TriadicFrameworks
Overview

PGA Operators — RTT/1

Operator Grammar for the Paradox Gradient Analyzer (PGA)#

These operators form the backbone of paradox‑layer intelligence and feed directly into:

  • CTE (Coherence Tensor Engine)
  • DS (Drift Sentinel)
  • SFD (Structural Faultline Detector)
  • SBC (Stability Basin Cartographer)
  • TRS‑Temporal (Temporal Regime Sequencer)
  • CW (Cross‑Domain Causality Weaver)
  • DRS (Dimensional Resonance Scanner)

1. PGA‑Detect#

Detect paradox sources and contradictions#

Purpose
Identify paradox sources across conceptual, computational, physical, and dimensional regimes.

Capabilities

  • detects structural contradictions
  • detects gradient opposition
  • detects boundary paradoxes
  • detects tensor paradox violations
  • detects drift‑induced paradoxes

Output Fields

  • paradox_source
  • regime
  • onset_condition
  • coherence_dependency

2. PGA‑Source#

Classify paradox origin and onset conditions#

Purpose
Determine the origin, type, and structural signature of a paradox.

Capabilities

  • classifies paradox type
  • identifies onset conditions
  • identifies structural invariants
  • identifies tensor constraints
  • identifies drift envelopes

Output Fields

  • paradox_source
  • source_class
  • onset_condition
  • structural_signature

3. PGA‑Gradient#

Compute paradox gradient vectors#

Purpose
Calculate paradox gradient magnitude, direction, and coherence curvature.

Capabilities

  • computes gradient magnitude
  • computes gradient direction
  • computes coherence curvature
  • computes drift curvature
  • computes tensor curvature

Output Fields

  • gradient_magnitude
  • gradient_direction
  • coherence_curvature
  • drift_curvature
  • tensor_curvature

4. PGA‑Intensity#

Measure paradox intensity and stability#

Purpose
Quantify paradox intensity and evaluate stability across regimes.

Capabilities

  • computes paradox intensity
  • computes stability rating
  • computes basin depth
  • computes field curvature
  • computes coherence dependency

Output Fields

  • intensity
  • stability_rating
  • basin_depth
  • field_curvature

5. PGA‑Field#

Map paradox fields and basin topology#

Purpose
Generate paradox field maps showing curvature, basin geometry, and paradox ridges.

Capabilities

  • maps paradox fields
  • maps basin geometry
  • maps curvature topology
  • maps gradient flows
  • maps tensor paradox topology

Output Fields

  • field_map
  • basin_map
  • curvature_map
  • gradient_flow_map

6. PGA‑Resolve#

Suggest structural decompositions or paradox routing#

Purpose
Provide stabilization pathways or structural decompositions for paradoxes.

Capabilities

  • suggests structural decompositions
  • suggests coherence alignment
  • suggests drift reduction
  • suggests tensor rebalancing
  • suggests paradox routing

Output Fields

  • resolution_strategy
  • stabilization_pathway
  • coherence_alignment
  • drift_reduction

7. Operator Interaction Grammar#

Detection → Source Classification → Gradient Computation → Field Mapping → Intensity Analysis → Resolution#

  1. PGA‑Detect
    Finds paradox sources and contradictions.

  2. PGA‑Source
    Classifies paradox origin and onset conditions.

  3. PGA‑Gradient
    Computes gradient vectors and curvature.

  4. PGA‑Field
    Maps paradox fields and basin geometry.

  5. PGA‑Intensity
    Measures intensity and stability.

  6. PGA‑Resolve
    Produces stabilization or decomposition strategies.

This grammar ensures deterministic paradox‑layer behavior.

8. Operator Matrix Snippet#

{
  "operator": "PGA-Gradient",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "coherence_curvature": 0.51,
  "drift_curvature": 0.27,
  "tensor_curvature": 0.44
}

Status#

  • Version: 1.0
  • Status: canon‑stable
  • Category: rtt‑structural
  • Module Path: /docs/rtt/Paradox_Gradient_Analyzer/
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