ILC as the Geometric Inverse of TNBC: Structural Lock versus Epigenetic Lock on the Same Luminal Identity Axis — Mechanistically Opposite Entry Points for Therapy

Invasive Lobular Carcinoma (ILC) and Triple-Negative Breast Cancer (TNBC) are typically described as opposite extremes of breast cancer — ILC is ER-positive, low-grade, and indolent; TNBC is ER-negative, high-grade, and aggressive. The OrganismCore Waddington attractor geometry framework, applied to 19,542 single cancer cells (GSE176078), reveals that this clinical opposition is the surface expression of a precise geometric inversion on a single molecular axis: both subtypes are arrested forms of luminal identity, but by mechanistically opposite locks. ILC is a structural lock (Attractor Type 3): FOXA1 is hyperactivated above normal Luminal A levels, CDH1 (E-cadherin) is absent (~65% mutation, ~35% methylation), and EZH2 is low. The cell is overcommitted to luminal identity with no structural containment. TNBC is an epigenetic lock (composite Type 1→2): FOXA1 is epigenetically silenced by EZH2/PRC2 H3K27me3 deposition (+189% above normal, highest of all subtypes), CDH1 is present, and the luminal programme is locked away rather than absent. On the FOXA1/EZH2 ratio axis (validated across ~7,500 patients in seven independent datasets; CS-LIT-1, DOI: 10.5281/zenodo.18883922), ILC sits above LumA (FOXA1 hyperactivated beyond the normal luminal maximum) and TNBC sits at 0.52 near the lowest end (FOXA1 silenced). They are the opposite poles. The therapeutic consequence is inverted: ILC requires full ER receptor degradation (fulvestrant > aromatase inhibitor) because FOXA1 amplification makes ligand depletion alone insufficient — the amplified FOXA1 circuit partially compensates for reduced estrogen, maintaining ER output despite AI. Fulvestrant eliminates the receptor itself, upstream of FOXA1 amplification. TNBC requires EZH2 inhibition (tazemetostat) to remove the H3K27me3 lock from FOXA1 and ESR1 promoters before any endocrine agent can engage — there is no expressed ER to degrade until the epigenetic lock is removed. The same drug (fulvestrant) is the correct last step in the TNBC tazemetostat sequence (CS-LIT-16, DOI: 10.5281/zenodo.18884003) and the correct first step in ILC — for completely inverted biological reasons. The individual features (FOXA1-high ILC, FOXA1-absent TNBC, CDH1-absent ILC, CDH1-present TNBC, EZH2-high TNBC) are each published. The unifying geometric inversion framing — same axis, opposite poles, opposite locks, opposite therapeutic entry points — has no published equivalent as of 2026-03-06. Confirmed by ILC biology (Frontiers Oncology 2025 ILC review: FOXA1 hyperactivation and altered endocrine sensitivity) and TNBC epigenetics (Schade et al., Nature, 2024: EZH2/PRC2 as convergence node silencing FOXA1/GATA3/ESR1 in TNBC). Verdict: CONVERGENT-NOVEL. This document is the foundational architecture document for ILC within the OrganismCore BRCA cross-subtype series and is required before CS-LIT-18 (fulvestrant superiority in FOXA1-stratified ILC, in preparation).