The Basin Depth–Sleep–Longevity Theorem: Sleep Requirement as a Readout of Attractor Landscape Position — A Unified Geometric Framework Spanning Cellular Biology to 500 Million Years of Evolutionary Evidence

Sleep duration varies by orders of magnitude across the animal kingdom, from zero in the horseshoe crab (Limulus polyphemus, lineage ~450 Mya) and functionally zero in the Greenland shark (Somniosus microcephalus, lifespan up to 400 years, the longest-lived vertebrate) to approximately eight hours of REM-rich sleep in humans. The prevailing explanation treats sleep as a universal biological necessity with conserved functions. This paper proposes and defends an alternative: sleep is a cost-discharge mechanism, not a fundamental necessity. Sleep requirement is proportional to the sum of three cost axes that accumulate during waking — oxidative/metabolic cost (Axis 2), attractor switching cost (Axis 1), and synaptic/computational cost (Axis 3) — and approaches zero when all three approach zero. This occurs when an organism occupies a deep, stable attractor basin (the Lock strategy). The Basin Depth–Sleep–Longevity Theorem is formally stated with five falsifiable predictions, all confirmed by the comparative and evolutionary record. The decisive experimental proof is provided by Astyanax mexicanus cavefish (North et al., 2024), in which sleep was lost convergently and independently in at least three cave populations from a surface-sleeping ancestor upon colonisation of a deep, stable, no-light niche. The theorem unifies sleep biology, longevity biology, and evolutionary theory within the Waddington attractor landscape framework (S + N + G → R), and identifies basin depth, sleep requirement, and lifespan as co-expressions of the same underlying thermodynamic quantity: position-dependent cost accumulation rate in a biological landscape. A novel clinical prediction is generated by convergence with the Identity Axis Theorem (IAT): IAT drug efficacy will be inversely correlated with epigenetic degradation at identity anchor gene loci, testable in existing trial datasets with matched epigenomic data.