The Derivation Chain Closure: Sleep, Epigenetics, Cancer, and the Molecular Substrate of the Attractor Landscape

This document records four geometric findings that emerged from exploratory research conducted after deposition of the Dimensional Invariant v3.0, each establishing priority for a new formal claim within the attractor geometry framework (S + N + G → R). Finding 1: G = epigenetic state. The attractor landscape G is physically implemented as the organism's epigenetic state: histone modification patterns, DNA methylation, and chromatin accessibility. Sleep is the daily maintenance process that restores G to its functional state. Chronic sleep deprivation degrades G irreversibly through progressive epigenetic damage and neuronal loss. Finding 2: Derivation chain geometric convergence point. The sleep geometry arrived at BMAL1 as the molecular N field governing cellular repair basin entry. BMAL1 loss collapses the N field, makes the repair basin epigenetically inaccessible, and stabilises the cancer attractor. This is geometrically identical to the Identity Axis Theorem (doi:10.5281/zenodo.18898788, 2026-03-07), which was derived entirely independently from cancer molecular biology. The two derivation paths — one from evolutionary biology and deep-time survival, one from cancer transcriptomics — arrived at the same geometric structure with zero incompatibility. This is a demonstration of internal consistency across the framework, not a new cancer finding. The formal compatibility record is deposited separately. Finding 3: Social information as primary N field. Social cues are confirmed co-primary zeitgebers for the circadian clock, entraining it independently of light. The social N field specifies sleep basin occupation at group level. Dominant baboons (Current Biology, 2025) sleep worse than subordinates because their social landscape position imposes continuous navigational cost that does not cease at night. Artificial light at night (ALAN) is a global primary N field disruption affecting the sleep basin entry of thousands of species simultaneously. Finding 4: T8 topology. Hibernation is geometrically distinct from T5 (external suppression with rebound). In T8, both navigational activity and sleep architecture are suspended by temperature constraints, but homeostatic pressure continues to build in the complete absence of navigational activity. Post-emergence rebound duration is predicted by hibernation duration alone, not by pre-hibernation navigational cost. Finding 5: Somatic G maintenance. Sleep maintains S (structural substrate) via growth hormone-driven stem cell renewal and tissue repair simultaneously with G maintenance. Sleep deprivation degrades both G and S in the same window. Five predictions stated (P-CLOSURE-1 through P-CLOSURE-5) before any confirming dataset was examined.