Neural Dissipation and the Pₙoncalc Boundary: The Dissipative Vector Δ as an Operational Criterion for Phenomenal Transition in EEG

Abstract Standard analysis of neural oscillatory power distinguishes amplitude (total energy) from Effective Power (Eff = Amp × Sγ, organised energy). We introduce the Dissipative Vector Δ = Amp × (1 − max (Sγ, 0) ), which captures energy expenditure that fails to produce a coherent spatial output — neural dissipation. We test whether Δ and Eff show a mirror pattern (Eff↓/Δ↑) at the same frequency band and cognitive event, across three EEG datasets: probabilistic reversal learning (ds004295, N=22), anagram insight (Oh et al. 2020, N=30), and meditation mind-wandering (ds001787, N=24). The mirror pattern is confirmed in the alpha band for both insight (dEff=−0. 640, d_Δ=+0. 626) and meditation mind-wandering (dEff=−0. 499, d_Δ=+0. 505), but not for reversal learning, where Eff and Δ rise together across all bands. We propose that the Eff↓/Δ↑ mirror is the operational EEG criterion for the RDRT halt boundary — the point at which organised computation saturates and Pₙoncalc (the non-calculable phenomenal residue) is generated. Reversal learning, which produces a global energetic surge without band-specific mirror, represents a qualitatively different type of phenomenal transition: an integrated amplitude modulation rather than a localised computational halt.