Unified Semiotic Mechanics 2

Integrating Referential Centration Theory (RCT) and Information‑Field Interaction (IFI) Kernel

Author: MPSoL / Containment Unit 7 – Semiotics Division

Date: 16 June 2025

Abstract

This document consolidates two complementary models developed by MPSoL: (1) Referential Centration Theory (RCT), which reframes gravity as symbolic adherence, and (2) the Information‑Field Interaction (IFI) kernel, which governs dynamic signal, distortion, and belief‑actuator terms within the Simulation. We demonstrate formal compatibility, provide an integrated mathematics, and outline operator workflow for tactical coherence control.

1. Model Summaries

1.1 Referential Centration Theory (RCT)

RCT defines gravity as emergent referential coherence. Key variables:
• Centration Index 𝐶_i = (R_c · B_i) / D_{i,c}^α
• Φ_c, the centration potential, with ∇Φ_c = R_c / D^α
• Inversion transform: R_c(t+Δt)=−R_c(t)

1.2 Information‑Field Interaction (IFI) Kernel

IFI treats information density I as diffusive, damped by distortion potential Ψ, and driven by belief‑actuator input B_a:
∂I/∂t = κ∇²I − λΨ + βB_a
Signal density σ = ∇·(∇B_a) and Signal‑Distortion Index SDI = ∫σ² / ∫Ψ².

2. Coherence Mapping

The bridge—belief and coherence:

Concept IFI Term RCT Term
Central Attractor R_c
Belief Density B_a (source) B_i (state)
Distortion Ψ α (turbulence exponent)
Signal Density / Gradient σ ∇Φ_c, ∇C_i
Stability Metric SDI mean 𝐶_i across region

3. Unified Field Equation

Combining kernels yields a coupled system:
1. Centration evolution:
∂C_i/∂t = (β/R_c) ∇²B_a − λ (Ψ/R_c) + κ ∇²C_i
2. Information density:
∂I/∂t = κ∇²I − λΨ + βB_a
where Ψ = f(C_i, Φ_c) encodes local turbulence; α becomes dynamic: α = 1 + Ψ/Ψ₀.

4. Operator Interface Workflow

Step 1: Monitor SDI bar (derived from 𝐶 & Ψ).
Step 2: Inject B_a via sigil scripts; observe real‑time shift in Φ_c contours.
Step 3: Confirm target 𝐶_i > 1.5 for lock‑on; archive breach data.
Step 4: Deploy narrative dampers if SDI exceeds 3 (risk of coherence collapse).

5. Implications

• Cosmology: Dark‑matter anomalies map to regions of low Ψ but high collective B.
• Engineering: Centration Modulation Devices exploit B_a pulses tuned to Ψ minima.
• Psychological: Trauma raises Ψ, reducing individual 𝐶_i ("ungrounded").

6. Future Work

Develop lattice‑based simulations to validate coupled equations; integrate operator UI with live SDI analytics.