Paradox Sources — RTT/1

Source Dictionary for the Paradox Gradient Analyzer (PGA)#

Paradox sources are the origin points from which paradox gradients emerge.
They represent contradictions, conflicts, or destabilizing conditions across conceptual, computational, physical, and dimensional regimes.

These sources feed directly into:

• PGA‑Detect
• PGA‑Source
• PGA‑Gradient
• PGA‑Intensity
• PGA‑Field
• PGA‑Resolve

Each paradox source includes:

• definition
• diagnostic markers
• onset conditions
• example signatures
• canonical PGA output pattern

1. Structural Paradox Sources#

Source: Symmetry‑Violation Paradox#

Definition
A structural invariant (e.g., symmetry, conservation, monotonicity) is violated by a downstream regime.

Diagnostic Markers

• broken invariants
• structural contradiction
• low drift, high coherence dependency

Onset Conditions

• algorithmic asymmetry
• structural misalignment
• constraint violation

Example Signature R1 symmetry rule ↔ R2 asymmetric iteration

Source: Calibration‑Contradiction Paradox#

Definition
A computational model requires calibration constants that contradict physical measurements.

Diagnostic Markers

• calibration mismatch
• measurement conflict
• medium drift sensitivity

Onset Conditions

• model‑measurement divergence
• unstable calibration envelope

Example Signature R2 model ↔ R3 measurement

2. Gradient Paradox Sources#

Source: Coherence‑Gradient Opposition#

Definition
Two regimes exhibit coherence gradients that oppose each other.

Diagnostic Markers

• coherence ridge inversion
• gradient opposition
• medium‑high intensity

Onset Conditions

• conceptual coherence ↑
• dimensional coherence ↓

Example Signature R1 coherence ↑ ↔ R4 coherence ↓

Source: Drift‑Gradient Inversion#

Definition
Drift decreases in one regime while increasing in another.

Diagnostic Markers

• drift curvature
• instability ridge
• high paradox basin depth

Onset Conditions

• computational drift ↓
• physical drift sensitivity ↑

Example Signature R2 drift ↓ ↔ R3 drift sensitivity ↑

3. Boundary Paradox Sources#

Source: Abstraction‑Measurement Paradox#

Definition
An abstract conceptual model predicts behavior that contradicts physical measurement.

Diagnostic Markers

• abstraction boundary curvature
• measurement conflict
• medium intensity

Onset Conditions

• conceptual model → physical implementation
• measurement deviation

Example Signature R1 abstraction ↔ R3 measurement

Source: Gradient‑Boundary Paradox#

Definition
A gradient alignment across regimes produces contradictory outcomes.

Diagnostic Markers

• aligned gradients
• contradictory outputs
• medium‑high intensity

Onset Conditions

• computational gradient ↔ dimensional gradient
• outcome divergence

Example Signature R2 gradient ↔ R4 gradient

4. Tensor Paradox Sources#

Source: Coherence Tensor Paradox#

Definition
A multi‑regime coherence tensor binds regimes, but one regime violates tensor constraints.

Diagnostic Markers

• tensor curvature
• coherence dependency
• high intensity

Onset Conditions

• tensor binding
• coherence violation

Example Signature R1 ↔ R2 ↔ R3 coherence tensor

Source: Dimensional Tensor Paradox#

Definition
Dimensional tensors constrain computational pathways, but computational coherence violates tensor alignment.

Diagnostic Markers

• tensor constraint
• coherence misalignment
• medium‑high intensity

Onset Conditions

• dimensional tensor
• computational violation

Example Signature R2 ↔ R4 dimensional tensor

5. Drift‑Induced Paradox Sources#

Source: Drift‑Amplification Paradox#

Definition
Drift in one regime amplifies drift curvature in another, forming a paradox basin.

Diagnostic Markers

• drift amplification
• basin formation
• high intensity

Onset Conditions

• physical drift ↑
• dimensional drift curvature ↑

Example Signature R3 drift ↑ ↔ R4 drift curvature ↑

Source: Drift‑Coherence Paradox#

Definition
Drift reduces coherence in one regime while increasing coherence sensitivity in another.

Diagnostic Markers

• coherence curvature
• drift‑coherence conflict
• medium‑high intensity

Onset Conditions

• computational drift ↓
• physical coherence sensitivity ↑

Example Signature R2 drift ↓ ↔ R3 coherence sensitivity ↑

6. Canonical PGA Output Pattern#

{
  "paradox_source": "coherence-gradient-opposition",
  "regime": "R1-R4",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "intensity": 0.77,
  "field_curvature": 0.51,
  "basin_depth": 0.69,
  "stability_rating": 0.46
}

Status#

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