A Mind Cannot Be Smeared Across Time

arXiv:2601.11620v2 Announce Type: replace Abstract: Whether machines can be conscious depends not only on what they compute, but \emph{when} they compute it. Most deployed artificial systems realise their functions via sequential or time-multiplexed updates, yet a moment of conscious experience feels unified and simultaneous. I prove that this difference matters. I augment Stack Theory with algebraic laws relating within time-window constraint satisfaction to conjunction. I introduce a temporal semantics over windowed trajectories $\tau_{\Delta}$ and prove that existential temporal realisation $\Diamond_{\Delta}$ does not preserve conjunction. A system can realise all the ingredients of experience across time without ever instantiating the experienced conjunction itself. I then distinguish two postulates, Chord and Arpeggio. Chord is the position that conscious unity requires \textit{objective co-instantiation} of the grounded conjunction within the window, like a musical chord. Arpeggio only needs the ingredients to \textit{occur} within window, like a melody. I formalise concurrency-capacity to measure what is needed to satisfy co-instantiation. Finally, I review neurophysiological evidence suggesting that consciousness depends on phase synchrony and effective connectivity, and that loss of consciousness is associated with its breakdown. Under Chord, software consciousness on strictly sequential substrates is impossible for contents whose grounding requires two or more simultaneous contributors. The hardware matters.