# UTFANSWF v23 Row 19 executable scope

Row 19 was hardened on 2026-08-17 before the v23 manuscript was revised.
The public manuscript (`main.tex`) and PDF are intentionally not modified by this bundle pass.

## Why Row 19 changed

The previous executable mixed four claims with insufficiently related code:

1. FRG used an explicitly labeled two-coupling toy beta-function slice and converged near the Gaussian point, while the manuscript printed a non-Gaussian Einstein-Hilbert/Litim benchmark.
2. The so-called Jacobian check compared analytic and finite-difference derivatives of the toy FRG beta functions, not cosmological observables.
3. `gamma-1`, `beta-1`, and `cT/c-1` were inserted as literal zeros before the PPN/GW bounds were evaluated.
4. Positivity used a small toy coefficient check even though v23 now has the upstream ANSWF executable positivity gate.

The legacy Row 19 runner is preserved unchanged as `legacy_run_row19_toy_v22.py` (SHA-256 `763bc90126894b26b5cc87505c3b15d1645bfe220cc25b3d02442b2f60166480`).

## v23 executable Row 19

### FRG

`tools/row19/frg_eh_litim.py` implements the Einstein-Hilbert/Litim beta functions printed as Eqs. 124-125 of Frank Saueressig, arXiv:2302.14152, and solves those equations directly.  The direct printed-equation solution is approximately

- `g* = 0.875888555049176`
- `lambda* = 0.156604266763380`
- `theta = 1.86654707333725 +/- 2.35256720924354 i`

The numerical values printed later in the cited source differ from the direct solution of its printed equations.  The bundle records the discrepancy and does not infer its cause.

This is an Einstein-Hilbert benchmark.  It does not numerically close the manuscript's larger curvature-squared/scalar-portal FRG truncation.

### PPN/GW

The declared benchmark `alpha0=2.5e-3`, `beta0=0.05` is evaluated using the manuscript formulas for `gamma-1` and `beta-1`.  These are no longer hard-coded to zero.

The manuscript's declared cutoff-scale condition (`Lambda=1e9 GeV` versus stated `Lambda >= 1e7 GeV`) is checked as a scale benchmark.  The bundle does **not** claim that it has independently derived numerical values for:

- `alpha1`
- `cT/c - 1`
- `Mstar^2`
- `mT`
- `nu`
- spin-2 eikonal/Shapiro time delay.

Those remain open implementation boundaries.

### Positivity

Row 19 consumes the result of the upstream Row 0.2 ANSWF positivity gate.  The old toy `a1/a2` positivity helper remains in the archive but is not the active physical positivity proof.

### Cosmology derivative validation

`tools/row19/cosmology_jacobian_cpl.py` executes the explicit flat-w0waCDM derivative test printed in the manuscript:

- parameters `(Omega_m,h,w0,wa)=(0.315,0.674,-1,0)`
- redshifts `{0.1,0.3,0.6,1.0,1.5,2.0}`
- observables `{H,D_A,D_L}`
- complex-step epsilon `1e-30`
- central-difference step `1e-5`
- acceptance `max relative error <= 1e-3`.

The larger curvature-aware compressed vector `{R,l_A,D_M/r_d,D_H/r_d}` is **not** claimed complete by this executable and remains open.

## Row 19 meaning

A Row 19 PASS now means that the implemented/scoped executable core is internally reproduced without fake zeros or a toy-FRG substitution.  It does not mean every broader formula printed historically under Row 19 has already been turned into executable code.
