Carcinogen barrier-Kramers kernel

A carcinogen is a sustained aberrant drive that lowers the R19 cell-fate barrier, raising the Kramers crossing rate into a malignant basin; relative risk is RR(dose)=rate(dose)/rate(0). The exact cubic barrier vanishes as (h_sp−h)^{3/2} near the spinodal, and one shared noise scale D=0.0417 serves every organ site. The kernel is forced [F]; per-site anchors are cited [L].

The carcinogen kernel reuses the organ-building R19 switch: a sustained bias lowers the exact cubic barrier (vanishing as (h_sp−h)^1.5), and a Kramers rate gives RR(dose)=rate(dose)/rate(0). One noise scale D=0.0417 serves all sites; the only per-site number is a calibrated dose-to-bias slope. The kernel is [F].

A carcinogen is modelled as a sustained aberrant drive that lowers the R19 cell-fate barrier, raising the Kramers crossing rate into a malignant basin; relative risk is RR(dose) = rate(dose)/rate(0). The cell-fate switch is the same R19 primitive that builds organs — carcinogenesis is a biased basin crossing, not a separate mechanism.

The exact barrier is the healthy-well-to-saddle height of the biased cubic s³ − g·s − h = 0; it vanishes as (h_sp − h)^{3/2} as the bias approaches the spinodal. One shared substrate noise scale D = 0.041667 serves every organ site, and the only per-site number is a slope κ mapping physical dose to bias, calibrated to a single cited epidemiological anchor by bisection — never a curve-shape fit.

The kernel is forced by the substrate [F]; the per-site anchors are cited [L]; absolute incidence rates are open [O] because they need external population calibration, exactly as absolute organ size is open. The three site pages (colorectal, pancreatic, gastric) each instantiate this one kernel with their own cited anchor.