Fluctuation Depth Scans

Squared Deviation Contribution Cross-Scan

Each fluctuation term is a weight times one checked squared deviation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Squared contribution row 1

Deviation -2 squares to 4. Weight 1 makes contribution 4.

w(x−μ)2=1⋅4=4w(x-\mu)^{2}=1\cdot4=4
Squared contribution row 1Each term is weight times the checked squared deviation.xwdsqterm01-2442200041244w=1, square=4, term=4

Squared contribution row 2

Deviation 0 squares to 0. Weight 2 makes contribution 0.

w(x−μ)2=2⋅0=0w(x-\mu)^{2}=2\cdot0=0
Squared contribution row 2Each term is weight times the checked squared deviation.xwdsqterm01-2442200041244w=2, square=0, term=0

Squared contribution row 3

Deviation 2 squares to 4. Weight 1 makes contribution 4.

w(x−μ)2=1⋅4=4w(x-\mu)^{2}=1\cdot4=4
Squared contribution row 3Each term is weight times the checked squared deviation.xwdsqterm01-2442200041244w=1, square=4, term=4

The middle state has weight but zero squared deviation

Weight alone is not a fluctuation contribution. The middle row has weight two, but its deviation is zero, so its contribution is zero.

xwsqterm014422004144\begin{array}{c|c|c|c}x&w&sq&term\\0&1&4&4\\2&2&0&0\\4&1&4&4\\\end{array}
Squared contribution cross-scanThe four-column table is the full numerator ledger.xwdsqterm01-2442200041244weighted squared terms are 4, 0, 4