neoryae-aegis / VECTOR_REALIZATION_VERIFICATION.json
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{
"status": "PASS",
"scope": "Explicit D4 square construction, exact finite formulas evaluated in float64; sampling diagnostics are not proofs of the limiting theorem.",
"mathematical_facts": [
"Each bin has eight D4 image sectors; selecting determinant*bit>0 chooses exactly four, so Hausdorff length is exactly 2.",
"Normal-axis reflections at multiples of pi/4 reverse determinant and preserve the bin; adding all corners and edge midpoints gives exact four-direction coverage.",
"The three nontrivial costs are nonnegative because |h|<=1/(24*sqrt(3)) on the square boundary and r^2<=1/2.",
"Independent fair bits give cost mean half the full boundary cost and variance equal to the sum of squared linear coefficients."
],
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"sobol_power": 19,
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},
"sampling_limitations": "One fixed scrambled Sobol sample in a line rectangle is rejected to the square cylinder. No IID error bars, continuum opacity inference, or monotone convergence claim is made.",
"bit_selection": "Each displayed realization is the best of 32 reproducible independent candidate bit vectors by the recorded polynomial-cost score. Unconditioned variances describe the independent-bit model before this search.",
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