We encode the orientation of any cell as a normalised vector ψ = [p, n, f] where p + n + f = 1 and each component represents a measurable biological axis:
The cancer cell genome is an extraction vector: it consumes host resources without integrating into host architecture, projects growth without coherence, and cannot be recalled to differentiation because it retains no memory of its tissue identity.
The extraction vector framework maps directly onto the established hallmarks of cancer (Hanahan & Weinberg, 2000, 2011):
| Axis | Deficit State | Corresponding Cancer Hallmark | Molecular Marker |
|---|---|---|---|
| PAST → 0 | Loss of cellular identity | Dedifferentiation; replicative immortality; genome instability | Loss of p53, Rb; telomerase reactivation; epigenetic silencing of lineage genes |
| PRESENT → 0 | Loss of host coherence | Evasion of growth suppressors; immune evasion; tissue invasion | Loss of E-cadherin; PD-L1 upregulation; TGF-β secretion; loss of contact inhibition |
| FUTURE → 1 | Maximal proliferation drive | Sustained proliferative signalling; angiogenesis; metastasis | EGFR/RAS/MYC amplification; VEGF upregulation; EMT activation |
We define a cellular absence score A(ψ) with differential weighting reflecting the relative diagnostic significance of each deficit:
The PAST axis carries highest diagnostic weight (0.50) because loss of differentiation identity is the initiating event in malignant transformation. PRESENT axis deficit (0.40) drives invasion and immune evasion. FUTURE axis deficit carries low weight (0.10) because low proliferation drive, while clinically significant, does not produce the extractive behaviour characteristic of aggressive malignancy.
Testable prediction: A(ψ) computed from biopsy gene expression data (p from differentiation marker panel; n from immune recognition and adhesion panel; f from proliferation marker panel) correlates with clinical staging, lymph node involvement, and overall survival more strongly than any single-axis marker alone.
The framework reframes several proven therapies as axis restoration operations, explaining their mechanisms through a unified lens:
| Therapy | Axis Restored | Mechanism | Example |
|---|---|---|---|
| Differentiation therapy | PAST (p ↑) | Forces re-expression of lineage identity genes; restores apoptotic competence | ATRA in acute promyelocytic leukaemia; HDAC inhibitors |
| Immune checkpoint blockade | PRESENT (n ↑) | Restores immune visibility; re-establishes host coherence around tumour | Anti-PD-1/PD-L1 (pembrolizumab, nivolumab) |
| Contact inhibition restoration | PRESENT (n ↑) | Re-establishes spatial coherence signalling between cells | E-cadherin restoration; YAP/TAZ inhibition |
| p53 reactivation | PAST (p ↑) | Restores apoptotic memory; re-enables cellular self-recognition of damage | APR-246 (eprenetapopt) |
Notably, the most durable responses in clinical oncology occur when both axes are restored simultaneously — as in the combination of differentiation therapy with immune checkpoint blockade in haematological malignancies — consistent with the dual-axis restoration hypothesis.
The framework generates one primary falsifiable prediction not derivable from existing single-hallmark models:
Hypothesis: Simultaneous restoration of both PAST axis (p) and PRESENT axis (n) produces synergistic anti-tumour effect exceeding the sum of single-axis restoration alone, because extraction behaviour requires the co-absence of both axes — restoring either alone leaves the extraction dynamic partially intact.
Proposed experiment: In a suitable cell line model (e.g. triple-negative breast cancer), compare: (A) differentiation agent alone; (B) immune coherence restoration alone; (C) simultaneous combination; (D) control. Primary endpoint: A(ψ) reduction at 72h measured by the three-panel gene expression assay. Secondary endpoint: proliferation, invasion, immune recognition. Prediction: C > A + B (synergistic, not additive).
The extraction vector model of malignancy is not a metaphor. It is a quantitative framework in which cancer's defining characteristics — loss of identity, loss of coherence, uncontrolled growth — are encoded as measurable axis deficits in a normalised three-component vector. It unifies the established hallmarks under a single diagnostic score, maps directly onto proven therapies, and generates novel falsifiable predictions. The framework extends naturally to any biological system exhibiting extraction behaviour, including viral infection, autoimmunity, and cellular senescence, and provides a mathematical basis for nanotech targeting systems that identify cells by ψ profile rather than by surface antigen alone.
Data, implementation code, and the full mathematical framework are available on request.