Period Ratios and Observation Audit

Wrong Period Square Breaks the Ratio

A wrong period square renders as an exact rejected ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The candidate ratio is computed exactly

The rejected candidate has 36 over 64.

T2a3=3664=916\frac{T^{2}}{a^{3}}=\frac{36}{64}=\tfrac{9}{16}
Wrong period squareThe ratio is still computed before rejection.lawConstant=1/2periodSquared=36radiusCubed=64ratio=9/16acceptedBit=0 bit

The accepted bit is zero because the ratio misses K

The source K is 1/2, but the candidate ratio is 9/16, so accepted bit is 0.

916≠12,acceptedBit=0\tfrac{9}{16}\ne\tfrac{1}{2},\quad acceptedBit=0
Checked rejectionA stale accepted bit cannot render.lawConstant=1/2periodSquared=36radiusCubed=64ratio=9/16acceptedBit=0 bit