The Dilation Depth from the Rupture Rule

The Dilation Depth from the Rupture Rule is the depth L that the Rupture Rule reads off the universe and then into the substrate: L = 202 binary doublings separate observation from the substrate, and 2^L · f^L = ①⥂⧗⌂ / ℨ. The continuum bounds give a tile of order one, so they contribute no depth. The depth comes from the universe itself: by the Rupture Rule a universe spawns when its own pulse count reaches 2^L, so L = log₂(t↯ / ①⥂⧗⌂), which is 202 for ours by every marker (2²⁰² · ①⥂⧗⌂ = 11.0 Gyr; dark-energy–matter equality at 10.2 Gyr gives 201.9; the age today gives 202.33). An earlier draft fixed the depth by a domain nesting index p = 203 chosen by a minimality principle, under the name Spectral Domain Nesting; that index was the same number restated and was withdrawn on 2026-10-11. The book keeps the rationale for binary powers: the Prime Pulse has two phases, 0→1 and 1→0, null-well recursion preserves phase parity, and admissible tilings form a 2-adic spectrum that yields powers of two. The total dilation the depth implies is the Universal Scaling Factor. Formally, 2^L · f^L = ①⥂⧗⌂ / ℨ with L = log₂(t↯ / ①⥂⧗⌂), where L is the temporal dilation depth [∅], f ≈ 1.018 the heritage per level [∅], ①⥂⧗⌂ the Local Pulse Tempo (Planck time) [𝕋], ℨ the Zinf full cycle [ℨ] and t↯ the universe's age at rupture [𝕋]: [∅] = log₂([𝕋]/[𝕋]) = [∅]. It connects to Rupture Rule, Solving for L from the Rupture Rule, Two-Sided Growth, The Universal Scaling Factor, Minimum Viable Universe and Prime Pulse.