X-amine509: Predicting the Practical Risk Level of Enterprise X.509 Certificates

An unconditional risk bound on automated decisions can be satisfied without automating anything, since a selector that never acts drives the bound to zero. We show this is structural: any risk certificate is defined over a decision contract, the inputs a system acts on plus the semantic relation under which an output counts correct, and weakening either hides base-classifier error. We develop a decision-contract theory: an error-conservation law showing error is only reassigned among harmful automation, human deferral, and semantic masking; a label-free singleton capacity certifying structural incapacity, with a risk-feasible refinement separating recoverable threshold misalignment from risk-constrained incapacity; and a non-degenerate actionability certificate excluding all-abstain solutions by construction. We instantiate this on ATT&CK-aligned alert triage for LLM-based intrusion detection, the setting that exposed the vacuity failure. Across 3 IDS datasets, 6 LLMs, and 4 error-rate thresholds, empirical false-attribution risk stays at or below target in 90.3% of configurations, with 83.4% mean correct automation. The capacity diagnostic explains every low-utility configuration; its refinement separates genuine misalignment from risk-constrained incapacity, confirmed by an exhibited alternative threshold; a training-stability re-run finds no confirmed structural-incapacity instance; and real fine-grained attack-subtype labels confirm the coarsening-transfer identity under a genuine many-to-one map, with small but non-zero masking mass.

Certified selective predictors attain whatever coverage they attain; operators impose an automation floor: answer at least a $β$-fraction of shifted target traffic with at most an $α$-fraction of answers wrong. Under bounded-ratio covariate shift we prove the Floor Certification Map: once that floor must be certified alongside the selection-conditioned risk $α$, certification acquires a feasibility frontier and a two-resource complexity map, additive up to constants: risk in labeled source, the floor in unlabeled target samples. The rates are local, needing a regular frontier margin, slack below the local-regime threshold, and lattice conditions: pre-registered with a lattice margin for the upper bounds, compatible per-slack for the lower. The displayed split is the operational route; oracle weights also allow a labeled-source floor estimate. Three model-tagged results: a lower bound (Model-B), a matching oracle-weight upper bound (Model-A), and an implementable upper bound (Model-B') valid under a pre-registered exact stratified-shift model with nuisance cost priced explicitly. The match is across these models rather than a single-model minimax theorem, and necessarily so: over the full bounded-ratio class no unknown-weight procedure matches at any sample size (Model-B is inconsistent, witnessed at $α=β=1/2$). The nuisance's necessity is only partially settled. Complexity tracks a localized accepted-region functional, not global effective sample size (ESS), on both sides, though a fixed-ESS separation theorem is left open; both lower-bound axes vanish as $β\to0$, so the floor creates the map. Empirically, the registered bite family diverges with log-log slope $-2.002$ within its pre-registered band; a 1,024-cell audit records 0 violations where the formal certificates fire; and a single-corpus SQuAD-to-NewsQA feasibility audit returns honest refusal.

Autonomous security agents operate as staged pipelines, such as classifying network traffic and then attributing attacks to a specific technique. Split conformal prediction gives each stage finite-sample coverage, but deployment requires a trajectory-level guarantee across the full chain. These guarantees do not compose automatically when stages are independently trained and calibrated. Bonferroni allocation is distribution-free but conservative under correlated errors. We show that a natural pairwise-correlation extension to three or more stages is invalid because it gives a lower rather than an upper bound, and derive a valid spanning-tree alternative. We distinguish whether stages are dependent from whether an audit sample is large enough to certify that dependence, and give matching upper and information-theoretic lower sample-complexity bounds. We also show that coarse-to-fine label selection can create near-perfect measured correlation without learned dependence. On a two-stage intrusion-detection pipeline across 6 open LLMs and 2 datasets, removing this artifact reduces measured correlation from near 1 to 0-0.78. A direct audit of trajectory failure becomes 13.7% tighter than Bonferroni once the audit reaches the required sample size, but is worse when undersized. A modular certificate using per-stage certificates and a pairwise overlap bound yields a positive average gain of 0.6%, quantifying the cost of lacking joint access. Same-model, cross-model, and permuted-pairing tests show that residual dependence reflects shared sample difficulty, not shared model representations. Average trajectory coverage across 12 configurations is 92.7% +/- 2.4% at alpha = 0.10. Under cross-dataset deployment, single-step miscoverage reaches 100% even when accuracy remains 78%, showing that distribution shift destroys calibrated confidence before raw accuracy.