refactor(constants): centralize magic constants from functionals (N4/N6 audit)

- Add LOG_EDGE_LENGTH_FLOOR (-30.0) for degenerate edge handling
- Add HYPER_IDEAL_SCALE_FLOOR (0.01) for negative-scale clamping
- Add ASIN_DOMAIN_GUARD (1.0 - 1e-15) for asin argument bounding
- Each constant is documented with rationale and units
- Update 4 usage sites: euclidean_functional, hyper_ideal_functional,
  spherical_functional, spherical_geometry
- Add constants.hpp include to hyper_ideal_functional and spherical_functional

282/282 tests pass. Addresses N4 (unnamed magic constants) and N6 (centralize
tolerances) from numerical-stability audit.

Co-Authored-By: Claude Haiku 4.5 <noreply@anthropic.com>

code/include/constants.hpp

@@ -17,4 +17,21 @@ constexpr double PI     = 3.14159265358979323846264338328;
 /// 2π (full turn).
 constexpr double TWO_PI = 2.0 * PI;
 
+// ── Numerical thresholds and bounds (N4/N6 audit) ──────────────────────────
+
+/// Edge length floor for log-scale functionals (euclidean_functional, spherical_functional).
+/// exp(-30.0) ≈ 3e-7: edges below this length are treated as degenerate/zero.
+/// Rationale: avoids log(tiny) overflow and enforces a minimum edge scale.
+constexpr double LOG_EDGE_LENGTH_FLOOR = -30.0;
+
+/// Hyper-ideal scale factor lower bound (hyper_ideal_functional:179-181).
+/// If b (scale) becomes negative (infeasible), clamp to 0.01 to keep geometry valid.
+/// Rationale: ensures b > 0 maintains the Lorentzian model's causal structure.
+constexpr double HYPER_IDEAL_SCALE_FLOOR = 0.01;
+
+/// Domain guard for asin in spherical_l (spherical_geometry:34).
+/// Clamps exp(λ/2) to slightly below 1.0 so asin stays in [−π/2, π/2].
+/// Rationale: asin(x) is undefined for |x| > 1; this prevents IEEE Inf/NaN.
+constexpr double ASIN_DOMAIN_GUARD = 1.0 - 1e-15;
+
 } // namespace conformallab