SCFL Operators Testing and Validation Notebook: Loss Development Triangles as a Repeated-Trial Empirical Testbed — Path 1 Lag-2 Drift Primary Result, Path 2 Exploratory Arm, Rupture Redundancy Diagnostic, and Six-Line Multi-Line Replication (Late Jul

This notebook constitutes the complete, chronological permanent record of the SCFL loss-development-triangle testbed. It documents a pre-registered, leakage-free evaluation of SCFL operators (Drift, Stress, Rupture, Shift) on NAIC Schedule P triangles, treating each accident-year trajectory as a repeated trial in a coherence state space. The design distinguishes two sequenced paths locked before data examination: • Path 1 (primary): strict lag-2 freeze, Drift only. This is the sole test against which the governing research question is judged. • Path 2 (exploratory): lag-3 freeze with the full operator family. Results are reported alongside Path 1 but do not reinterpret the primary finding. Primary data comprise Workers’ Compensation triangles (940 usable carrier × accident-year trajectories). The locked incremental predictive value metric is ΔAUC of a joint model (conventional age-to-age factor + SCFL operator) versus the conventional factor alone. Cluster-respecting year-block and carrier-block bootstrap confidence intervals are treated as the figures of record for all incremental-value claims. Key results: • Lag-2 Drift shows a real univariate association with ≥10 % adverse development (AUC 0.62–0.65) that survives within-carrier standardization and precedes the conventional 1→2 link factor. Incremental value is positive in point estimate but not sharply resolved from zero under clustering. • At lag-3 the conventional link factor becomes dominant (AUC ≈ 0.81). Lag-3 Drift largely collapses into a between-carrier scale artifact; Rupture retains a real within-carrier signal that proves redundant with LDF 2→3; Shift remains near null. • Multi-line replication across six Schedule P lines (Commercial Auto, Other Liability, PP Auto, Workers’ Comp, Products Liability, Medical Malpractice; 5,588 trajectories) yields positive ΔAUC point estimates in every line, with year-block bootstrap confidence intervals excluding zero in three lines plus the pooled panel. The differential behavior of the operators under a single locked protocol supplies the first repeated-trial evidence that the SCFL family is not homogeneous. This begins to convert the operator set from a collection of candidate signals into a measurement framework capable of internal quality control—operators can be provisionally retained, flagged as redundant, or retired on the basis of increasingly stringent empirical tests. That differential characterization, rather than any single positive AUC, is the principal scientific contribution of the notebook. All definitions, thresholds, freeze points, adverse-outcome criteria, primary metrics, and sequencing decisions were fixed in writing before outcome-linked examination. No operator result is labeled “validated” or “confirmed” beyond the strength of the evidence assembled under the locked protocol. The notebook supersedes all prior interim working documents on the triangle testbed and is intended as the archival record for publication.