#

The Echo Strength Index (ESI) measures the intensity, stability, and
propagation potential of echoes across the TriadicFrameworks canon.

Echo strength determines:

• how strongly a concept recurs
• how far an echo spreads across substrates
• how likely an echo is to trigger recursion
• how likely an echo is to amplify drift
• how stable or unstable an echo cluster is

This module defines the four‑level ESI scale, its metrics, and its usage.

🔷 1. Purpose of the Echo Strength Index#

ESI answers:

• How strong is this echo?
• Is it stabilizing or destabilizing?
• Is it likely to trigger recursion?
• Is it likely to amplify drift?

ESI is used during:

• echo analysis
• recursion diagnostics
• drift detection
• stability audits
• canon sweeps

🔷 2. ESI Levels (Overview)#

The Echo Strength Index has four canonical levels:

These levels are determined by the metrics below.

🔷 3. ESI Metrics#

ESI is computed from five RTT‑native metrics:

3.1 Recurrence Frequency (RF)#

How often the echo appears across modules.

3.2 Substrate Spread (SS)#

How many substrates the echo spans:

• symbolic
• cognitive
• harmonic
• social
• atlas

3.3 Semantic Density (SD)#

How much meaning the echo carries.

3.4 Harmonic Alignment (HA)#

How well the echo aligns with interval structure.

3.5 Recursion Coupling (RC)#

How strongly the echo interacts with recursion modes.

Each metric is scored 0–3.

🔷 4. ESI Calculation Formula#

The Echo Strength Index is computed as:

ESI = RF + SS + SD + HA + RC

Then mapped to levels:

0–3   → ESI‑1 (Weak)
4–6   → ESI‑2 (Moderate)
7–10  → ESI‑3 (Strong)
11–15 → ESI‑4 (Dominant)

This formula ensures:

• transparency
• repeatability
• zero drift in measurement

🔷 5. ESI Examples (Generic)#

Weak Echo (ESI‑1)#

• appears once or twice
• single substrate
• low semantic density

Moderate Echo (ESI‑2)#

• appears in several modules
• spans 1–2 substrates
• mild recursion coupling

Strong Echo (ESI‑3)#

• appears across multiple modules
• spans 2–3 substrates
• high semantic density
• recursion‑linked

Dominant Echo (ESI‑4)#

• pervasive across canon
• spans 3–5 substrates
• high recursion coupling
• potential drift or recursion trigger

🔷 6. ESI Interaction With Stability#

Echo strength is a stability diagnostic.

🔷 7. ESI Interaction With Drift#

• ESI‑1: no drift risk
• ESI‑2: early instability possible
• ESI‑3: drift‑pressure likely
• ESI‑4: drift‑shadow or projection drift possible

ESI is a drift predictor.

🔷 8. ESI Interaction With Recursion#

• ESI‑1: no recursion
• ESI‑2: mild cycle alignment
• ESI‑3: cycle → map alignment
• ESI‑4: map → atlas forcing

Echo strength is a recursion trigger.

🔷 9. Usage Notes#

Use this file when:

• measuring echo intensity
• diagnosing echo‑pressure
• predicting drift
• analyzing recursion behavior
• performing canon sweeps

Referenced by:

• 04_Canon_SelfEcho_Map.md
• 04a_Echo_Families.md
• 04b_Echo_Diagrams_ASCII.md
• 04d_Echo_Summary.md

🔷 Footer#

HSP Module 04c — Loaded
Version: v1.0
Status: Canon-Stable