A geometric derivation of the necessary and sufficient conditions for complex life in carbon chemistry, arriving at the Last Eukaryotic Common Ancestor (LECA) attractor as the universal base state of all complex life. Derived from three absolute structural requirements for multicellular organisation: nuclear compartmentalisation, mitochondrial energy density, and eukaryotic cytoskeletal organisation. These three requirements admit exactly one stable configuration in carbon chemistry — the LECA attractor — making it the necessary base state of any complex life anywhere in the universe. Derives the LECA Attractor Habitability Standard as a replacement for the Goldilocks habitable zone. Applies this standard to ancient Mars and confirms 5 of 6 conditions are satisfied by independent Perseverance rover data (Hurowitz et al., Nature, September 2025), derived from a completely independent research program without prior knowledge of this framework. The independent convergence of geometric derivation with NASA planetary data constitutes the first principles-first mathematical proof structure for LECA-grade extraterrestrial life on ancient Mars. Pre-registration DOI: 10.5281/zenodo.18986790 (timestamp 2026-03-12, prior to this analysis). Derivation origin: attractor geometry applied to cancer drug targets, proceeding through the Reproduction Theorem and Inverse Accessibility Theorem. No prior knowledge of astrobiology was involved in the geometric derivation.