# DEST Runtime v0.7-alpha — Dependency Cascades, Deadlines, Dynamic Costs, and Diminishing-Returns Diagnostic **Date:** 2026-08-14 **Frozen holdout:** 60 episodes × 24 certificate/debt nodes = 1,440 nodes **Rounds per episode:** 18 **Diminishing-return comparisons:** 30,000 per diagnostic layer **Regression suite:** 30/30 PASS ## 1. Research question v0.6 established only a calibrated adaptive signal; it did **not** establish adaptive submodularity. v0.7 asks two different questions: 1. Does explicit certificate dependency structure improve evidence scheduling under deadlines and changing inspection cost? 2. Which parts of the resulting utility exhibit empirical diminishing returns, and which parts break it? ## 2. Runtime additions New replayed state: ```text cascade_nodes cascade_edges deadline_states dynamic_costs adaptive_rounds ``` New event classes: ```text CASCADE_NODE_INIT CASCADE_EDGE_INIT CASCADE_STATUS DEADLINE_SET DEADLINE_MISS DYNAMIC_COST_SET ADAPTIVE_ROUND_OPEN ADAPTIVE_ROUND_EVENT ADAPTIVE_ROUND_CLOSE ``` Each node also receives a real `VERIFICATION` certificate in the existing CertificateStore. Parent→child DAG edges are mirrored into the certificate dependency graph. If an inspected certificate is invalid and revoked, descendant certificates become stale through the normal revocation propagation mechanism. ## 3. Benchmark world Each episode uses a three-layer DAG: ```text 4 roots → 8 middle certificates → 12 leaf certificates ``` with overlapping parents. Every debt has: - risk / impact / leverage; - uncertainty; - current quarantine state; - deadline; - base inspection cost; - dynamic cost profile (`FLAT`, `RISING`, `FALLING`, `U_SHAPE`); - estimated invalidity and resolution probabilities; - certificate ancestors / descendants. Hidden benchmark state contains actual local/effective invalidity and whether inspection resolves. Policies never receive those hidden fields. Inspection budget arrives gradually and unused budget carries forward. ## 4. Important runtime correction An early v0.7 implementation removed a debt from the exposure world when inspection itself failed. That is wrong: ```text inspection failed != debt resolved ``` The final runtime keeps failed-inspection debts exposed while marking them as attempted so the same task is not retried within the benchmark horizon. ## 5. Holdout scheduler results | Policy | Avg cumulative exposure ↓ | Avg exposure reduction ↑ | Avg deadline misses ↓ | Avg cascade closures | |---|---:|---:|---:|---:| | v0.6 EIV | 11.2597 | 61.79% | 6.27 | 6.25 | | Deadline-only | 10.6093 | 63.81% | 6.02 | 6.35 | | Cascade-risk | 9.9367 | 64.64% | 5.20 | 7.78 | | **v0.7 combined** | **9.6651** | **65.85%** | **5.22** | **7.65** | Replay audit on a fixed 5-episode v0.7 sample: ```text knowledge state: True certificate graph: True ``` ## 6. Paired holdout statistics ### v0.7 vs v0.6 EIV Cumulative exposure difference (lower is better): \[ \Delta E=-1.5946 \] 95% paired bootstrap interval: \[ [-2.8335,\ -0.5090] \] Deadline-miss difference: \[ \Delta D=-1.0500 \] 95% interval: \[ [-1.7667,\ -0.4167] \] Exposure-reduction-ratio improvement: \[ \Delta R=0.0406 \] 95% interval: \[ [0.0083,\ 0.0767] \] These three intervals do not cross zero. ### v0.7 vs Cascade-risk Exposure difference: \[ \Delta E=-0.2716 \] 95% interval: \[ [-0.7933,\ 0.2026] \] This interval crosses zero. Therefore the strongest current conclusion is: > **Explicit dependency-cascade awareness has a stable benefit over the v0.6 direct-EIV baseline on this holdout. The additional advantage of the full deadline-aware v0.7 score over a simpler cascade-aware scheduler is not yet established.** ## 7. Diminishing-returns diagnostic The diagnostic intentionally separates three notions. ### A. Pure structural cascade affected-set utility For sampled \(S\subset T\) and candidate inspection \(e\): \[ \Delta(e\mid S)\stackrel{?}{\ge}\Delta(e\mid T). \] Observed: ```text violations = 0 / 30000 rate = 0.0000% ``` This is consistent with a weighted coverage / overlapping-cascade substructure on the sampled worlds, but it is **not a formal proof**. ### B. Belief-conditioned expected marginal score After resolved evidence changes related invalidity estimates: ```text violations = 1963 / 30000 rate = 6.54% ``` So additional observations sometimes **increase** the estimated marginal value of another inspection. ### C. Deadline + dynamic-cost adjusted marginal score ```text violations = 20309 / 30000 rate = 67.70% ``` This is a direct empirical counterexample to treating the full runtime objective as globally diminishing-return. Deadlines can make a later inspection more urgent; falling/rising tool costs can also change its net value. Therefore: \[ \boxed{ \text{submodular-like cascade core} \not\Rightarrow \text{globally adaptive-submodular DEST runtime} } \] ## 8. Engineering interpretation The current evidence supports a decomposition: ```text certificate cascade / affected-set coverage → strong diminishing-return-like signal belief transfer → occasional complementarity / marginal-value increase deadline + dynamic cost → frequent nonstationary marginal-value increase ``` This means a future proof effort should not target the entire Runtime at once. A more defensible mathematical program is: 1. isolate a fixed-cost / no-deadline certificate-cascade utility; 2. prove or disprove submodularity there; 3. treat belief updates, deadlines, and dynamic costs as separate extensions; 4. derive approximation guarantees only under explicit conditions. ## 9. External formal alignment - Golovin & Krause formalize adaptive submodularity as a diminishing-returns property under partial observability and obtain greedy guarantees only when the property holds. - Parthasarathy studies adaptive submodular maximization under stochastic item costs and stochastic knapsack constraints. - Stochastic scheduling literature shows that release/due dates and time-dependent feasibility can fundamentally change scheduling objectives. These are formal comparison points, not proofs about DEST. ## 10. Next falsifiable frontier v0.8 should stop adding scheduler adjectives and instead isolate the mathematical core: ```text Fixed-Cost Certificate Cascade Model ``` Then create: - an exact finite utility function; - exhaustive small-DAG submodularity checks; - counterexample search; - monotonicity check; - conditions under which cascade utility is provably weighted coverage; - explicit constructions showing where belief/deadline extensions break those conditions. That would be the correct bridge from Runtime experiments back into theorem-style mathematics.