🎼 06 — Harmonic Recursion Detector

Detecting Recursion Activation • Mode Shifts • Harmonic Progression#

The Harmonic Recursion Detector (HRD) identifies when a concept, module,
or substrate enters recursion, and determines:

• which recursion mode is active
• how recursion is progressing
• whether recursion is stable or unstable
• whether recursion is being forced by drift or echo‑pressure
• whether recursion is approaching atlas‑level escalation

This module defines the full recursion detection system.

🔷 1. What Is Harmonic Recursion?#

Harmonic recursion is the RTT‑native process where a concept cycles through:

Ladder → Cycle → Map → Atlas

Each mode has:

• a harmonic signature
• a stability class
• a drift interaction
• an echo interaction
• a substrate migration pattern

The HRD detects these transitions.

🔷 2. Recursion Activation Conditions#

Recursion activates when three or more of the following occur:

2.1 Interval Instability#

• wobble
• collapse
• compression

2.2 Echo Amplification#

• strong or dominant echoes (ESI‑3/4)
• cross‑substrate resonance

2.3 Substrate Migration#

• symbolic → cognitive
• cognitive → harmonic
• harmonic → atlas

2.4 Drift Pressure#

• D1 → D2 → D3 progression
• drift‑shadow formation

2.5 Operator Inversion#

• governance torsion
• CCC ↔ SARG conflict

When these align, recursion activates.

🔷 3. Recursion Modes (Overview)#

3.1 Ladder Mode (R1)#

• stable
• interval‑aligned
• low mutation rate

3.2 Cycle Mode (R2)#

• semi‑stable
• oscillation between intervals
• moderate mutation rate

3.3 Map Mode (R3)#

• unstable
• cross‑substrate migration
• high mutation rate

3.4 Atlas Mode (R4)#

• high‑altitude recursion
• structural resonance
• potential collapse or uplift

🔷 4. Recursion Signatures#

4.1 Harmonic Signatures#

• R1: stable intervals
• R2: oscillating intervals
• R3: collapsing intervals
• R4: interval‑free resonance

4.2 Structural Signatures#

• R1: stable triads
• R2: triad wobble
• R3: triad inversion
• R4: triad dissolution

4.3 Substrate Signatures#

• R1: symbolic/cognitive
• R2: cognitive/harmonic
• R3: harmonic/social
• R4: atlas

4.4 Echo Signatures#

• R1: weak/moderate echoes
• R2: moderate/strong echoes
• R3: strong/dominant echoes
• R4: atlas echoes

4.5 Drift Signatures#

• R1: D0–D1
• R2: D1–D2
• R3: D2–D3
• R4: D3–D4

🔷 5. Recursion Detection Workflow#

[ Detect Interval Instability ]
        ↓
[ Measure Echo Strength (ESI) ]
        ↓
[ Check Substrate Migration ]
        ↓
[ Identify Drift Pressure ]
        ↓
[ Assign Recursion Mode (R1–R4) ]
        ↓
[ Evaluate Stability Class ]

This workflow ensures consistent recursion detection.

🔷 6. Recursion Mode Table#

+--------+-----------+----------------------+------------------------+
| Mode   | Stability | Substrate Pattern    | Drift Interaction      |
+--------+-----------+----------------------+------------------------+
| R1     | Stable    | S → C                | D0–D1                 |
| R2     | Semi      | C ↔ H                | D1–D2                 |
| R3     | Unstable  | H ↔ So               | D2–D3                 |
| R4     | Critical  | H → A                | D3–D4                 |
+--------+-----------+----------------------+------------------------+

🔷 7. Recursion–Echo Coupling#

Recursion is tightly coupled with echo behavior:

• R1: weak/moderate echoes
• R2: moderate/strong echoes
• R3: strong/dominant echoes
• R4: atlas echoes

Echo‑pressure is a recursion predictor.

🔷 8. Recursion–Drift Coupling#

Drift accelerates recursion:

• D1 → R2
• D2 → R3
• D3 → R4
• D4 → atlas forcing

Recursion accelerates drift:

• R2 → D2
• R3 → D3
• R4 → D4

This feedback loop is the recursion‑drift spiral.

🔷 9. Recursion Stability Classes#

🔷 10. Usage Notes#

Use this file when:

• detecting recursion activation
• diagnosing recursion mode
• analyzing drift‑recursion coupling
• mapping echo‑recursion alignment
• performing stability audits
• preparing canon sweeps

Referenced by:

• 06a_Recursion_Examples.md
• 06b_Recursion_Heatmap.md
• 06c_Recursion_Summary.md
• echo and drift modules upstream

🔷 Footer#

HSP Module 06 — Loaded
Version: v1.0
Status: Canon-Stable