Restore the analytic validation with the corrected sheath sign, measured signed

README.md

@@ -69,20 +69,26 @@ tracks each substrate's own internal-gradient variance, not the compression.
 ## Is the physics right?
 
 Against an **exact** answer, not against another simulation. For an infinite coaxial hollow cylinder the
-field inside the lumen is **exactly zero** at every orientation, so any non-zero lumen field is pure
-discretisation error with no fitting freedom to hide it:
+answer is known in closed form, with no fitting freedom to hide an error in:
+
+* the field inside the lumen is **exactly zero** at every orientation;
+* inside the sheath at θ = 90°, `ΔB/B₀ = χ[−1/6 − ½(R_i²/r²)cos 2φ]`;
+* inside a *solid* cylinder the interior is uniform at `χ/6·(3cos²θ − 1)`.
+
+![analytic validation](figures/fig_analytic_validation.png)
 
 | | measured | exact |
 |---|---|---|
 | lumen field | **0.131%** of χ·B₀ | 0 |
-
-For a solid cylinder the interior field is uniform at `χ/6·(3cos²θ − 1)`, and the generator matches that
-within 10% at both 0° and 90° — a signed comparison, so it pins the absolute amplitude and sign.
-
-Both are permanent gates in the generator's test suite (`test_susceptibility_field_oracle.py`), not
-one-off checks. The lumen null is the sharp one: a hard binary myelin source rings into the lumen at ~2.6%
-of χ·B₀ through the non-decaying dipole kernel, which would silently inflate intra-axonal dephasing;
-partial-volume occupancy suppresses it to ~0.1%.
+| sheath amplitude | **0.9996×** analytic | 1 |
+| sheath structure, signed | **corr +0.9995, slope +0.999** | +1 |
+| solid-cylinder interior (θ=90°) | **−0.1649** χ·B₀ | −1/6 |
+
+All are permanent gates in the generator's test suite (`test_susceptibility_field_oracle.py`), not one-off
+checks, and the sheath comparison is **signed** — an inverted field fails it. The lumen null is the sharp
+one: a hard binary myelin source rings into the lumen at ~2.6% of χ·B₀ through the non-decaying dipole
+kernel, which would silently inflate intra-axonal dephasing; partial-volume occupancy suppresses it to
+~0.1%.
 
 ## Susceptibility dephasing vs B₀ orientation