The verification basis

v13.23 · finite form, infinite content

Every formal structure is valid — or invalid — in one of a small closed set of ways. These are the modalities. Content (atoms, models, claims) is unbounded and projects onto this finite basis, so completeness is something you can measure, not hope for.

Cyc tried to enumerate the content and never finished, because content is infinite. The form is a finite closed set — so the substrate holds.

18 active1 universal backstop (z3)▶ Run the gateone call runs every applicable check at once — not a plugin chain
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.