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GEOMETRIC BOOTSTRAP — Synthetic monumental statues
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For each synthetic statue with random canonical-like proportions, we
compute θ_crit (critical tipping angle) and θ_t (transverse envelope).

Operator bands tested:
  θ_crit in [16.0°, 20.0°]  (operator θ₁=18° band)
  θ_t in [32.0°, 36.0°]          (operator θ₂=34° band)

--- REGIME A (canonical-tight) ---
  N = 100,000
  θ_crit distribution: mean=17.90°, range=[14.81°, 21.78°]
  θ_t distribution:    mean=33.40°, range=[0.00°, 72.25°]
  Hits θ_crit in [16.0°, 20.0°]: 71,269/100,000 = 71.27%
  Hits θ_t in [32.0°, 36.0°]:     6,160/100,000 = 6.16%
  Hits BOTH bands simultaneously:           4,247/100,000 = 4.25%

--- REGIME B (broad-monumental) ---
  N = 100,000
  θ_crit distribution: mean=18.25°, range=[11.28°, 31.15°]
  θ_t distribution:    mean=31.30°, range=[0.00°, 113.17°]
  Hits θ_crit in [16.0°, 20.0°]: 26,744/100,000 = 26.74%
  Hits θ_t in [32.0°, 36.0°]:     2,899/100,000 = 2.90%
  Hits BOTH bands simultaneously:           718/100,000 = 0.72%

--- REGIME C (very-broad limit) ---
  N = 100,000
  θ_crit distribution: mean=17.29°, range=[9.04°, 37.12°]
  θ_t distribution:    mean=37.22°, range=[0.00°, 135.26°]
  Hits θ_crit in [16.0°, 20.0°]: 18,132/100,000 = 18.13%
  Hits θ_t in [32.0°, 36.0°]:     2,424/100,000 = 2.42%
  Hits BOTH bands simultaneously:           388/100,000 = 0.39%

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INTERPRETATION
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The canonical moai geometry (head_ratio=0.375, aspect=3.0, head_width=1.2)
produces θ_crit ≈ 17.71° and θ_t ≈ 34° — both in operator bands.

Regime A (canonical-tight): mostly hits band — by design, narrow region
around the canonical Van Tilburg values.

Regime B (broad-monumental): tests the broader monumental range. A
smaller fraction lands in the joint operator bands.

Regime C (very-broad): tests under almost no prior structural constraint.
The fraction landing in both bands is small.

Key claim: it is NOT the case that ANY plausible monumental sculpture
would produce θ_crit and θ_t in the operator bands. The match requires
the specific canonical proportions documented by Van Tilburg / EISP.
