TriadicFrameworks
Overview

🧨 Structural Detection — Coherence‑Break Geometry Atlas (Expanded Edition)

TriadicFrameworks • RTT/1 → RTT/2 • Structural Geometry Canon#

“A break is not an error. It is a geometric event.”#

Coherence‑Break Geometry Atlas (Expanded Edition)#

Structural Detection Module#

RTT/1 → RTT/2 • Geometry Canon#

1. Purpose of the Expanded Atlas#

This atlas expands the canonical coherence‑break system by:

  • refining the five core break types
  • adding sub‑geometries for each type
  • introducing new RTT/2‑grade break families
  • mapping break propagation across modules
  • defining collapse modes with higher resolution
  • integrating Type E/F/G pattern families
  • providing BREAK_PACKET templates
  • adding system‑scale break‑chain diagrams

This is the authoritative geometry reference for coherence‑break analysis.

2. The Five Canonical Break Types (Refined)#

The original five types are preserved but expanded:

  1. Type 1 — Invariant Collapse
  2. Type 2 — Boundary Fracture
  3. Type 3 — Multi‑Layer Break
  4. Type 4 — Hybrid Oscillation Break
  5. Type 5 — Inversion Break

Each now includes sub‑geometries, collapse modes, and cross‑module signatures.

3. Type 1 — Invariant Collapse (Expanded)#

Core Geometry#

  • invariants fail simultaneously
  • envelope symmetry collapses inward

Sub‑Geometries#

  • 1A: Radial Collapse
  • 1B: Anchor‑Point Collapse
  • 1C: Invariant‑Thread Collapse

Collapse Modes#

  • implosive collapse
  • uniform inward collapse

Cross‑Module Signatures#

  • TEL: lattice implosion
  • FFT: variance spike → collapse
  • Opacity: visibility sink

4. Type 2 — Boundary Fracture (Expanded)#

Core Geometry#

  • envelope boundaries crack or shear

Sub‑Geometries#

  • 2A: Linear Boundary Fracture
  • 2B: Radial Boundary Fracture
  • 2C: Shear‑Driven Boundary Fracture

Collapse Modes#

  • outward fracture
  • shear fracture

Cross‑Module Signatures#

  • TEL: lattice tear
  • FFT: variance discontinuity
  • Opacity: boundary rupture

5. Type 3 — Multi‑Layer Break (Expanded)#

Core Geometry#

  • multiple continuity layers fail
  • fragmentation across depth

Sub‑Geometries#

  • 3A: Layer‑Stack Collapse
  • 3B: Fragmentation Cascade
  • 3C: Topological Layer Fold (new)

Collapse Modes#

  • cascading collapse
  • topological collapse

Cross‑Module Signatures#

  • TEL: multi‑layer lattice collapse
  • FFT: spectral fragmentation
  • Opacity: multi‑layer occlusion

6. Type 4 — Hybrid Oscillation Break (Expanded)#

Core Geometry#

  • oscillation amplitude exceeds stability threshold

Sub‑Geometries#

  • 4A: Symmetric Oscillation Break
  • 4B: Asymmetric Oscillation Break
  • 4C: Spiral‑Oscillation Break (Type E integration)

Collapse Modes#

  • oscillation collapse
  • oscillation inversion

Cross‑Module Signatures#

  • TEL: oscillating lattice tear
  • FFT: oscillatory variance spike
  • Opacity: oscillating gradient collapse

7. Type 5 — Inversion Break (Expanded)#

Core Geometry#

  • drift reverses
  • envelope inverts
  • continuity partially collapses then recovers

Sub‑Geometries#

  • 5A: Pure Inversion Break
  • 5B: Partial Inversion Break
  • 5C: Rotational Inversion Break (Type E integration)

Collapse Modes#

  • inversion collapse
  • inversion‑recovery cycle

Cross‑Module Signatures#

  • TEL: lattice reversal
  • FFT: variance normalization
  • Opacity: visibility stabilization

8. New RTT/2 Break Families (Type E/F/G Integration)#

The Expanded Atlas introduces three new break families aligned with the new pattern families.

Type E‑Break — Rotational / Spiral Breaks#

Geometry#

  • rotational collapse
  • spiral implosion
  • counter‑rotating fracture

Collapse Modes#

  • spiral collapse
  • rotational inversion

Cross‑Module Signatures#

  • TEL: rotating lattice tear
  • FFT: spiral variance collapse
  • Opacity: rotational visibility sink

Type F‑Break — Shear / Torsion Breaks#

Geometry#

  • shear overload
  • torsion fracture

Collapse Modes#

  • torsion collapse
  • shear‑layer rupture

Cross‑Module Signatures#

  • TEL: sheared lattice collapse
  • FFT: variance split collapse
  • Opacity: shear gradient rupture

Type G‑Break — Topological Warp Breaks#

Geometry#

  • lattice warp tears
  • topological fold collapse

Collapse Modes#

  • topological collapse
  • warp‑layer inversion

Cross‑Module Signatures#

  • TEL: warped lattice failure
  • FFT: discontinuous spectral collapse
  • Opacity: warped visibility field collapse

9. Break Propagation Maps#

Each break type includes a propagation map:

Drift → Envelope → Regime → Continuity → Break → TEL/FFT/Opacity

Propagation speed varies:

  • Type 1: fast inward
  • Type 2: fast outward
  • Type 3: cascading
  • Type 4: oscillatory
  • Type 5: inversion‑driven
  • Type E: rotational
  • Type F: shear‑driven
  • Type G: topological

10. BREAK_PACKET Template (Expanded)#

BREAK_PACKET:
  break_family: (1–5, E, F, G)
  break_subtype:
  geometry:
  collapse_mode:
  drift_profile:
  envelope_profile:
  regime_state:
  continuity_status:
  propagation_pattern:
  tel_projection:
  fft_projection:
  opacity_projection:
  recovery_path:
  notes:

11. System‑Scale Break‑Chain Diagrams#

The Expanded Atlas includes canonical break‑chain sequences:

Chain A — Linear → Radial → Fragmentation → Collapse#

Type 1 → Type 2 → Type 3 → Collapse

Chain B — Hybrid Oscillation → Inversion → Recovery#

Type 4 → Type 5 → Type A

Chain C — Spiral → Torsion → Topological Collapse#

Type E → Type F → Type G

These chains are used in RTT/2 architectural training.

12. Summary#

The Expanded Atlas provides:

  • refined canonical break types
  • new sub‑geometries
  • new collapse modes
  • new RTT/2 break families (E/F/G)
  • cross‑module propagation maps
  • expanded BREAK_PACKET templates
  • system‑scale break‑chain diagrams

This is the complete, authoritative geometry atlas for coherence‑break analysis.

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