fix: sympify Littlewood-Paley sqrt/bracket inputs

[Chessing234]

Problem

In src/estimates/littlewood_paley.py, sqrt(x) computes x ** Fraction(1, 2) directly. When x is a plain Python int/float (rather than an already-sympified Expr), this evaluates using Python's built-in numeric **, which returns an inexact float:

>>> from estimates.littlewood_paley import sqrt, bracket
>>> type(sqrt(2))
<class 'float'>
>>> sqrt(2)
1.4142135623730951

bracket(x) = sqrt(1 + abs(x) ** 2) inherits the same issue. This defeats the purpose of using sympy Expr objects for exact symbolic/order-of-magnitude reasoning elsewhere in the library (e.g. comparisons with Theta/asymp expect exact sympy expressions, not floats).

Fix

Wrap the input in sympy.S(...) before exponentiation/absolute value so the arithmetic stays in exact sympy form:

def sqrt(x: Expr) -> Expr:
    return S(x) ** Fraction(1, 2)

def bracket(x: Expr) -> Expr:
    return sqrt(1 + abs(S(x)) ** 2)

After the fix:

>>> type(sqrt(2))
<class 'sympy.core.power.Pow'>
>>> sqrt(2)
sqrt(2)
>>> bracket(3)
sqrt(10)

Verification

• Reproduced the bug on current main via uv run python -c "..." (shown above, returns float).
• Confirmed the fix resolves it on this branch (returns exact sympy Pow).
• uv run pytest tests/ -k littlewood -q passes (2 passed).
• Ran the full suite (uv run pytest tests/ -q): 1 pre-existing failure (test_linarith_failure_example, a z3 exception) reproduces identically on unmodified upstream/main, so it is unrelated to this change; all other 23 tests pass on both.