test: Java golden-value oracles for the five DCE math cores + P1-2/P1-3 fixes
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Add bit-for-bit (1e-12) golden-value oracle tests pinning the C++ pure-math and functional cores against the compiled upstream Java library (openjdk 17): - HyperIdealGoldenJava: Clausen/Л/ImLi2, ζ13/14/15/ζ, both tetrahedron-volume formulas (real de.varylab…Clausen / HyperIdealUtility). - EuclideanGoldenJava / SphericalGoldenJava: angle formulas + β relations + Л energy terms, plus FULL-MESH oracles driving the real EuclideanCyclicFunctional / SphericalFunctional on a shared tetrahedron — per-vertex gradient (Θ−Σα) and ΔE = E(x)−E(0) (C++ Gauss-Legendre path integral vs Java closed form). - SphericalGoldenJava.FullMeshEdgeDofGradient: edge-DOF gradient (vertex + edge components, α_opp⁺+α_opp⁻−θ_e) vs raw conformalEnergyAndGradient — locks Finding 3 at the solution level (audit items 4 & 5). - PeriodMatrix.NormalizeModulus_GoldenJava: τ-reduction fold convention vs the real DiscreteEllipticUtility.normalizeModulus (audit items 7 & 8). Subtlety documented: the spherical oracles call Java's raw conformalEnergyAndGradient, not evaluate() (which pre-runs a Brent gauge maximization that C++ factors into the Newton solver's spherical_gauge_shift). Also: - P1-2 (layout.hpp): Euclidean holonomy now uses a per-cut-edge rigid-motion fit g(z)=a·z+b, exposing residual_rotation = |arg(a)| as a diagnostic; non- regressive (flat case a=1 reduces to the old midpoint formula). - P1-3 (period_matrix.hpp): is_in_fundamental_domain fixed to the correct half-open SL(2,ℤ) domain (−½ ≤ Re < ½). Updated the now-exposed ComputePeriodMatrix_ReducedTau_InFD to assert the normalizeModulus domain (closed +½ edge) instead. Test counts (single source of truth = doc/api/tests.md): 272/272 pass, 0 skipped (26 non-CGAL + 246 CGAL). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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@@ -114,11 +114,18 @@ inline std::complex<double> reduce_to_fundamental_domain(std::complex<double> ta
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// is_in_fundamental_domain — check membership in F with tolerance tol.
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// ─────────────────────────────────────────────────────────────────────────────
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/// `true` iff `τ` lies inside the standard SL(2,ℤ) fundamental domain
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/// with tolerance `tol`.
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/// `F = { Im τ > 0, −½ ≤ Re τ < ½, |τ| ≥ 1 }` with tolerance `tol`.
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///
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/// This is the half-open domain produced by `reduce_to_fundamental_domain`
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/// (the right boundary `Re τ = +½ ≡ −½` is excluded via `T`). It is NOT the
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/// mirror-folded `0 ≤ Re τ ≤ ½` domain produced by `normalizeModulus` (used
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/// inside `compute_period_matrix`); a τ with `Re τ < 0` is a legitimate member
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/// of `F` here but would be folded to `Re ≥ 0` by `normalizeModulus`.
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inline bool is_in_fundamental_domain(std::complex<double> tau, double tol = 1e-9)
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{
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if (tau.imag() <= 0.0) return false;
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if (std::abs(tau.real()) > 0.5 + tol) return false;
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if (tau.real() < -0.5 - tol) return false; // left boundary closed
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if (tau.real() > 0.5 - tol) return false; // right boundary Re = +½ excluded (≡ −½)
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if (std::abs(tau) < 1.0 - tol) return false;
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return true;
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}
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