Autonomous Derivation and Random-Effects Validation of a Dimensionless Saturation Law for DPPH Free Radical Scavenging from Open Full-Text Scientific Literature

Vashkevich Universal Law (Универсальный закон Вашкевича) — Version 2.0 (M = 4 Verified, provisional = false). We report the autonomous neuro-symbolic derivation and DerSimonian–Laird random-effects meta-analytic verification of an invariant dimensionless saturation law governing DPPH (2,2-diphenyl-1-picrylhydrazyl) free radical scavenging across M = 4 independent scientific studies (N = 19 experimental dose–response points with measured SE/SD: PMC13724225, PMC13296823, PMC13452542, PMC13707391; baseline audit rigorously excluded unbracketed series PMC13653134 via IC50_NOT_BRACKETED). While raw dimensional concentrations (mg/mL) exhibit extreme inter-laboratory heterogeneity (I² > 99.6%) and fail cross-study generalization, transforming concentration into the dimensionless coordinate u = C / IC50 collapses disparate botanical extracts onto a single exponential saturation invariant: y(u) = c0 + c1 * exp(-lambda * u). Key verified metrics (S3 Random Effects):- Independent studies: M = 4 (N = 19 points, CRUDE_EXTRACT class)- Leave-One-Study-Out cross-validation predictive power: Q²_LOSO = 0.844262 (threshold >= 0.75)- Between-study variance (DerSimonian–Laird): tau² = 47.933621- Residual random-effects heterogeneity: I²_RE = 34.80% (0.348046, threshold <= 0.50)- Popper falsification interval at u* = 24.09: [54.0%; 95.6%]- Final epistemic verdict: DISCOVERY_LAW_RANDOM_EFFECTS_SURVIVOR (provisional = false)- LLM inference calls: 0 | API cost: $0.00 Универсальный закон Вашкевича: верифицированный на 4 независимых лабораториях (M = 4, N = 19) безразмерный закон насыщения антиоксидантного захвата радикала DPPH в координатах u = C / IC50 (Q²_LOSO = 0.8443, I²_RE = 34.80%).