Flake band gap

• 2026-08-28 [Verified] The base-2 flake's Laplacian has an interior band gap whose upper edge is exactly 4: on the bang dim 3, code 23 flake (4^level nodes, 4^level - 1 edges, connected), exact rational elimination of Lap - 4I has a single zero pivot, 3 * 4^(level-1) eigenvalues lie below 2 and none in [2, 4), the lower edge climbs 1.000000, 1.827520, 1.975680, 1.996862, 1.999605, 1.999950 at level = 1..6, and the top eigenvalue is 3 + sqrt(5) = 5.2360679775 at level = 2 climbing to 5.7090316570 at level = 6. Witness: lab/py/flake-band-gap.
• 2026-08-28 [Conjecture] The lower edge closes at a fitted c * 8^(-level) with c near 12.9868 over ten levels, (2 - lo) * 8^level reaching 12.984807 and 12.986289 at level = 7, 8, a fit with no mechanism. Witness: lab/py/flake-band-gap.