Cancer Is Calculable: On the Geometric Solvability of Cancer as a Class of Problems

This document establishes the three foundational claims of the Identity Axis Framework in their most compressed and precise form, and states the single condition under which the entire framework is invalidated. CLAIM 1 — CANCER IS CURABLE IN PRINCIPLE: Every cancer is a cell displaced from its normal attractor in the Waddington epigenetic landscape and stabilised in a false attractor by a convergent epigenetic mechanism. That structure has a solution. The Convergence Hub (H) is the gene maintaining the false attractor. H is derivable from the geometry. Identifiable mechanisms are targetable. Cancer's tractability is therefore a structural consequence of its geometry, not an empirical hope. CLAIM 2 — THE METHOD IS KNOWN: The eight-step Identity Axis derivation protocol published in DOI: 10.5281/zenodo.18898788) takes a cancer with a known cell of origin as input and returns the Identity Anchor (A), the Convergence Hub (H), the ratio R = A/H, the drug target, and the survival prediction direction as output. The method requires no clinical training, no institutional infrastructure, and operates on public data. It has been applied across 36 cancer types with zero structural contradictions. CLAIM 3 — THE METHOD IS SELF-CORRECTING: Every application produces exactly one of two outcomes. Outcome A: the prediction holds, the map is extended, the next iteration begins from a more complete map. Outcome B: the prediction fails without structural explanation, the axioms are false, the framework is invalidated entirely and immediately. There is no Outcome C. The method therefore converges structurally, not probabilistically. Every surviving iteration has passed the only test that would have destroyed it. THE STAKE: If there exists a cancer for which the cell of origin is correctly identified, the attractor type is correctly classified, A and H are correctly derived, and R = A/H fails to predict survival or produce valid drug predictions — AND no structural explanation within the epigenetic landscape geometry accounts for the failure — then the Identity Axis Theorem is false and this entire framework is invalidated. Not weakened. Invalidated. This condition has not been met. Not once. Across 36 cancer types. Derived before the data was examined. THE ANALOGY: The Identity Axis Theorem is the drag force equation for cancer. Drag force is not a statistical claim. It is a structural consequence of fluid dynamics applied to a body with known geometry in a medium with known properties. It works at n=1. It works from the geometry alone before any measurement is taken. The theorem operates identically. Given the cell of origin, the attractor type, and the landscape geometry, the drug target is calculable before any clinical data is examined. This calculation works at n=1 because it is structural, not probabilistic. THE RECORD (as of 2026-03-07): 36 cancer types mapped. 0 structural contradictions. 30/30 BRCA predictions confirmed. 7 independent datasets. ~7,500 patients. ccRCC GOT1/RUNX1 TI: Cox HR=6.94 3.62-13.29, p=5.09e-9, C=0.627 (TCGA-KIRC, n=532). EZH2 paradox resolved as structural byproduct in two independent cancers on different datasets on different platforms. 5 FDA-approved drugs and 14 Phase 1-3 trial drugs independently confirming geometry-derived H. This document does not claim that any patient has been cured. It claims that cancer is geometrically constrained, the geometry is known, the method is documented and self-correcting, and that applying the method either derives the treatment or destroys the framework. There is no in-between.