A Statistically-Validated Reduced-Form Model with Identifiable Cliff Layer for Technological Trajectory Analysis

Industrial Defectivity Prediction (IDP) V6 introduces a two-layer extension of the 60-year-old Negative Binomial (NB) yield model, separating an information-loss correction layer from a cliff-threshold transition layer. Two variants are presented: a single-cliff sigmoid form and a two-cliff valley form. The two-cliff variant is structurally compatible with the Imec stochastic valley framework (De Bisschop, Leray; SPIE 2020) while extending it through a process-maturation factor. Validation across nine industries (semiconductor, battery NMC, battery LFP, solar PV, display, defense, solid-state battery, quantum computing, pharmaceutical) demonstrates strong fit (Pearson rho > +0.9) in eight of nine industries, with statistically significant improvement (Delta AIC < -50) over baseline NB models in the strongest cases. The framework operates on publicly disclosed aggregate data (IEDM, SPIE, NREL Best Research-Cell Chart, Argonne CAMP, DSCC, FDA submissions, DOD/GAO reports), enabling forward-looking forecasting and cross-industry comparison without access to fab-internal wafer data. The cosmological foundation introduced in earlier versions (Landauer-Holographic coupling, k = 0.206) is retained unchanged in V6. The V6 contribution focuses exclusively on the industrial yield prediction layer extension. V6 is intended as a complementary public-disclosure forecasting tool, not as a replacement for established industry-specific in-house process control models (Imec, IBM, KLA, Synopsys, PDF Solutions in semiconductor; NREL, Argonne in battery; KIT, HZB, Imec EnergyVille in solar; FDA QbD/PAT in pharmaceutical), which retain superior precision through underlying physics-based parametrization. Honest limitations: All cross-industry validation conducted on samples drawn from public-disclosure aggregates; in-house wafer/cell-level data validation pending. The two-cliff valley variant achieves AIC parity with Imec valley benchmark on semiconductor (Delta AIC +2 to +3, indicating compatibility rather than supersession). Display and Battery LFP show simulation sample-dependence requiring real-data revalidation. Patent: Korean Patent Application KR 10-2026-0077383 (filed April 29, 2026; PCT international filing deadline April 29, 2027) covers the framework. Doctrine-of-equivalents protection includes function-form variants (sigmoid, tanh, probit, Hill). Two-cliff valley supplemental claim under preparation for PCT filing.