# Dated transitions and competing exits

`structured_lifecycle` supplements the four product recipes and their governance and workout examples. It runs observation-window construction, multistate estimation, conditional prediction, competing cause hazards and dependency events for each product. Historical synthetic training is complete before the January 16, 2024 decision. Times are elapsed days, with an explicit historical calendar origin and information cutoff. These tiny reference populations demonstrate mechanics; they do not estimate representative product transition rates.

Two historical claims start performing. One becomes delinquent on day 14, restructured on day 15, defaults on day 31 and settles on day 121; the other remains observed performing through day 150. The unconditional first-default probability is therefore 0.5 after day 31 and remains 0.5 after settlement. Default-state occupancy falls to zero after settlement. Settlement is neither cure nor removal of a historical first default. Conditional on the observed restructured state at day 15, the historical reference path defaults with probability one after 16 more days. This is an observational conditional forecast, not the causal effect of executing the currently proposed treatment.

A separate four-claim competing-risk sample has one default and one nondefault exit at day 30 and two censored observations at day 60. Each cause-specific Breslow hazard jump is 1/4. Joint survival is exp(-1/2), and each cumulative incidence is [1-exp(-1/2)]/2. Default, nondefault exit and survival sum to one; separately computing one minus each cause survival would not do so.

The current claim's default occurs February 1 and is known February 2. Its January 31 target remains censored. A separate sale-control claim exits January 20 and retains a null default target. The January 15 payment-delay event is deferred before its January 16 knowledge date. A distinct restructuring proposal identifies the affected frozen assessment without executing a contract change or overwriting the original risk values. The prior governance example performs the subsequent assessment closure and historical model replay; the workout example evaluates conditional treatment cashflows and actual settlement losses.

This supplement completes delinquency transitions and adds the survival and event pieces of restructuring and exit. Together with the named companion examples it covers those phase methods. Portfolio loss validation remains separate evidence.
