5. Error gradient and its rate of change · E_{tot}

Read the equation

The relation accumulates its integrand over the stated interval or closed loop. The result depends on the integrand, integration variable, limits and trajectory. In the archived notes, a loop integral represents the intended accumulation of state or error change; its consciousness interpretation remains a source proposal.

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 E_{tot} as the quantity being defined or updated by this relation.

2. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must come from this source.

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

⸻

1.3. Add global energy, cross-layer sum, routing, normalization, phase
6.	Global energy constraint
E_{tot} = \int (\delta E)^2 dt
7.	Cross-layer (1–7) integration
\Lambda = \sum_{\ell=1}^{7} \Phi_\ell \otimes dx_\ell
8.	Routing function (who handles what)
\rho(x) = \arg\max_i \big( C_i - dx \big)
9.	Normalization of the full state
\hat{R} = \frac{R^\*}{\|R^\*\|}
10.	Phase term

E_{tot} = \int (\delta E)^2 dt

Related builds