Carcinogenesis root: the reversibility threshold
Taking the R19 root seriously, the malignant transition is REVERSIBLE by removing the carcinogen drive only below the spinodal h_sp≈0.75 (RCC), 0.72 (HCC): past it the healthy basin has annihilated and the cell is committed. The simulated threshold equals the analytic spinodal exactly — a predicted responder boundary for de-driving therapy. Grade [H] prediction on [F]/[V] dynamics.
Cell fate is the same R19 bistable switch whose escape barrier is γ²/4 (read from the measured master-gene γ); a carcinogen is a sustained drive collapsing it. This section asks the treatment question: a driven pre-malignant cell, on drive-removal, returns to health iff the drive stayed below the spinodal; beyond it the transition is irreversible. The threshold is sharp and the near-threshold reversion time diverges with the universal 1/2 fold exponent.
Why the clearance organs, and why a barrier
The kidney and liver meet carcinogens precisely because they are the clearance organs — aristolochic acid is concentrated by renal filtration, aflatoxin is activated by hepatic metabolism. On the R19 picture (§7) each cell's fate is a bistable switch with an escape barrier γ²/4 set by the measured master-gene promoter stacking energy (SIX2 γ=1.5556, HHEX γ=1.525); the carcinogen is a sustained drive that lowers that barrier until the malignant crossing becomes likely.
The spinodal is a reversibility threshold
Start a cell in the healthy basin, apply a drive, then remove it and let it relax. Below the spinodal h_sp = 2(γ/3)^1.5 the healthy basin still exists, so the cell returns to health (RCC: final state -1.25, healthy); above it the healthy basin has annihilated, the cell has fallen into the malignant basin, and drive-removal cannot retrieve it (RCC: final state +1.25, committed). The simulated threshold (0.749) equals the analytic spinodal (0.747) for RCC and likewise for HCC (0.727 vs 0.725). The biological reading: de-driving / differentiation therapy can revert a lesion only while it is pre-spinodal — a sharp responder boundary set by how far the driver burden has pushed the cell.
Critical slowing: near-threshold lesions are relapse-prone
As the drive approaches the threshold the healthy basin goes marginally stable: its relaxation rate λ = γ − 3 s_h² → 0, so the reversion time τ = 1/|λ| diverges with the universal saddle-node exponent 1/2 (fitted -0.506 for RCC, -0.507 for HCC). A pre-malignant lesion sitting near threshold therefore reverts slowly and is easily re-driven — a predicted relapse-prone, bistable state.
What is, and is not, new here (honest boundary)
Bistable cell-fate landscapes (Waddington; Huang & Kauffman) and the reversion logic behind differentiation therapy — APL with retinoic acid, IDH inhibitors in AML and glioma — are established systems biology; the reversion-on-drive-removal idea is not introduced here. What this package adds, and therefore what carries the falsifiable burden, is quantitative: (i) that the escape barrier equals γ²/4 read from the measured promoter stacking energy, and (ii) that the spinodal is a sharp irreversibility threshold with a 1/2 critical exponent. The dynamics and threshold are forced [F] and reproduced [V]; the claim that a real tumour's barrier equals γ²/4 is unmeasured and graded [O]/[H]. This is a testable mechanistic prediction, not clinical guidance.