This article concentrates the truth-criterion branch of the project: projective truth, harmonic closure, and the passage from local inference to doctrinal evaluation.
In NAPG 2.0 truth is read as the harmonic coherence of a configuration. The limit Ξ» = -1 fixes universal truth, while deviation from it measures the defect of truth.
The quadratic obstruction is the class πͺB arising from the quadratic part of the deformation equation. It measures the impossibility of extending an admissible infinitesimal deformation without violating package constraints.
If πͺBβ=β{0}, the geometry remains in a linear or Hilbertian regime. Nontriviality of πͺB signals the passage to a projective or stratified nonlinear organization.
If the obstruction space has dimension 2 over β, it admits the model ββ2; if it has dimension 3 over π½2, one gets the Fano plane. In both models the improper line is naturally associated with hyparxis, and the criterion of structural truth takes the form $$\crossratio{A}{B}{C}{D}=-1.$$
Let $$\lambda = \crossratio{A}{B}{C}{D}.$$ Then Ξ»β=ββ1 is universal truth, while the deviation from it defines the truth defect: Ξ΄truthβ=β|Ξ»β +β 1|.
The projective criterion of truth should not be read only as a local test for isolated inferences. It naturally lifts to doctrines, perceptual regimes, and historical epistemes.
Falsifiability is not abolished here, but rewritten: instead of a binary opposition βtheory is correct / theory is falsifiedβ we obtain a field of values Ξ», where Ξ»β=ββ1 denotes universal truth, while the deviation from it is measured by the defect Ξ΄truthβ=β|Ξ»β +β 1|.
Theories therefore differ not only by whether they are refuted, but also by their degree of harmonic proximity to the universal limit of truth.