Time Is Not the Distance: The Books' Definition of Time, Attacked as a Derivation and Closed as an Obstruction

*2026-11-03 — draft — not deposited* I defined time in my books, in one sentence. From *Pain Is Love*, Chapter 1 (extract E5 in the correlations record): This paper attacks that sentence as a derivation target inside the mechanics my frame owns (correlations record §4, target M3): define a separation from the pair-separation data the sever actually owns, and derive a monotone time t(separation) with t → 0 at zero separation, from the frame's own laws. The derivation fails, and this paper proves where and why, completely. **Step 1: "the separation" is not one owned number.** The record prints two pair-separation formalisations — the operator count k_f, a function of the state's self-twin population (paper #207, completed in paper #581's line), and the surplus count k_s, a function of the sign split alone (paper #238); infinitely many functions of the same profile data are computable, and these are the two the record has printed as separations — and the two candidate separations k_f/411 and k_s/411 disagree on 99.8% of grain-count states — 84,872 of the 85,078 count-triples (n₊, n₋, n₀) summing to 411, **uniformly counted**: the measure is counting measure over count-triples, declared here because the number depends on it (under multinomial microstate weighting the fraction would differ; the qualitative disagreement does not). No owned statement selects one. **Step 2: monotone functions are cheap and worthless alone.** For every scale a > 0, t(s) = a·s/(1−s) is monotone with t(0) = 0 on s < 1 (the family is singular at s = 1, a value both candidates attain; §4 prints the restriction); the family disagrees by arbitrary factors (×1000 exhibited), and no owned statement fixes the scale — owned objects offer several distinct candidate time constants, and nothing owned selects