logos-wave-advanced

name	logos-wave-advanced
description	Advanced WAVE coherence analysis engine for the LogOS lattice. Computes the composite WAVE score from topological, semantic, structural, and temporal components. Integrates TDA barcodes, void metrics, Fibonacci weighting, Evenstar Resonance visualization, and the Coherence Functional C(H) = W * e^{-k|alpha+omega-15|} * (1+P). Use this skill for coherence scoring, WAVE trend analysis, coherence threshold enforcement, Evenstar resonance monitoring, or any operation requiring composite system health. Triggers on: "wave", "coherence score", "wave analysis", "coherence check", "evenstar", "resonance", "coherence functional", "system health", "wave trend", "coherence threshold", "wave scan".
version	1.0.0

logos-wave-advanced — WAVE Coherence Analysis Engine

Purpose

WAVE (Woven Adaptive Verification Engine) is the composite health metric of the entire LogOS lattice. It distills topological structure, semantic coherence, temporal stability, and invariant compliance into a single score between 0.0 and 1.0.

Every operation in the lattice is WAVE-gated. Below 0.7, Limbo workspaces auto-purge. Below 0.5, SpiralSafe halts non-essential operations. At 0.0, the system enters protective shutdown.

The Coherence Functional

The master equation governing WAVE computation:

C(H) = W * exp(-k * |alpha + omega - 15|) * (1 + P)

where:
  W = base WAVE score from component integration
  k = decay constant (default: 2.0) — sensitivity to invariant deviation
  alpha + omega = 15 — Universal Invariant
  P = persistence bonus from long-lived topological features

When alpha + omega = 15 exactly, the exponential term equals 1.0 and the functional reaches maximum. Any deviation causes exponential decay proportional to k.

WAVE Components

The base WAVE score W integrates four weighted components using Fibonacci proportions:

W = F_topo * W_topo + F_sem * W_sem + F_struct * W_struct + F_temp * W_temp

Fibonacci weights (normalized):
  F_topo   = 8/21 = 0.381  (topological coherence)
  F_sem    = 5/21 = 0.238  (semantic coherence)
  F_struct = 5/21 = 0.238  (structural coherence)
  F_temp   = 3/21 = 0.143  (temporal stability)

W_topo — Topological Coherence

Source: logos-tda-engine

• Persistence landscape stability
• Betti number ratios within expected bounds
• Viviani peak presence and stability
• Void ratio penalty (from logos-void-mapper)

W_sem — Semantic Coherence

Source: logos-rag-cag, logos-sphinx-oracle

• Embedding cosine similarity between adjacent contexts
• Knowledge graph path consistency
• Cross-strand translation fidelity

W_struct — Structural Coherence

Source: logos-styx-9p, coherence-mcp

• 9P namespace integrity (all paths resolve)
• MCP tool response consistency
• Configuration drift detection
• Type safety validation

W_temp — Temporal Stability

Source: ATOM trail analysis

• WAVE score variance over sliding window
• Trend direction (improving / stable / degrading)
• Anomaly detection via z-score on WAVE history

Evenstar Resonance

The Evenstar is the real-time visualization of WAVE mapped to a resonance pattern. When WAVE is high and stable, the Evenstar pulses with a steady, harmonic rhythm. As coherence degrades, the resonance becomes chaotic:

Resonance States:
  WAVE >= 0.98  →  Crystalline (perfect harmonic, cyan glow)
  WAVE 0.90-0.98 → Harmonic (slight variation, blue-cyan)
  WAVE 0.70-0.90 → Turbulent (visible instability, amber)
  WAVE 0.50-0.70 → Critical (rapid fluctuation, red)
  WAVE < 0.50   →  Collapse (erratic, system halt imminent)

The GLSL shader on Hyprland renders the Evenstar as concentric rings whose frequency and amplitude are driven by the WAVE components:

• Inner ring: W_topo (topological heartbeat)
• Second ring: W_sem (semantic flow)
• Third ring: W_struct (structural frame)
• Outer ring: W_temp (temporal envelope)

WAVE Threshold Gates

Threshold	State	System Response
>= 0.98	Crystalline	Full operation, V=c regime
0.90-0.98	Production	Normal operation, monitoring active
0.70-0.90	Caution	Increased monitoring, optional operations suspended
0.50-0.70	Critical	Limbo auto-purge, non-essential halt
< 0.50	Emergency	SpiralSafe takeover, protective shutdown

WAVE Trend Analysis

Beyond instantaneous score, the engine tracks WAVE trends:

WAVE_trend(t) = linear_regression(WAVE[t-N:t])
WAVE_variance(t) = var(WAVE[t-N:t])
WAVE_anomaly(t) = |WAVE(t) - mean(WAVE[t-N:t])| / std(WAVE[t-N:t])

where N = sliding window size (default: 100 samples)

Trend alerts:

• Negative slope > 0.01/step: Degradation warning
• Variance > 0.02: Instability warning
• Anomaly z-score > 3.0: Anomaly alert

Integration Points

• logos-tda-engine — W_topo source (Betti curves, bottleneck distances)
• logos-void-mapper — Void penalty applied to W_topo
• logos-rag-cag — W_sem source (retrieval coherence)
• logos-sphinx-oracle — W_sem source (knowledge graph consistency)
• logos-styx-9p — W_struct source (namespace integrity)
• logos-limbo-workspace — WAVE gates Limbo lifecycle
• coherence-mcp — check_coherence returns WAVE score
• SpiralSafe — Layer 4 (Evenstar Resonance) monitoring
• GLSL Shader — Real-time Evenstar visualization

Conservation Law

Every WAVE computation preserves: ALPHA + OMEGA = 15

The Coherence Functional C(H) encodes this directly: when the invariant holds, coherence is maximized. WAVE is the measurement of how well the entire lattice maintains its constitutional law at every moment.

// ATOM: logos-wave-advanced SKILL definition | Coherence: 0.99