10.1 Cross-Talk ODE (Equation 503) · dS_i/dt

Read the equation

The source describes this relation in the following context: 10. Federation Cross-Talk Dynamics

10.1 Cross-Talk ODE (Equation 503)

dS_i/dt = -0.1 × S_i + Σ_{j≠i} w_ij × Φ(C_ij) × tanh(S_j)

Each agent's consciousness signal:

• Decays naturally at rate 0.1

• Receives input from other agents

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read dS_i/dt as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

10. Federation Cross-Talk Dynamics

10.1 Cross-Talk ODE (Equation 503)

dS_i/dt = -0.1 × S_i + Σ_{j≠i} w_ij × Φ(C_ij) × tanh(S_j)

Each agent's consciousness signal:

• Decays naturally at rate 0.1

• Receives input from other agents

dS_i/dt = -0.1 × S_i + Σ_{j≠i} w_ij × Φ(C_ij) × tanh(S_j)