symmetry · not in domain-math.js · 11 records · all concepts
runs9 · +2 retired
119On the 19 cut-2 census patterns, does flipping one cell of the 15-cell wedge break boundary isotropy visibly — the left–right and top–bottom transfer operators acquiring different singular values — for every flip that removes the pattern's D4 symmetry, and does the size of the break order by the flipped cell's symmetry class?run
122On census generators run 119 did not build, does a single-cell flip change the block transfer operator T exactly when the cell lies on a simple path between two distinct cells of the left and right columns?run
127On the census generators other than generator 1, does the number of one-way pairs of the block transfer operator equal |U|·(511 − |U|), with U fixed by the right-column holes alone?run
130A host that keeps the dilations by 3 (H) may carry comb teeth only at the frequencies those dilations allow, the even teeth of the base-64 comb in ln(burst size).run
131On sixteen fresh 9 × 9 blocks, none in the census and half with a kept column-7 cell cut off from the left, does the number of one-way pairs of the block transfer operator equal |U′|·(511 − |U′|), with U′ from the corrected flood-fill rule?run
132On five census blocks no operator run has built (20, 35, 36, 39, 44), does the graph-only core rule say exactly which single-cell toggles give the same block operator?run
133On fresh draws of H at L = 2187, if the comb's even-tooth period P is fitted instead of fixed at 8, do the odd teeth vanish at the fitted period?run
134Does the forbidden k = 3 tooth on H come from the full-side source?run
138(T) On fresh full-side draws of H8 at L = 6561, does the 3/2 tooth (k = 3) survive every member of the declared set of backgrounds when both steps are modelled?run
126On the 63 census generators, does the number of one-way pairs of the block transfer operator equal |U|·(511 − |U|), with U fixed by the right-column holes alone?run
137(T) On fresh full-side draws of H8 at L = 6561, does the 3/2 tooth (k = 3) survive every member of the declared set of backgrounds?run
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