active
Algebraic / equational
catches: an equation or identity does not hold
e.g. is f(x) = g(x) the same relation?
active
Order / qualitative shape
catches: wrong monotonicity, curvature, or bounds
e.g. does this actually decrease and stay bounded?
active
Dimensional / quantity
catches: units / quantity-kind mismatch
e.g. you added a concentration to a rate
active
Assumption axes
catches: composing under conflicting premises
e.g. steady-state here, transient there — refuse
active
Combinatorial / graph
catches: degree / valency / connectivity violation
e.g. a carbon with five bonds (RDKit-free)
active
Probability / measure
catches: not a valid distribution: ∫ ≠ 1, or P < 0
e.g. a “density” that integrates to 1.3
active
Operator / calculus
catches: a claimed derived metric is wrong (AUC=∫, Cmax/Tmax, t½, C_ss)
e.g. AUC of C₀·e^−kt is C₀/k — verify it
∫ Exposure metrics →active
Population / hierarchical
catches: an invalid random-effects covariance (Ω/Σ not PSD, η-mean ≠ 0)
e.g. a $OMEGA with a correlation of 1.5
Σ Variance validator →active
Conservation / invariant
catches: a flux that breaks a conserved quantity (mass / count / charge)
e.g. a mis-scaled term, so the total no longer holds
active
Stoichiometric consistency
catches: a reaction network where no positive mass can be assigned to every species
e.g. a published model (BIOMD255) where species c10 must weigh zero
active
Quantum / unitarity
catches: a complex-amplitude evolution whose norm |ψ|² is not conserved
e.g. a non-Hermitian generator: probability leaks
active
Thermodynamic / loop law
catches: a closed cycle that makes free energy from nothing (an energy-generating loop)
e.g. a battery-free loop that regenerates ATP — mass-balanced yet energy-infeasible
active
Topological / invariant
catches: two objects claimed deformable into each other when an invariant differs
e.g. a sphere (χ=2) is not a torus (χ=0) — no deformation changes χ
active
Combinatorial existence / realizability
catches: a discrete object that cannot exist (parity · Erdős–Gallai · degree of unsaturation)
e.g. a degree sequence with an odd number of odd degrees
active
Structural identifiability
catches: parameters that cannot be recovered from the model structure + design
e.g. a PK model a fitter still returns numbers for — but they are meaningless
active
Information / channel inequalities
catches: a violated channel inequality (data-processing, Fano, a capacity bound)
e.g. I(X;Z) > I(X;Y) under a claimed Markov chain X→Y→Z
active
Tensor / index consistency
catches: additive tensor terms that do not share a free-index signature
e.g. ν contravariant in one term, covariant in the equation it equals
active
Variational / optimality
catches: a claimed optimum / equilibrium that is not stationary, or the wrong type
e.g. a "minimum" whose Hessian is not PSD — it is a saddle
backstop
Logical / axiomatic
catches: anything a fast modality cannot decide — consistent with its axioms?
e.g. the universal z3 fallback
For pharma PK/PD, the basis is closed.
Representation:
⚗ algebraic + ODE-system. Derived exposure:
∫ operator. Population variance:
Σ hierarchical. Cross-domain structure:
◎ Resonance. Each result is exact-or-refused — never a guess.