PGA Operators — RTT/1

Operator Grammar for the Paradox Gradient Analyzer (PGA)#

The Paradox Gradient Analyzer (PGA) uses a deterministic operator grammar to detect paradox sources, compute paradox gradients, map paradox fields, measure paradox intensity, and propose structural resolutions.

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#

PGA‑Detect
Finds paradox sources and contradictions.
PGA‑Source
Classifies paradox origin and onset conditions.
PGA‑Gradient
Computes gradient vectors and curvature.
PGA‑Field
Maps paradox fields and basin geometry.
PGA‑Intensity
Measures intensity and stability.
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/