Hepatobiliary / bile layer (cholelithiasis nucleation barrier, dissolution hysteresis, biliary seams)

The hepatobiliary / bile layer rides a new Tier-3 primitive: a nucleation barrier. Cholelithiasis is cholesterol crystallising out of bile, and supersaturation (CSI > 1) is metastable, not sufficient — a stone nucleates only once the drive clears the barrier at CSI > 1 + spinodal (the Kramers crossing). A formed stone then shows dissolution hysteresis, persisting below saturation, which is exactly why UDCA dissolution works only on small, early stones. Gallbladder stasis and cholecystitis are declared B1-gate and C1-flare seams; the felt biliary colic is mind's.

The fourth Tier-3 primitive is a nucleation barrier: cholesterol-bile crystallisation read as the §2 R19 double well ds/dt = g·s − s³ + h with the dissolved phase as the rest basin and the cholesterol saturation index (CSI) as the bias (vendored single-source as nucleation_barrier / supersaturation_drive / stone_nucleates in the substrate). The first reading is that supersaturation is metastable, not sufficient: bile with CSI just above 1 is supersaturated yet remains stone-free (most people with lithogenic bile never form stones), and a stone nucleates only once the drive clears the barrier at CSI > 1 + spinodal. The second, clinically decisive reading is dissolution hysteresis: a formed stone does not redissolve the instant bile drops below saturation — it persists, redissolving only far below it (a wide hysteresis gap), which is exactly why medical (UDCA) dissolution succeeds only on small, early, cholesterol-rich stones in a functioning gallbladder and why stones recur once therapy stops unless the lithogenic drive itself is removed. The remaining biliary syndromes are declared seams to primitives this package already owns, not re-modelled: gallbladder stasis (the second arm of stone risk) is the §16 B1 sphincter-gate primitive, cholecystitis (a stone obstructing then inflaming) is the B1 gate plus the cited §22 C1 flare, biliary dyskinesia is the B1 gate, and the nucleation time is the §7 Kramers barrier-crossing rate. The metastable supersaturation, the barrier-gated nucleation, and the dissolution hysteresis are [V], the nucleation and dissolution thresholds exact spinodal identities and the nucleation time the Kramers rate [F]; the absolute cholesterol-saturation-index scale (a model unit), the stasis and cholecystitis syndromes (owned by the B1 gate and C1 flare), and the cholesterol-delivery (circulatory) and felt-pain (mind) seams are [O] with stated obstacles.

The §24 perfusion layer handled supply and demand; this section opens the hepatobiliary / bile layer, where the disease is a phase transition in a fluid rather than a switch in a tissue. Cholelithiasis — gallstone formation — is cholesterol crystallising out of supersaturated bile, and it needs one new reading of the R19 substrate: a nucleation barrier. A supersaturated solution does not crystallise the instant it passes saturation; it sits metastably until the drive clears a barrier. That is the §2 R19 double well ds/dt = g·s − s³ + h with the dissolved phase as the rest basin and the cholesterol saturation index (CSI) as the bias. Nothing is fitted; the thresholds are exact spinodal identities.

The first reading is that supersaturation is metastable, not sufficient. Bile with CSI just above 1 is supersaturated yet remains stone-free — the everyday observation that most people with lithogenic bile never form stones. A stone nucleates only once the drive clears the barrier at CSI > 1 + spinodal (here CSI = 1.385). The sweep shows bile supersaturated well before it nucleates:

The second reading is dissolution hysteresis, and it is the clinically decisive one. A formed stone does not redissolve the moment bile drops back below saturation; it persists, redissolving only far below it (here below CSI = 0.615, a hysteresis gap of 0.770). This is exactly why medical (UDCA) dissolution succeeds only on small, early, cholesterol-rich stones in a still-functioning gallbladder, and why stones recur once therapy stops unless the lithogenic drive itself is removed:

The remaining biliary syndromes are declared seams to primitives this package already owns, not re-modelled here. Gallbladder stasis (impaired emptying, the second arm of stone risk) is the §16 B1 sphincter-gate primitive (stasis_is_b1_gate_seam = True); cholecystitis (a stone obstructing the cystic duct, then inflaming) is the B1 gate plus the cited §22 C1 inflammatory flare (cholecystitis_is_b1_gate_plus_c1_flare = True); biliary dyskinesia is the B1 gate; and the nucleation time is the Kramers barrier-crossing rate the §7 kernel already uses. Cholesterol delivery is a circulatory seam and the felt biliary colic is mind's — the firewall keeps only the crystallisation thermodynamics here. Both seams are now wired in §27: the cholesterol delivery rests on the consumed circulatory hepatic perfusion [O], and the felt colic is deferred to mind by a one-way pointer. The peripheral visceral-afferent lever — which non-opioid intervention raises the firing threshold of the colic afferent, and the drug class it points to — is mapped in §28.

Treatment (model reading). Cholelithiasis -- LOWER the cholesterol saturation index (reduce biliary cholesterol secretion: weight loss, statins/ezetimibe effects; or bile-acid therapy, UDCA), but the dissolution hysteresis means lowering CSI below 1 is NOT enough -- the stone persists until CSI < 1 - spinodal, so UDCA is feasible only for small / early / non-calcified stones; CHOLECYSTECTOMY (removing the supersaturated reservoir) is definitive. RESTORE gallbladder emptying (treat stasis -- the B1 gate) to prevent nucleation. Cholecystitis is the stone obstructing the cystic duct (a stuck B1 gate) plus a C1 inflammatory flare -- relieve the obstruction and suppress the flare. Cirrhosis / hepatitis / cholestasis are sibling/`circulatory`-owned; hepatic encephalopathy's ammonia source is in scope (lactulose/rifaximin lower it) while the felt/cognitive effect is `mind`'s. Target directions [V]; absolute CSI/stone-size scales and the nucleation timescale [O].

The metastable supersaturation, the barrier-gated nucleation, and the dissolution hysteresis (UDCA only on small early stones) are forced by the substrate [V], with the nucleation and dissolution thresholds exact spinodal identities and the nucleation time the Kramers rate [F]. What stays open [O], each with its obstacle: the absolute cholesterol-saturation-index scale (a model unit needing clinical calibration), the stasis and cholecystitis syndromes (owned by the B1 gate and C1 flare — cited seams), and the cholesterol-delivery (circulatory) and felt-pain (mind) seams.