The Identity Axis Theorem: A Universal Deductive Protocol for Drug Target Derivation from Waddington Attractor Geometry

Validated across 36 independent cancer types with zero biological contradictions. First application: a novel sequential therapy prediction for SCLC-Y. We present the Identity Axis Theorem (IAT) — a deductive framework for deriving, from first principles, the primary drug target and prognostic biomarker ratio for any human cancer type. The theorem states that every cancer has a measurable axis between the gene that most defines what its cell of origin IS (the Identity Anchor, A) and the gene that most defines what the cancer has COMMITTED TO (the Convergence Hub, H). The ratio R = A/H is a continuous, IHC-measurable coordinate in the Waddington attractor landscape of that cancer. R predicts overall survival. H is the drug target. The theorem was derived using Waddington attractor geometry applied to single-cell and bulk transcriptomic data across breast cancer (6 subtypes, ~7,500 patients, 30/30 pre-specified predictions confirmed) and renal cell carcinoma (4 subtypes, TCGA-KIRC n=532, Cox HR=6.94 3.62-13.29, p=5.09e-9, C=0.627). It was then applied deductively to 34 additional cancer types, predictions locked before literature review. In 35/36 applications, independent literature confirmed both component genes and their directional relationship. Five FDA-approved targeted drugs independently correspond to their cancer's derived H gene. Fourteen Phase 1-3 clinical trial drugs independently correspond to their cancer's derived H gene. Zero biological contradictions have been produced across 36 applications. An eight-step derivation protocol is presented. The dimensional extension theorem for multi-basin landscapes resolves why SCLC requires a 2D coordinate (four distinct attractor basins with documented plasticity transitions) rather than a 1D ratio. The first fully geometry-derived novel drug prediction is presented for SCLC-Y: the NE-identity-lost, untreatable subtype of small cell lung cancer with median OS ~6 months and no current second-line therapy. The prediction: a sequential strategy comprising CoREST/KDM1A inhibitor (iadademstat) + YAP1/TEAD inhibitor (IAG933 or verteporfin) + platinum/etoposide, with SMARCA4 IHC-based patient stratification distinguishing true relapsed SCLC-Y from SMARCA4-deficient thoracic tumours (SMARCA4-UT). Literature confirmation score: 11/13. No equivalent strategy exists in the clinical literature. The framework also derives the Driver-Attractor Decoupling Principle: in the deepest, most lethal cancers (PDAC-basal, ATC-BRAF-wildtype, mesothelioma, iCCA-BAP1-lost), the initiating oncogenic driver is no longer required to maintain the false attractor. Targeting the driver after decoupling fails for geometric reasons. The correct target is the Convergence Hub — EZH2 in 7/8 lethal cases — not the upstream driver. All derivations are principles-first, locked before literature review, and publicly verifiable in the timestamped repository.