definitiondefinitionalmainmatter
SRMF Energy Functional
definition:bk1_srmf_energy_functional
Exact LaTeX body
\begin{definition}[SRMF Energy Functional]
\label{definition:bk1_srmf_energy_functional}
The symbolic energy of a configuration $\rho$ under SRMF dynamics (see \ref{definition:bk1_self_regulating_mapping_function_srmf}) is given by:
\[
E[\rho] = \int_S \|\nabla \rho\|^2 dx + \lambda \int_S \delta_{\mathcal{C}}(x)^2 dx
\]
Where $\lambda$ is the contradiction tolerance parameter, and $S$ is the symbolic manifold (see \ref{definition:bk1_symbolic_manifold}).
\end{definition}Depends on
Cites
Cited by
Reference roles
| Target | Role | Logical support |
|---|---|---|
definition:bk1_self_regulating_mapping_function_srmf | definition_anchor | yes |
definition:bk1_symbolic_manifold | definition_anchor | yes |
Complete structured record
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"latex_body": "\\begin{definition}[SRMF Energy Functional]\n\\label{definition:bk1_srmf_energy_functional}\nThe symbolic energy of a configuration $\\rho$ under SRMF dynamics (see \\ref{definition:bk1_self_regulating_mapping_function_srmf}) is given by:\n\\[\nE[\\rho] = \\int_S \\|\\nabla \\rho\\|^2 dx + \\lambda \\int_S \\delta_{\\mathcal{C}}(x)^2 dx\n\\]\nWhere $\\lambda$ is the contradiction tolerance parameter, and $S$ is the symbolic manifold (see \\ref{definition:bk1_symbolic_manifold}).\n\\end{definition}",
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"the circle part of a revolution is the identity by construction; injections are data; no claim about this file or any system proving its own consistency",
"the helix is FOR approaching the equilibrium circle, not a telos; non-closure is not idolized"
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"The Godel-safe cycle potential as the energy functional kernel; the appB form is separately bound."
],
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{
"context": "l] \\label{definition:bk1_srmf_energy_functional} The symbolic energy of a configuration $\\rho$ under SRMF dynamics (see \\ref{definition:bk1_self_regulating_mapping_function_srmf}) is given by: \\[ E[\\rho] = \\int_S \\|\\nabla \\rho\\|^2 dx + \\lambda \\int_S \\delta_{\\mathcal{C}}(x)^2 dx \\] Where $\\lambda$",
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"context": "\\mathcal{C}}(x)^2 dx \\] Where $\\lambda$ is the contradiction tolerance parameter, and $S$ is the symbolic manifold (see \\ref{definition:bk1_symbolic_manifold}). \\end{definition}",
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