Wire critical symbolic anchors into SageMath CI (C1/C2/M2 + Bach on non-Einstein metric) - #4
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…stein metric) Wire the audit's critical symbolic fixes into the already-running SageMath CI (Track A runs tests/test_pe/). New discriminating anchors, values independently re-derived in sympy: - round S^3 (n != 4, where C1/C2 no longer coincide with correct at n=4): v_2 = -3/4 (C2), Fefferman-Graham g_4 = (1/16) g_0 (C1), Q_4 = 15/8. - non-Einstein S^2(1) x S^2(2): Schouten P[0,0]=7/24, P[2,2]=-1/3, J=5/12; conformal Laplacian P_2(1) = -5/12 isolating the curvature term (M2; the old bare-Laplacian returned 0); and Bach != 0 (Einstein/Ricci-flat metrics have Bach=0 and would mask Bach-coefficient bugs -- here Cotton=0 but the algebraic P^cd W part is nonzero).
The conformal Laplacian P_2, Paneitz P_4, and Q_4 formed their rational coefficients via Python division on cs.dimension (a Python int), e.g. (n-2)/(4(n-1)) and n/2, contaminating the symbolic result with floats. This was masked wherever the exact value is binary-representable (6, 15/8) but surfaced as P_2(1) = -0.41666... instead of -5/12 on S^2(1)xS^2(2). Reorder so a Sage object is divided by the integer denominator, keeping results exact (matching schouten.py, which derives n from g.domain().dim()).
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Adds discriminating SageMath regression anchors so the audit's critical fixes are re-proven on every push (Track A already runs
tests/test_pe/), not just trusted. Values independently re-derived in sympy.v_2 = -3/4(C2), FGg_4 = (1/16) g_0(C1),Q_4 = 15/8.P[0,0]=7/24,P[2,2]=-1/3,J=5/12; conformal LaplacianP_2(1) = -5/12isolating the curvature term (M2 — bare Laplacian returned 0);Bach != 0(Einstein/Ricci-flat metrics have Bach=0 and mask Bach-coeff bugs; here Cotton=0 but the algebraicP^cd Wpart is nonzero, Bach=diag(5/32,..,-5/8,..), trace-free).