Sponge Window

• Falsifies the tube of the Menger sponge's plus past 1/6 and the corner volume Deep at every radius, as written in dimensions, subsection "The tube past 1/6, and Deep in closed form", against the crate's exact distance mrlyrs::math::three::sponge::distance.
• Thresholds: delta_m = sqrt(1/36 + s_m^2/4), s_m = 3^(-m-1), for m = 1..5, with sqrt(10)/18 and sqrt(2)/6.
• Levels: at 15 radii, eleven spread over the sub-intervals of (1/6, sqrt(2)/6] down to (delta_5, delta_4), then 1/6, 0.148, 1/8 and 1/12, it enumerates the crossing holes of the line across = min(radius, 1/6) to level 12, integrates each level's pair integral by its own adaptive Simpson rule in a, prints the sum against the crate's deep, which sums the same integrals by Gauss-Legendre in the angle, and the largest gap over all radii, and rasters the crate's distance on every crossing row to level 4 inside the box the lemma confines it to, 40 x 40 across and 800 along, printing the midpoint volume and the bracket of cells beyond the radius plus or minus the half diagonal; it asserts every bracket contains its level integral.
• Outside the boxes: on a 72^3 raster of one arm it prints the largest distance at a cell centre outside every confinement box, asserted at most the radius, for every radius from 1/6 on.
• Centre: on [1/6, sqrt(2)/6] it rasters the centre cube near its middle, 120^3 cells on [1/3 + c, 1/2]^3 with c = sqrt(radius^2 - 1/36), times 8, against 7/27 - T - 24 Deep, asserting the bracket.
• Period: p(eps) = eps^(D-3) (20/27 + sum_(l = 0..40) (27/20)^l T(eps/3^l)) with T the crate's exact, on 3000 and 6000 steps of u = ln(1/eps) over one period from sqrt(2)/6; golden-section search for the maximum and the minimum, the swing, the logarithmic mean, the range on (1/6, sqrt(2)/6] and whether p falls there at every step, and p at five phases beside the crate's upper-edge profile.

RUN

• CARGO_BUILD_JOBS=4 cargo run --release -p sponge-window
• About 8 seconds after the build; prints only, writes nothing.

WITNESSES

• dimensions.md, subsection "The tube past 1/6, and Deep in closed form": the thresholds delta_2 = 0.167692, delta_3 = 0.166781, delta_4 = 0.166679; the level integrals against the crate's deep, gap at most 3.2e-21 at all fifteen radii; the row rasters within 6.12e-3 relative of their level integrals on [1/6, sqrt(2)/6], down to 3.988024e-13 at level 4, every bracket containing them; the centre rasters within 2.31e-3 of the closed uncovered part; the largest distance outside the boxes, below the radius; Deep(1/6) = 1.894504e-6, Deep(1/8) = 4.827978e-8, Deep(1/12) = 0, T(1/6) = 0.2570649366.
• The same subsection: the maximum p = 2.139869 at eps = 0.148577, the minimum 2.122663 at 0.081380, the swing 0.8106 %, the logarithmic mean 2.130510, p(1/6) = 2.136706, p(1/8) = 2.135739, and p falling across (1/6, sqrt(2)/6] to p(sqrt(2)/6) = 2.122798.