menger-slice-sources.md

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Menger slice sources

  • 2026-08-28 [Verified] Cook's 2011 slice code is a point-sampled raster, not an array-free predicate: the listing allocates a side x side integer array, fills it by sampling the digit predicate and renders it, so the exact-census method is this tree's and not Cook's; its prose puts the normal through (1, 1, 1) while the listing sets (1, 1, 0.5). Witness: REFS.md.
  • 2026-08-28 [Verified] Hart 2012 is an exact citation for the diagonal Menger slice: the Simons Foundation page carries his byline, the title "Mathematical Impressions: The Surprising Menger Sponge Slice" and a photograph credit. Witness: REFS.md.
  • 2026-08-28 [Verified] "The Marstrand value is the dimension minus one" is the wrong attribution for a plane cutting a solid in R^3: Marstrand 1954 concerns plane sets and lines in R^2, and the hyperplane generalisation is Mattila 1975; both are almost-everywhere statements, so one maximally arithmetic plane landing above or below that value contradicts neither. Witness: REFS.md.
  • 2026-08-28 [Verified] A299916's Menger reading is not its definition: the entry's name is a(n) = A299914(2n+1), offset 0, signature (9, -12), terms 1, 6, 42, 306, 2250, 16578, its reference is number theory with no sponge in it, and the hexagram-hole geometry lives in one comment with one uploaded picture, which Wikipedia sources onward beside a newspaper article; it must be cited as a comment, never as the sequence's definition. Witness: A299916.
  • 2026-08-28 [Verified] Abel 2012 claims no proof of the base-3 slice dimension, only a computation, naming mass distributions and similarity graphs as routes to one, so every generalised dimension inherits that status. Witness: REFS.md.