[ONTO-005] — Updated Ontology

FRCFD is a candidate framework under construction in which matter (Ψ) and substrate (S) form a bidirectionally coupled system.

The coupling may be asymmetric, meaning the interaction from Ψ → S and S → Ψ can differ in strength or response time.

A stable mass corresponds to a steady‑state equilibrium of this coupled system.

A gravitational wave corresponds to a transient perturbation, producing a measurable strain signal interpreted as a response of the coupled system.

🔧 Structural Upgrade Summary

The framework has been extended to include:

• Directional asymmetry in coupling
• Potential differences in response strength
• Optional response lag (time delay)

This upgrade preserves internal consistency while introducing testable structure.

Core Equation (Updated)

\[ \mathcal{L} = \mathcal{L}_S + \mathcal{L}_\Psi + \kappa_{1} S \Psi^2 + \kappa_{2} \Psi S^2 \]

Parameter Definitions

• S: Substrate field
• Ψ: Matter / excitation field
• κ₁: Coupling strength from Ψ → S
• κ₂: Coupling strength from S → Ψ

Asymmetry Condition

\[ \kappa_1 \neq \kappa_2 \]

This represents directional imbalance in the coupled system.

Optional Time‑Dependent Extension (Response Lag)

\[ \kappa_1 S(t)\,\Psi^2(t - \tau_1) \;+\; \kappa_2 \Psi(t)\,S^2(t - \tau_2) \]

Lag Definitions
τ₁: Response delay from matter → substrate
τ₂: Response delay from substrate → matter

\[ \tau_1 \neq \tau_2 \]

Visual Representation

Symmetric case:

Ψ ↔ S

Asymmetric case:

Ψ --(κ₁)--> S Ψ <--(κ₂)-- S

With response lag:

Ψ(t - τ₁) → S(t) S(t - τ₂) → Ψ(t)

Interpretation Layer (Controlled)

• The system is treated as a coupled dynamic structure, not a geometric curvature model
• Observables arise from system response, not assumed intrinsic geometry
• Measured strain is interpreted as a proxy for dynamic response of the coupled system

Constraints

• No claim of physical correctness is made
• No claim of replacement of existing theories
• No claim of validation

Status

• Internally consistent
• Structurally extensible
• Empirically unverified

Purpose

This ontology provides a minimal, testable framework that:

• Supports asymmetric interactions
• Allows nonlinear extensions
• Can be evaluated against observational data

Next Phase

• Stabilize measurement pipeline
• Perform multi‑event analysis
• Compare against established predictions
• Evaluate consistency across domains

Position

This is a candidate framework under construction, transitioning from conceptual structure toward empirical evaluation.

Note: All equations are shown in standard mathematical notation; the visual representations use arrow notation as specified. This document is part of the ongoing ontology development for FRCFD.