Displaymode-like theorem environment

Question

I am having trouble recreating this theorem environment. I want to create an environment that is essentially on its own line, much like a block quote.

The only code I have so far just makes the this specific environment that is pictured

\newtheorem*{theorem}{Theorem}
\newtheoremstyle{named}{}{}{\itshape}{}{\normalfont\scshape}{.}{.5em}{\thmnote{#3}#1}
\theoremstyle{named}
\newtheorem*{namedtheorem}{}

Answer 1

You need no special \newtheorem declaration:

\documentclass{article}
\usepackage{amsmath}

\usepackage{lipsum} % for context

\newenvironment{namedtheorem}[1]
 {\begin{quotation}\noindent\textsc{#1.} \itshape\ignorespaces}
 {\end{quotation}}

\begin{document}

\lipsum[1][1-5]

\begin{namedtheorem}{Scale-Invariance} 
For any distance function $d$ and any $\alpha>0$,
we have $f(d)=f(\alpha\cdot d)$.
\end{namedtheorem}

\lipsum[4]

\end{document}

A more customizable version:

\documentclass{article}
\usepackage{amsmath,amsthm,microtype}

\usepackage{lipsum} % for context

\newtheoremstyle{personal}
  {\topsep}   % ABOVESPACE
  {\topsep}   % BELOWSPACE
  {\itshape}  % BODYFONT
  {0pt}       % INDENT (empty value is the same as 0pt)
  {\scshape}  % HEADFONT
  {.}         % HEADPUNCT
  {5pt plus 1pt minus 1pt} % HEADSPACE
  {\thmname{{\lsstyle#1}}\thmnote{ (#3)}} % CUSTOM-HEAD-SPEC
\theoremstyle{personal}

\newtheorem*{namedtheoreminner}{\namedtheoremname}
\newenvironment{namedtheorem}[1]
  {\par\addvspace{\bigskipamount}
   \dimen0=\parindent
   \centering\begin{minipage}{\dimexpr\textwidth-2\dimen0\relax}
   \parindent=\dimen0
   \newcommand\namedtheoremname{#1}%
   \begin{namedtheoreminner}}
  {\end{namedtheoreminner}\end{minipage}\par
   \addvspace{\bigskipamount}}

\begin{document}

\lipsum[1][1-5]

\begin{namedtheorem}{Scale-Invariance}
For any distance function $d$ and any $\alpha>0$,
we have $f(d)=f(\alpha\cdot d)$.
\end{namedtheorem}

\lipsum[4]

\end{document}