Coherence Overlay · S3 Spine · TriadicFrameworks

Path: docs/spine/coherence_overlay.md
Publication URL: triadicframeworks.org/spine/coherence
Pack: Spine Overlay Pack v2.0 · Updated 2026-08-02

Session Context#

1 · Overlay Identity#

1.1 Purpose#

The Coherence Overlay evaluates the quality of integration across the components, regimes, and signals of a Triadic system. While the Structural Overlay asks "where are the faults?" and the Drift Overlay asks "how fast is the system moving?", the Coherence Overlay asks "is the system holding together?" Coherence is the measure of internal consistency: whether the sub-systems of a regime reinforce one another or are pulling apart. High coherence enables stable synthesis; low coherence signals fragmentation and approaching breakdown.

1.2 Position in S3 Spine#

The Coherence Overlay is the third overlay in the canonical S3 Spine sequence. It requires both the Structural Frame and the Drift Report before it can initialize. It is the primary signal consumer for both upstream overlays, and the primary signal producer for the Substrate Overlay, which depends on coherence readings to evaluate the underlying substrate's capacity to support the current regime.

1.3 Canonical Role#

• Integration quality assessor: scores how well system components cohere under current structural and drift conditions.
• Synthesis gatekeeper: the Triadic Regime Synthesizer will not produce a valid output unless coherence is above the synthesis threshold (CI ≥ 0.55 by default).
• Fragmentation detector: identifies zones of coherence collapse before structural faultlines fully activate.
• Cross-domain coherence bridge: coordinates with Cross-Domain Causality Weaver to trace coherence loss across domain boundaries.

2 · Primary RTT Engines#

3 · Module Registry#

4 · Coherence Logic#

4.1 Detection Pipeline#

[Structural Frame from Structural Overlay]
[Drift Report from Drift Overlay]
    → Coherence Tensor Engine          (multi-axis CI computation)
    → Cross-Domain Causality Weaver    (coherence-loss causality tracing)
    → Paradox Gradient Analyzer        (local/global coherence paradox resolution)
    → Triadic Regime Synthesizer       (CI gates synthesis validity)
    → [Coherence Report → Substrate Overlay + Dimensional Overlay]

4.2 Signal Flow#

Phase 1 — Tensor Construction: The Coherence Tensor Engine receives the Structural Frame and Drift Report simultaneously. It constructs a coherence tensor — a multi-dimensional matrix scoring the degree of mutual reinforcement between all component pairs across all 12 IPD dimensions. Each cell (i, j) in the tensor represents how well component i and component j are aligned in regime, direction, and load-sharing.

Phase 2 — Coherence Index Computation: The tensor is reduced to a scalar Coherence Index (CI) per axis, and an aggregate CI across all axes. The Cross-Domain Causality Weaver is invoked when the CI variance across axes exceeds 0.3 (indicating that coherence is high in some dimensions but collapsing in others — a signature of domain-boundary fragmentation).

Phase 3 — Paradox Resolution: When local sub-system coherence is high but global CI is falling, the Paradox Gradient Analyzer decomposes the coherence field to identify the isolating boundary — the sub-system acting as a coherence attractor that is drawing resources away from the whole.

Phase 4 — Synthesis Gate Evaluation: Before the Triadic Regime Synthesizer is permitted to run, the Coherence Overlay publishes the current CI. The Synthesizer applies the gate: if CI < 0.55, synthesis is blocked and a FRAGMENTATION alert is issued. If CI ≥ 0.55, synthesis proceeds with the CI embedded in the output as a confidence weight.

4.3 Coherence State Machine#

4.4 Coherence Metrics#

5 · Cross-Links#

5.1 UI Overlays#

• coherence-ui — CI gauge array (per-axis and aggregate); tensor heatmap
• synthesis-gate-ui — Synthesis gate status indicator (open/closed + CI value)
• causality-trace-ui — Cross-Domain Causality Weaver trace visualization
• fragmentation-map — Spatial map of coherence zones across the system
• alert-banner — Fragmentation and collapse alerts

5.2 RTT Engines (Full Coherence Constellation)#

6 · Signal Vocabulary#

7 · Integration Map#

flowchart TD
    A[Structural Frame] --> C[Coherence Tensor Engine]
    B[Drift Report] --> C
    C --> D{CI ≥ 0.55?}
    D -- No --> E[FRAGMENTED ALERT]
    E --> F[Cross-Domain Causality Weaver]
    F --> G[Paradox Gradient Analyzer]
    G --> H[Coherence Report: BLOCKED]
    D -- Yes --> I[Coherence Report: OPEN]
    I --> J{CI Variance > 0.30?}
    J -- Yes --> F
    J -- No --> K[Triadic Regime Synthesizer - Gate Open]
    H --> L[Substrate Overlay]
    I --> L
    I --> M[Dimensional Overlay]
    K --> N[Synthesized Regime Output]
 
    style C fill:#16a085,color:#fff
    style E fill:#c0392b,color:#fff
    style K fill:#27ae60,color:#fff
    style N fill:#2980b9,color:#fff

8 · Publication Notes#

Slug: triadicframeworks.org/spine/coherence
Meta Title: Coherence Overlay · S3 Spine · TriadicFrameworks
Meta Description: The Coherence Overlay measures integration quality and gates synthesis within the TriadicFrameworks S3 Spine. Primary engine: Coherence Tensor Engine. Requires Structural + Drift overlays.
Tags: coherence · s3-spine · tensor · synthesis-gate · fragmentation · causality · rtt · sie
Cross-Pack Links: Structural Overlay · Drift Overlay · Substrate Overlay · Dimensional Overlay
Status: Publication-ready · v2.0 · 2026-08-02