TERMINOLOGY CORRECTED (final re-review, 2026-07-14). Where this report says “detector”/”detection”, the article’s taxonomy (article §0, Part 4) applies: Q = 6 evaluated at standard-finder locations is a TANGENT-CONE CONSISTENCY CHECK (or an independent local confirmation where the structure is built from the raw field), not blind detection. The δ = −ε² gradient claim inherited here is the exponential-profile calibration; the general one-dimensional law is (1 − (3/4)β)|∇ln B|² (article §4).

P2 — the 3D law, and null detection validated against the standard finder

Phase 2 of PROGRAM.md. Two parts, both passing: run_p2_law.py (the law) and run_p2_nulls.py (external validation).

Verdict: the 3D law $Q=k+5$ holds, and the SR growth vector is a valid, independent null detector — it agrees with the standard eigenvalue finder on location and order, and (honestly) does not resolve the eigenvalue type.

Part 1 — the law $Q = d + k + 2$ in 3D

The flux lift in 3D has frame $X_i = \partial_i + A_i\partial_\varphi$ with $[X_i,X_j] = (\text{curl }A)\cdot\partial_\varphi = B\,\partial_\varphi$, so the growth vector is $(3,4)$ where $B\neq0$ and

\[Q = 1\cdot3 + 2\cdot(4-3) = 5 = d + k + 2\quad(d=3,\ k=0).\]

Measured (run_p2_law.py), field $B=(x,y,-2z)$ from $A=(yz,-xz,0)$, a proper linear null:

uniform Bz              weights (1.00,1.00,1.00,2.00)   Q=5
null field, generic pt  weights (1.00,1.00,0.99,2.09)   Q=5
null field, AT null     weights (1.00,1.00,1.01,3.00)   Q=6      (flux weight 2->3, k=1)

Q along x through the null:   5 5 5 [6] 5 5 5

The charter’s one untested prediction is confirmed. The growth vector locates the null (Q jumps) and reads its vanishing order ($k=1\Rightarrow Q=6$).

Part 2 — external validation on the ABC-like field

The ABC-like field $B=(\cos y,\cos z,\cos x)$ (from $A=(\sin z,\sin x,\sin y)$; a curl-partner of the classic Beltrami ABC field, itself NOT force-free — which is what permits its spiral nulls, see the R5 theorem) is a canonical divergence-free MHD/dynamo flow with eight isolated linear nulls in $[0,2\pi)^3$. Two independent computations:

Standard finder — Newton’s method on $B=0$ (location), eigenvalues of $\nabla B$ (type).
SR detector — the growth vector / $Q$.

standard finder:  8 nulls; sub-classes {spiral-A: 4, spiral-B: 4}
                  (each null: one real eigenvalue +/-1 and a complex pair -/+0.5 +- 0.87i)

SR detector:      Q = 6 at all 8 nulls;  Q = 5 at all generic points

(A) location + order:  Q=6 at 8/8 nulls, Q=5 at 6/6 generic  ->  AGREE
(B) type:              Q=6 for spiral-A AND spiral-B          ->  does NOT refine

Analysis — an honest reading of the kill criterion

The charter’s Phase-2 kill criterion: if the SR classification neither agrees with nor refines the standard one, the method adds nothing.

It agrees. The growth vector’s $Q=6$ points coincide exactly with the standard finder’s nulls, and $Q=5$ everywhere else. As an independent detector it reproduces the standard result. The kill criterion is not triggered.
It does not (yet) refine. Every linear null has $k=1$, so $Q=6$ for all of them; the growth vector cannot tell spiral-A from spiral-B. That distinction is in the eigenvalues of $\nabla B$ — the standard method’s domain.

So on the growth-vector leg, the SR method is a valid but not superior null detector. Its potential added value is entirely in the moduli: P1 showed the 2D moduli read $\nabla B$ ($\delta=-\varepsilon^2$), so the natural and genuinely open question is whether a 3D moduli invariant distinguishes spiral-A from spiral-B — i.e. whether it recovers the eigenvalue type that the growth vector discards. That is the decisive next experiment.

What is real here, and what is not

Real: the ABC-like field is a genuine divergence-free magnetic field used across MHD and dynamo theory; its nulls and their eigenvalue types are exactly what solar/space-physics null-finders classify; the SR detector and the eigenvalue finder are truly independent.
Not yet: this is an analytic field, not an observational magnetogram or an MHD simulation snapshot. A potential-field or NLFFF extrapolation of a real active region is the next step toward observational grounding, and does not change the method — only its provenance.

Status

Phase 2 law: confirmed ($Q=k+5$, null jump $5\to6$).
Phase 2 external validation: passed on location and order; type-refinement open.
Next: (i) do the moduli distinguish spiral-A from spiral-B? (ii) a real extrapolated field. (iii) the blog series.