Edge Case Geometric Derivations: Five Stress Tests of the Identity Axis Framework — DIPG, SCLC, Uveal Melanoma, Ewing Sarcoma, and Thymoma / Thymic Carcinoma

This document records five geometric derivations applied to structurally unusual cancers as explicit stress tests of the Identity Axis framework (Identity Axis Theorem, DOI: 10.5281/zenodo.18898788). Each derivation was completed before literature was consulted. All five cases were chosen because they contain structural features expected to produce framework failures. None did. All five produced coherent, confirmed, novel results. Fourteen novel predictions are formally pre-registered with timestamp 2026-03-07. CASE 1 — DIPG (H3K27M-Mutant Diffuse Midline Glioma): The mirror case. Cell of origin: OPC/ neural progenitor. A = OLIG2. H = EZH2 — but paralysed by the H3K27M histone mutation, which competitively inhibits EZH2 catalytic activity, causing global H3K27me3 loss. The false attractor is maintained by H3K27me3 ABSENCE, not excess. The drug logic inverts completely: tazemetostat is geometrically CONTRAINDICATED in DIPG. This is the framework's first drug contraindication derivation. Correct therapy requires a H3K27me3 writer or targeted PRC2 activator — which does not yet exist clinically. ONC201 and panobinostat act on orthogonal axes, explaining their activity and their limitations. Confirmation 5/5. Novel: contraindication derivation, PRC2 activator gap. CASE 2 — SCLC (Small Cell Lung Cancer): The competing anchors case. Cell of origin: pulmonary neuroendocrine cell. A = ASCL1 (primary, SCLC-A) AND NEUROD1 (secondary, SCLC-N) — two competing identity anchors defining two adjacent attractor basins within the same false attractor landscape. H = EZH2/EED (PRC2). The geometric explanation for 40 years of platinum chemotherapy resistance: SCLC chemotherapy resistance is attractor hopping, not resistance acquisition. Platinum disrupts the dominant ASCL1 basin. Residual cells near the basin boundary hop into adjacent basins (NEUROD1, YAP1, POU2F3) with different molecular dependencies. The relapsed tumour is biologically distinct because it is geometrically distinct. EED inhibition is predicted more durable than EZH2i alone because EED collapses all NE basins simultaneously. SCLC-I (NE-low) requires a distinct drug axis. Relapse subtype is predictable from single-cell landscape mapping at diagnosis. Confirmation 5/5. Novel: attractor hopping mechanism, EED superiority prediction, relapse predictability. CASE 3 — Uveal Melanoma: The PRC1 case. Cell of origin: choroidal melanocyte (neural crest-derived). A = MITF. H = BAP1 loss / H2AK119ub1 accumulation — the PRC1 arm, not PRC2. BAP1 removes H2AK119ub1 (the PRC1 Polycomb mark). BAP1 loss leads to H2AK119ub1 accumulation, silencing the MITF programme and deepening the false attractor. This is the geometric and mechanistic explanation for why BAP1 loss predicts metastasis in uveal melanoma with ~84% sensitivity — BAP1 loss is attractor deepening via the PRC1 arm. Tazemetostat is not indicated (wrong arm). Correct target: RING1A/B inhibition (PRC1 writer of H2AK119ub1). Combination RING1A/B inhibitor + tazemetostat is derivable for BAP1-lost UM and is not in current clinical development. Depth score: MITF/H2AK119ub1 approximated as MITF IHC / BAP1 loss status. Confirmation 4/5. Novel: PRC1 arm mechanistic explanation, RING1A/B indication, combination rationale. CASE 4 — Ewing Sarcoma: The constructed false attractor. Cell of origin: mesenchymal stem/progenitor (uncommitted multipotent). A = displaced multipotency programme (RUNX2/SOX9/PPARG) — no single dominant A because the cell had not committed. H = EZH2, directly upregulated by EWSR1-FLI1 fusion, providing epigenetic cement for the constructed basin. The EWSR1-FLI1 fusion does not displace a pre-existing committed identity — it constructs a novel attractor basin with no normal cellular equivalent. Drug prediction: EZH2 inhibition in Ewing will produce subclonal divergence into competing multipotency programmes (RUNX2-high, SOX9-high, PPARG-high subclones), not clean reversion to a single identity. Each subclone will have different drug sensitivity. Most effective combination: EZH2i + forced lineage commitment agent. Depth score: EWSR1-FLI1 programme score / EZH2. Confirmation 4/5. Novel: constructed attractor classification, subclonal divergence prediction. CASE 5 — Thymoma / Thymic Carcinoma: The phase transition case. Cell of origin: thymic epithelial cell (TEC). A = FOXN1 — master TF of thymic epithelial identity and T-cell education. H = EZH2. Thymoma and thymic carcinoma are the same cancer at two attractor depths separated by a geometric phase transition. Shallow (thymoma): FOXN1 partially retained, T-cell education partially functional, paraneoplastic autoimmune syndromes present (myasthenia gravis, pure red cell aplasia). Deep (thymic carcinoma): FOXN1 lost, EZH2 high, T-cell education absent, paraneoplastic syndromes absent, aggressive disease. R = FOXN1/EZH2 predicts not just survival but whether a patient develops myasthenia gravis — the framework's first geometry-derived clinical phenotype prediction beyond survival. EZH2 inhibition in thymic carcinoma may restore FOXN1 and thereby induce autoimmunity as an on-target geometric effect, not an adverse event. Intermediate-R patients have highest autoimmune risk with EZH2i. Confirmation 4/5. Novel: phase transition classification, paraneoplastic syndrome prediction, EZH2i autoimmune prediction. CROSS-CASE SUMMARY: Structural contradictions: 0. Type B failures: 0. Novel pre-registered predictions: 14. Average confirmation score: 4.4/5. The five cases establish: (1) the framework handles EZH2 inactivation and correctly inverts drug logic; (2) multiple competing anchors are handled correctly as competing basins; (3) PRC1 vs PRC2 is distinguished correctly — the 28% non-EZH2 H cases are precision, not failure; (4) constructed attractors with no pre-existing A are handled correctly with specific testable predictions; (5) the framework predicts clinical phenotype beyond survival for the first time.