Carcinogen synergy generalized (HCC: HBV×aflatoxin; ESCC: smoking×alcohol)

Two carcinogenic drives read off the same exact R19 barrier reproduce epidemiological super-additivity and predict sub-multiplicativity near the spinodal. Hepatocellular carcinoma (HBV inflammation × dietary aflatoxin) and oesophageal squamous carcinoma (smoking × alcohol) both give a joint risk above the additive-null yet below the multiplicative-null — diminishing returns at extreme dual exposure, a falsifiable prediction [V].

The §10 gastric H. pylori×diet synergy generalizes: two drives on the same exact barrier reproduce super-additivity at two more organs. Hepatocellular carcinoma is the inflammation×bias case (chronic HBV lowers the barrier scale g, RR~7.3 alone; aflatoxin B1 adds a mutagenic bias h, RR~3.4 alone; joint ~22 exceeds the additive-null, cited Shanghai joint ~59). Oesophageal squamous carcinoma is the bias×bias case (smoking RR~4 and heavy alcohol RR~5 both add bias; joint ~17 exceeds the additive-null, cited combined-heavy ~40). On the same barrier both joints fall BELOW their multiplicative-null — the sub-multiplicativity (diminishing returns at extreme dual exposure) is a concrete falsifiable prediction, and newer/larger cohorts already trend this way. Treatment reading: removing either drive drops the joint risk along its own fan, the largest absolute benefit coming from removing one drive while the other is still present (the super-additive regime). Per-site anchors [L]; super-additivity [V]; absolute incidence [O] (population calibration); HCC carries a cited circulatory seam (hepatic first-pass), not re-emerged.

The gastric H. pylori×diet synergy of §10 is not a one-off: two carcinogenic drives read off the same exact R19 barrier reproduce epidemiological super-additivity at two more organs, and on the same kernel predict a sub-multiplicative ceiling near the spinodal. The structure is identical; only which knob each drive turns differs.

Hepatocellular carcinoma (HBV × aflatoxin) is the inflammation×bias case, exactly like gastric: chronic HBV lowers the barrier scale g (RR 7.3 alone), dietary aflatoxin B1 adds a mutagenic bias h (RR 3.4 alone), and their joint risk ≈ 21.7 exceeds the additive-null 9.7 — super-additive, against the classic Qian/Ross Shanghai cohort (cited joint ~59). On the same barrier the model predicts the joint risk sits below the multiplicative-null 24.8.

Oesophageal squamous carcinoma (smoking × alcohol) is the bias×bias case: both drives add bias on the same switch (smoking RR 4.0, heavy alcohol RR 5.0), joint ≈ 17.0 above the additive-null 8.0 (cited combined-heavy ~40) and below the multiplicative-null 20.0.

Treatment (model reading). The kernel makes risk-reduction multiplicative-in-reverse: removing either drive (HBV vaccination/suppression or aflatoxin avoidance; smoking or alcohol cessation) drops the joint risk back along its own fan toward the single-exposure curve — the largest absolute benefit comes from removing one drive while the other is still present, which is exactly the super-additive regime.

The per-site anchors are cited [L]; the reproduced super-additivity is verified [V] at both organs; and the sub-multiplicativity near the spinodal — diminishing returns at extreme dual exposure — is a concrete, falsifiable prediction the model makes on the same barrier (both joints fall below their multiplicative-null; newer/larger cohorts already trend this way). Absolute incidence stays open [O]: it needs external population calibration, exactly as for the single-site curves. HCC carries a circulatory seam (hepatic first-pass), cited, not re-emerged.