% PMAT-124 — Runtime witness for the notation contract.
%
% This fixture exists to provide a Runtime-stratum vote for:
%   C-NOTATION-LATEX-MATH-TO-EQUATION
%
% It's a minimal LaTeX document exercising the three display-math
% forms whose equivalence is the load-bearing claim of the contract:
% \[ ... \], \begin{equation} ... \end{equation}, and
% \begin{align} ... \end{align}. The Lean refinement theorem from
% PMAT-057 (`display_math_eq_equation_env_eq_align_env`) and its
% Kani-harness Rust mirror from PMAT-059 prove these three forms
% lower to the same `EquationsBlock` entry on the same formula
% input; this fixture is the concrete observed-evidence
% counterpart.
%
% latex-contract-frontend's `parse_to_equations` body is
% scaffold-stage at v0.1.0 (XPILE-LATEX-PARSER-001 future work);
% the fixture is in place ahead of that wiring so the contract
% can move from 3-stratum QUORUM (Sem+Sym+Ext) to full 4-stratum
% coverage immediately, matching the four-stratum tier other
% contracts in the substrate already occupy.
%
% A dedicated round-trip test that parses this fixture three ways
% (via the \[, equation, and align forms) and asserts they
% produce equal `EquationsBlock` entries is
% XPILE-NOTATION-RUNTIME-001 future work, deferred behind the
% real latex-contract-frontend parser.

\documentclass{article}
\begin{document}

% Form 1: \[ ... \] display-math
The Pythagorean identity:
\[ a^2 + b^2 = c^2 \]

% Form 2: equation environment
The same identity in an equation environment:
\begin{equation}
  a^2 + b^2 = c^2
\end{equation}

% Form 3: align environment (single equation)
And once more in an align environment:
\begin{align}
  a^2 + b^2 = c^2
\end{align}

\end{document}
