Toshisada Utsunomiya
This paper proposes a mathematical formalisation of Śūnyatā and enlightenment underconstraints explicitly stated in the Heart Sūtra (“neither arising nor ceasing”, “neitherincreasing nor decreasing”). In the framework used here, Śūnyatā is characterised asrelational invariance: a steady condition in which apparent change cancels through structureddependence rather than through absence. Enlightenment is characterised as a transition incognition in which prediction error collapses and attention stabilises through phase-locking tothat invariance. The argument proceeds by (i) separating the dissipative “vanity” (hevel) ofEcclesiastes from Mahāyāna Śūnyatā and restating this contrast in physical terms (entropydrift versus steady-state stability); (ii) analysing Arvo Pärt’s Spiegel im Spiegel (Tintinnabulistyle) as a linear construction with mirror symmetry and zero net displacement; and (iii)introducing an inter-agent indicator, the existence phase φ(t), whose stabilisation provides aprecise model for the “emptiness” at stake and for the stilling of cognition associated withenlightenment. “Proof” is used strictly as proof within a defined framework: once terms areformalised under stated constraints, the equivalences claimed are demonstrated by themodel’s internal consistency and by analysable features of the work.