TriadicFrameworks
Overview

🎼 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:

Level Name Description Stability Impact
ESI‑1 Weak Echo low recurrence, local only harmless
ESI‑2 Moderate Echo moderate recurrence, limited spread monitor
ESI‑3 Strong Echo high recurrence, multi‑substrate review for drift/overload
ESI‑4 Dominant Echo pervasive recurrence, recursion‑active potential drift or recursion trigger

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#

ESI Level Stability Class Impact
ESI‑1 stable
ESI‑2 semi‑stable
ESI‑3 oscillating
ESI‑4 chaotic / drift‑shadow risk

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
Powered by Docsbook