Medical Dosing — sealed pharmacokinetic one-compartment

GFTCL-LION-MEDICAL-001.

What the cell guarantees

Given (D, V, t½, n), the cell computes plasma concentration C(t) as an exact-Rat function: C = (D/V) · (1/2)ⁿ where n = elapsed half-lives. Bit-for-bit against proof/lean/FirstRoars/PharmacokineticOneComp.lean + RadioactiveTracerDecay.lean.

The safety-threshold rule fires when C(t) < threshold_pct · C_peak — the canonical "washed out" verdict.

Walkthrough

MedicalDomainPanel → tap a patient case card → DosingValidationWalkthrough opens:

1. Case confirmation — (D mg, V L, t½ h, safety_threshold_pct) from sealed substrate row; clinician CANNOT edit

2. Time-point slider — pick n half-lives elapsed (n=5 = canonical washout check)

3. Live concentration — C in exact reduced Rat

4. Bit-exact match vs sealed formula — substrate CHECK enforces match=1; divergence REFUSED at SQL

5. Safety threshold verdict — below_safety_threshold bit

6. Witness sealed — append-only dosing_validations; signed quintet; broadcast permitted; emission flows to federation_emissions

Federation

• NATS subject: gaiaftcl.medical.dosing.sealed
• AlertableDomain: MedicalAlertableEvents (seedRules: match=true → GOOD; match=false → BAD)
• Peer recompute: GET /federation/witnesses/{emission_id} returns canonical witness JSON

What stays NAMED OPEN

• Two-compartment / Michaelis-Menten kinetics (summit.medical.two_compartment_pk)
• Population variability / Bayesian priors (summit.medical.pop_pk)
• Drug-drug interaction matrix (summit.medical.ddi_witness)

Files

• Lean: proof/lean/FirstRoars/PharmacokineticOneComp.lean, RadioactiveTracerDecay.lean
• Engine: cells/xcode/Sources/MedicalUI/MedicalEngine.swift
• Panel: cells/xcode/Sources/MedicalUI/MedicalDomainPanel.swift
• Alertable: cells/xcode/Sources/MedicalAlertableEvents/
• Substrate: V124 patient_cases + dosing_validations