The Present on the Spiral

This paper takes a poetic intuition — that thought never holds the present, and that ending observation might be a "leap" into it — and makes it rigorous. Two clocks are separated: lookback (the now as the Δθ=0 boundary, a limit point the observation domain never contains, unmeasurable by any finite-power recorder) and the arrow (entropy rising unwatched on the past hypothesis; the participatory reading is refused). Observation draws a partition — decoherence raises the observed subsystem's von Neumann entropy while the global state stays unitary — and pays a Landauer cost in the observer's own substrate. With positive Λ the free-energy budget is finite (Dyson; Krauss–Starkman), so as S → S_dS ≈ 10^122 k_B (Gibbons–Hawking) the arrow dS/dt → 0 and the last bit costs the last gradient. The "leap into the present" is shown to be a degenerate limit: ending observation does not send Δθ→0 but renders Δθ undefined — nothing arrives, because the arrival and the arriver both require the gradient that has ended. One conceptual clarification, no new number. What is left open (constancy of Λ, finality of the ceiling, rigor of "observer") is stated plainly. The parent cosmology's falsification is reprinted.