Combination controllers — Lean-verified cross-domain combinations.
Where single agents under-control. Combination controllers are certified across modalities with Lean-checked stability claims.
Formally-verified multi-modal combination therapies
Combinations across modalities — peptide + designed-protein + small-molecule — treated as feedback controllers and machine-checked to be therapeutically adequate precisely where no single modality is. Orthogonal mechanisms compose super-additively; a Lean proof certifies stability across the dosing cycle.
The combined closed loop is Lyapunov-stable — V̇(x) ≤ −ε‖x‖² — reducing to a proven framework theorem.
Control-adequate without over-driving: kMin ≤ K ≤ kMax.
Below the cross-modal over-suppression ceiling (E ≤ ceiling).
Strictly better than any monotherapy — every single agent under-controls (Kmono < kMin).
All of the above hold at both the dosing-cycle peak and trough, not just an idealized steady state.
| Axis | Orthogonal modalities | K peak / trough | Over-suppression = | Robust* | Lean receipt |
|---|---|---|---|---|---|
C5a / C5aR1 inflammation | small-molecule receptor block ⊕ designed-protein ligand reduction | 0.112 / 0.106 | infection (serum-bactericidal) | 67% | lyapunov_c5a_combination |
IL-6 trans-signaling inflammation | designed-protein trap ⊕ small-molecule JAK ⊕ designed peptide receptor block | 0.131 / 0.109 | immunosuppression | 79% | lyapunov_il6_combination |
Glucose lowering metabolism (T2D triple) | GLP-1 peptide ⊕ insulin-analog protein ⊕ SGLT2i small molecule | 0.126 / 0.108 | hypoglycemia | 74% | lyapunov_glucose_combination |
Aggregation burden neurodegeneration (buntanetap) | small-molecule production reduction ⊕ designed-protein clearance ⊕ anti-aggregation peptide | 0.128 / 0.108 | over-broad proteostasis suppression | 74% | lyapunov_neuro_combination |
Cortisol circadian band endocrine (HPA axis) | CRF1-antagonist peptide ⊕ 11β-HSD1-inhibitor ⊕ selective GR-modulator small molecules | 0.116 / 0.108 | adrenal insufficiency / flat rhythm | 74% | lyapunov_cortisol_combination |
RA inflammatory tone rheumatoid arthritis (Rabeximod case) | IL-6 trap ⊕ JAK small molecule ⊕ designed peptide ⊕ Rabeximod macrophage arm | 0.141 / 0.124 | immunosuppression | 89% | lyapunov_rabeximod_ra_combination |
Band kMin–kMax = 0.10–0.16; every monotherapy gain is 0.072 (under-controls). *Robust = share of an ±15% potency × PK-trough perturbation grid (81 worlds) in which the combination remains a PK-robust controller; the dominant edge failure is consistently the dosing-cycle trough. Each receipt compiles under lake build and is re-verified in CI, with the manifest hash bound to the Lean source.
Claimed: a discrete, machine-checked predicate (“verified multi-modal controller”) with a reproducible Lean proof, a quantified robustness margin, and a pre-registered factorial per instance — runnable end-to-end via peptiter-reproduce-combination. Not claimed: any efficacy, safety, or clinical result. The efficacy and pharmacokinetic numbers are documented surrogates; the wet-lab factorial is what would make them real.