Clarify local log-matrix scope and independent pressure admissibility

experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md

@@ -108,6 +108,14 @@ log representation itself. The current barotropic Bernoulli equation is a
 separate modeling choice and does not automatically generalize to varying
 entropy or composition.
 
+In the current formulation, enthalpy is also an independent trial field. The
+prepared pressure operator rejects nonfinite or negative enthalpy at its own
+integration points (`libmeanfield/impl/operators/prepared_pressure_force.cpp`,
+lines 788–800). Pointwise-positive density alone therefore does not make a
+Newton candidate admissible. Any coupled log-density experiment must still test
+the enthalpy directions and pressure-preparation obstruction; the frozen
+density controls below establish no improvement in that separate guard.
+
 ### A vanishing reference factor
 
 Let
@@ -242,8 +250,8 @@ but can increase scale disparities across cells and coupled blocks.
 
 The small weighted matrices for the exact reference profiles have condition
 numbers approximately `7.87298`, `16.8523`, and `94.5609` for n=1,1.5,3. These
-are three-dimensional local polynomial-space measurements, not estimates of the
-stellar Jacobian's condition number. For the fitted exponential controls the
+are measurements of 3-by-3 matrices for one-dimensional quadratic trial/test
+spaces, not estimates of the stellar Jacobian's condition number. For the fitted exponential controls the
 corresponding numbers are `6.65377`, `13.7153`, and `74.9786`.
 
 The first-order identity `delta rho/rho=delta u` makes a log step a relative