# Independent reconstruction

The independent script uses a different stack from the Arb witness:

- regex extraction from the pinned FKS source text;
- AST extraction of the C-0050 source tuple;
- exact `Fraction` recomputation of every Table 4 requirement;
- SymPy expansion of the low-range, monotonicity, and tail identities;
- an 80-digit mpmath scan of the low-range required coefficient.

It recovered all 164 Table 4 rows and matched the C-0050 tuple exactly.
The parser separately identified the two PDF-text artifacts in which
\(10^6\) and \(10^7\) appear as `106` and `107`.

The exact active interval is \([2100,2200]\), with requirement

\[
\frac{
2709976113860085547103395243942841453423728245400
}{
61517068085059134496927148872832330483236342381
}.
\]

SymPy independently recovered

\[
1-s_A(t)(1+t+2t^2+6t^3+55t^4)
=
\frac{t^4}{1000}
\left(
53+111053t+161106t^2+429318t^3+2422915t^4
\right),
\]

the degree-20 monotonicity factor, and the degree-16 asymptotic
factor with constant term \(31053/2000\).

The dense mpmath scout placed the largest low-range coefficient
required merely to dominate \(\operatorname{li}(x)\) at

\[
\log x\approx9.23660178,
\qquad
A_{\rm low}\approx32.506385796,
\]

well below 44.053. This scan is not used as proof; it independently
checks the Arb low-range architecture and identifies its expected
worst region.

Command:

```sh
uv run --frozen python \
  scratch/adjacent-unconditional--axler-compact-pi-denominator-44-053/independent_check.py
```

Result: `PASS`.

