The abstract reports closure theorems, under the paper’s conditions, for deterministic semantic post-processing, Bayesian-compatible score aggregation, and expert routing. It also reports two calibration counterexamples and separates confidence-only claims from claims backed by checkable witnesses. Exact formal definitions and hypotheses remain unavailable without the manuscript.

1. definition

   Calibration

   defined in author abstract

   The abstract defines calibration operationally: among claims assigned score z, the average truth rate is z. The manuscript's probability space, conditioning, claim granularity, and approximation conventions remain unaudited.

   Author-supplied abstract
2. prior result

   Kalai–Vempala single-generator floor

   reported in author abstract not independently audited

   The abstract reports the prior result that a calibrated fact-level generator must hallucinate monofacts—facts occurring once in training—at a rate lower-bounded by the Good–Turing missing-mass estimate minus calibration error.

   Author-supplied abstract
3. theorem group Calibration closure under three operators reported in author abstract not independently audited

   The abstract reports that calibration is preserved by three specified composition operators under the paper's conditions; exact theorem statements, domains, measurability assumptions, and error propagation require the manuscript.

   Author-supplied abstract

   1. operator

      Deterministic semantic post-processing

      reported operator

      The first covered operator deterministically transforms generated semantic content. The abstract reports calibration closure but does not expose the formal semantic map or sufficient conditions.

      Author-supplied abstract
   2. operator

      Bayesian-compatible score aggregation

      reported operator

      The second operator combines scores in a Bayesian-compatible way. This is narrower than arbitrary averaging; the abstract's first counterexample warns that marginal calibration alone does not make an averaged ensemble calibrated.

      Author-supplied abstract
   3. operator

      Routing to expert models

      reported operator

      The third operator selects one of several expert models, sometimes described as a mixture of experts. The abstract reports a closure theorem under conditions and separately shows that global expert calibration alone is insufficient under arbitrary routing.

      Author-supplied abstract
4. theorem consequence

   Hallucination floor survives covered composition

   reported in author abstract not independently audited

   Because the covered operators preserve calibration, the abstract concludes that the Kalai–Vempala monofact floor also applies to composites built from those operators.

   Author-supplied abstract
5. boundary

   Ways to fall outside the conclusion

   reported in author abstract not independently audited

   An observed composite below the floor must, according to the abstract, be miscalibrated at its final output, violate a closure theorem's conditions, or operate after verification has changed the evidence state.

   Author-supplied abstract
6. counterexample group Two calibration counterexamples reported in author abstract not independently audited

   The abstract reports examples showing that natural but weaker premises do not guarantee calibration of the composite.

   Author-supplied abstract

   1. counterexample

      Marginally calibrated experts may not average safely

      reported in author abstract not independently audited

      Experts that are each marginally calibrated need not yield a calibrated ensemble when their outputs are simply averaged.

      Author-supplied abstract
   2. counterexample

      Globally calibrated experts may fail under routing

      reported in author abstract not independently audited

      Experts that are globally calibrated need not remain calibrated after a router selectively sends different cases to them.

      Author-supplied abstract
7. scope boundary

   Model-as-judge is motivation, not a listed closure operator

   abstract scope observation

   Model-as-judge mechanisms appear in the abstract's system motivation, but the three reported closure results are post-processing, Bayesian-compatible aggregation, and expert routing; the abstract does not claim a general model-as-judge closure theorem.

   Author-supplied abstract

The abstract reports that calibrated compositions built from the three covered operators retain the Kalai–Vempala monofact hallucination floor; a system that beats it must be finally miscalibrated, violate a closure condition, or change the evidence state through verification.

1. application context

   Cybersecurity workflows

   mapped in author abstract

   The abstract maps the theory to vulnerability discovery, code review and generation, test generation, log analysis, alert triage, and incident summarization by generative systems.

   Author-supplied abstract
2. concept

   Operational claims as facts

   mapped in author abstract

   Cybersecurity 'facts' include claims about vulnerability existence, exploitability, patch safety, alert validity, and incident attribution; rare claims in their tail are treated as analogous to monofacts.

   Author-supplied abstract
3. boundary

   Verification changes the evidence state

   explicitly reported boundary

   A rare-bug claim supported only by model confidence remains monofact-like, while a concrete exploit, proof certificate, or execution trace is a checkable witness. The abstract places verified witnesses outside its pre-verification composition analysis.

   Author-supplied abstract
4. evaluation method

   Evaluation procedure for composed systems

   reported in author abstract not independently audited

   The abstract reports a procedure for determining whether an observed hallucination reduction is compatible with the analysis and identifying whether calibration, operator conditions, or verification explain it; procedural steps and validation evidence require manuscript audit.

   Author-supplied abstract