The Patient Compass: Domain Walls, Oxygen Gating, and the 3-D Survival Manifold of 198,862 Tumors

Somatic mutation data from 198, 862 tumors across 378 independent studies (cBioPortal) were mapped to the eight hallmarks of cancer using a 45-gene panel. A pair completeness hypothesis was systematically tested, extended, and ultimately falsified as a survival framework. Three findings survived the falsification cascade. First, domain walls predict survival. Re-parameterizing the 8-bit hallmark vector into domain-wall coordinates yields the dominant survival features. The frustrated proliferator (proliferative signaling without invasion) is the single strongest hallmark-derived predictor: HR = 1. 81 in hypoxic tissue (p < 10^-145). TP53-coupled growth suppression and death evasion increases hazard by 32%. Hypoxic coupling (simultaneous immortality and metabolism) is massively protective (HR = 0. 40). Second, tissue oxygenation gates all hallmark effects. Oxygenation is the strongest independent survival predictor in the multivariate Cox model. The survival effect of Genome Instability inverts by oxygenation: harmful in normoxic tissue, protective in hypoxic tissue. Third, eight hallmarks collapse to three dimensions. Marchenko-Pastur random matrix analysis finds exactly 3 eigenvalues above the noise threshold. A 3-composite-score model (5 parameters) captures 96. 3% of the predictive power of the full 25-parameter interaction model with zero meaningful overfit. Companion papers: Active Transport on the Prime Gas (DOI: 10. 5281/zenodo. 19243258), The Arithmetic Black Hole (DOI: 10. 5281/zenodo. 19442006), and The Unity Clock (DOI: 10. 5281/zenodo. 19478727).