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:

cascade_nodes
cascade_edges
deadline_states
dynamic_costs
adaptive_rounds

New event classes:

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:

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:

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

Replay audit on a fixed 5-episode v0.7 sample:

knowledge state: True
certificate graph: True

6. Paired holdout statistics

v0.7 vs v0.6 EIV

Cumulative exposure difference (lower is better):

95% paired bootstrap interval:

[ [-2.8335,\ -0.5090] ]

Deadline-miss difference:

95% interval:

[ [-1.7667,\ -0.4167] ]

Exposure-reduction-ratio improvement:

95% interval:

[ [0.0083,\ 0.0767] ]

These three intervals do not cross zero.

v0.7 vs Cascade-risk

Exposure difference:

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):

Observed:

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:

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

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:

8. Engineering interpretation

The current evidence supports a decomposition:

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:

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.