MIsCORE-RIUD: Paper IV — Population Dynamics and a Frozen Physical Clock

This study tests whether frozen connected multiscale paths across a 99-event development cohort form a higher-order population dynamical object. Structural paths occur in 98/99 events, but rarity is graded rather than binary: 58 path-bearing events satisfy the frozen rare-path criterion and 40 do not, while node-count complexity correlates with the frozen rarity coordinate (Spearman ρ = 0.6619802493). A search-aware discrete-family model fails (7,565/9,999 null exceedances; p = 0.7566), motivating a move from event labels to event-internal geometry.Intrinsic registration yields a 97-event atlas with 1,077 nodes and 980 transitions. PRE and POST dynamics are strongly asymmetric: PRE contains 730 nodes and 633 transitions across 90 events with macro R² = 0.131234 and minimum-fold R² = 0.106708, whereas POST contains 347 nodes and 250 transitions across 92 events with macro R² = 0.033268 and minimum-fold R² = -0.104449. Rate balance, re-entry, multistate flow, run index, state age, history, and frozen forward replay establish a recurrent memory-conditioned process.Broad physical-covariate screening produces large apparent fits, but leverage and search-aware controls reject them as population laws. Three-phase organization survives removal of physical terms: the physics-free F0 score is 0.5952381984 versus 0.5970683812 for the best physical candidate. Only after this structural freeze does a state-first physical search survive full selection correction, with 5/9,999 primary null exceedances (p = 0.0006) and 0/9,999 fixed-score exceedances (p = 0.0001).The frozen score then modifies transition rate with γ = 0.3162354634393393, so a one-unit increase in S multiplies the conditional hazard by exp(γ) = 1.371953262430. The frozen clock gives 3/999 primary exceedances under the plus-one rule (p = 0.004). All four developmental views retain positive likelihood gain, and Holdout5 retains positive no-refit likelihood gain in W1–W4; W1–W3 reproduce the frozen ordering direction, while W4 is underpowered at four scorable events.A transition-local depletion interval has generic maximum-gap strength (p = 0.99) but specific frozen transition-local placement at the tested resolution (p = 0.01). The surviving object is therefore an effective, history-bearing population state system with intrinsic registration and a source-dependent traversal-rate modifier.