The Information Profit Principle

A reflexive self-maintaining system must generate information structure faster than it dissipates it. Within the MFRR framework, this requirement yields a sharp dimensionless threshold, the Information Profit Threshold (IPT): where φ = (1+ 5)/2, giving IPT ≈ 1.1309. A system with generative-to-drain ratio ρ = G/D > IPT can sustain coherent self-referential processing; one with ρ ≤ IPT cannot. All three structural premises and the IPT theorem are machine-certified in Lean~4 ( -lean, zero sorry; ). Three computational validations confirm the threshold across qualitatively distinct parameter regimes; eight real-world tests across seven domains support it as a genuine viability threshold. Key empirical results: published mean GPP/RECO for tropical moist forest is 1.130 (n=24 sites; Luyssaert et al.\ 2007), matching IPT to three decimal places; above-IPT populations grow at +1.46\%/yr versus near-zero in the buffer zone (p < 10^-4); self-organized criticality systems fall in the buffer zone, confirming the threshold is not a critical-point artifact; a three-regime organizational failure cascade in U.S.\ equity data echoes the threshold (ΔBIC = -92.19; AUC = 0.781; ^-). Deriving the PSC overhead functional analytically from first principles remains open.