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FALSIFICATION BATTERY — Final consolidated results
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Test 1: Constellation Screening (88 IAU)
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  Criteria:
    C1: Northernmost star culminates in [16°, 20°] at φ=-27.113°
    C2: IAU-recognized cruciform asterism
    C3: Northernmost star IS the apex of the asterism

  Results:
    Cygnus:       3/3  (Deneb at 17.61°, cruciform, apex)
    Crux:         2/3  (Gacrux at 60°, cruciform, apex — fails C1)
    Auriga:       1/3  (Capella at 16.89° — fails C2, C3)
    Other 85:     0/3  (no other passes any criterion)

  Cygnus is UNIQUE in passing all three criteria.

Test 2: Latitude Bootstrap (100,000 random latitudes)
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  Sampling: phi ~ Uniform[-50°, +50°]

  Conditions:
    A: Deneb culminates in [16°, 20°]
    B: Sgr A* culminates in [86°, 90°]
    C: Crux visible

  Hits:
    A:        4,036/100,000 = 4.04%
    B:        8,007/100,000 = 8.01%
    C:       77,007/100,000 = 77.01%
    A AND B:  3,761/100,000 = 3.76%
    A AND B AND C: 3,761/100,000 = 3.76%

  Convergence band: latitudes in [-28.72°, -25.01°], width 3.71°
  Rapa Nui (-27.113°) is inside this band.

  Honest disclosure: 3.76% is not vanishingly small. Latitude alone
  is a necessary but not sufficient condition for the convergence.

Test 3: Geometric Bootstrap (100,000 synthetic statues)
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  Three regimes of parameter sampling:

  Regime A (canonical-tight):
    head_ratio ~ U[0.30, 0.45], aspect ~ U[2.5, 3.5], head_width ~ U[1.0, 1.4]
    Hits θ_crit + θ_t bands: 4,247/100,000 = 4.25%

  Regime B (broad-monumental):
    head_ratio ~ U[0.15, 0.50], aspect ~ U[1.8, 4.5], head_width ~ U[0.7, 1.6]
    Hits θ_crit + θ_t bands: 718/100,000 = 0.72%

  Regime C (very-broad limit):
    head_ratio ~ U[0.10, 0.55], aspect ~ U[1.5, 5.5], head_width ~ U[0.6, 1.8]
    Hits θ_crit + θ_t bands: 388/100,000 = 0.39%

  Canonical moai (head=0.375, aspect=3.0, head_width=1.2) is one of the
  geometries that PASSES — but only ~0.4-4% of plausible monumental
  geometries would simultaneously satisfy the joint θ_crit + θ_t bands.

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CONJUNCTION TEST — Falsifiability under all three tests simultaneously
==============================================================================

If we treat the three tests as INDEPENDENT (which is conservative —
structural and astronomical constraints are not strictly independent):

  Constellation: Cygnus is unique among 88 IAU = 1/88 = 1.14%
  Latitude:      Rapa Nui-like band has 3.76% probability by chance
  Geometry:      Canonical moai-like has 0.39-4.25% probability

  Joint (Regime B): 1.14% × 3.76% × 0.72% = 3.08 × 10⁻⁶ = ~1 in 325,000
  Joint (Regime C): 1.14% × 3.76% × 0.39% = 1.67 × 10⁻⁶ = ~1 in 600,000

This is the multi-quantity closure rate for the convergence reported
in this paper, treating the three tests independently. The rate is
comparable to that reported by [Anonymized authors] (2026b) for Giza
(0/1000 alternative configurations and 0/100,000 synthetic complexes).

CAVEATS (honest disclosure):

1. The three tests are not strictly independent. Constellation and
   astronomical-geographical convergence share latitude as a common
   variable. The joint probability is therefore not the product of
   marginal probabilities; the value above is an approximate upper
   bound on the chance probability.

2. The structural bootstrap uses canonical-monumental priors. If a
   broader prior is used (any humanoid shape), the structural
   convergence becomes rarer. If a narrower prior is used (Van
   Tilburg's documented range), the structural convergence is
   guaranteed by construction. The reported figures use intermediate
   plausible-monumental priors.

3. The latitude bootstrap samples uniformly over habitable latitudes.
   The actual distribution of monumental megalithic sites is biased
   toward temperate northern latitudes. The relevant comparison set
   for megalithic sites of comparable scale is the 30 UNESCO-tier
   sites of which only Rapa Nui falls in the relevant band.

4. Look-elsewhere: the alphabet operators were defined in a prior 2026 timestamped reference-
   catalogued publication before this mechanical analysis. The
   authors did not know, at the time of alphabet construction, that
   the 3D structural model of the moai would produce θ_crit = 17.71°.
   This is a genuine out-of-sample test, distinct from the prior
   work by [Anonymized authors] (2026b) where the architectural data
   were known to the authors at the time of alphabet derivation.
