Sequential Certificate Risk

Keeping a certificate is a separate obligation

A noisy test can leave every state possible while a controller chooses to act on a smaller declared set. That smaller carrier is a probabilistic certificate, not the exact posterior support. If a carrier ever excludes the true state, later enlarging the set does not erase that failure.

This supporting addendum to Acquirable Predictive Models makes that distinction explicit. It retains the earlier RF legality rule but changes the execution contract: a policy declares a carrier for each test and accounts for the first exclusion of the true state. It does not authorize those tests under the earlier paper’s exact-support rule.

The model has four fixed states, two supplied binary queries and fresh independent readout errors with known probability 1/5. The main benchmark allows at most five observations, charges 1/50 per test, and bounds conditional remaining first-exclusion risk by 1/50. These are specified mathematical parameters, not measured device failure rates.

What the calculation establishes

The addendum gives an exact first-exclusion identity and a complete finite-history linear program for the conditional contract. The risk is conditioned on public action/answer history and survival, after selecting the current action but before executing it. Immediate exclusion counts toward the same remaining-risk allowance.

For that contract, the exact five-query minimax objective is 267963/640625, about 0.418284. The objective is the worst state’s error probability plus its own expected observation cost. It is not the sum of two separately maximized quantities.

A specified raw prior/posterior-ratio gate has the larger value 291433/640625, about 0.454920. This does not show that confidence sequences are generally inferior: a tailored time-uniform gate attains the first value. The distinction is between the particular admissibility contracts, not between two universally ranked methods.

Exact enumeration also shows that immediate risk caps imply the full conditional bound through six observations in this model at this allowance. No longer horizon is covered. Enlarging one carrier can nevertheless break a later conditional bound, even with the observations and performance unchanged. That example is not an optimized maximal-carrier value gap; the tested optima are equal.

Place beside the existing manuscripts

Diagnosing While Repairing studies interventions that change a system’s current state while identifying its original fault. Here the state never changes, there are no repair costs, and the failure event is exclusion from declared carriers. Its numerical values and restoration obligations cannot be transferred to this model.

For B-Theory’s self-diagnosis programme, the addendum supplies a small, reproducible account of how evidence, declared admissibility and accumulated certificate risk can differ. The RF structural criterion, sequence-form realization plans, dynamic programming and confidence-sequence methods retain their earlier or classical attribution. This is supporting technical material, not a broad theory of cognition, consciousness or physical safety.

Read and reproduce

Read the complete addendum online, download the unchanged eight-page PDF, or download the reviewed source, certificates and verification scripts. Release provenance and hashes distinguish the unchanged scientific files from whitespace-corrected public metadata.

Fresh publication checks reproduced 47 exact certificates, 254 conditional nodes, the independent five-query checks, the horizon-five and horizon-six risk bounds, and the 85 conditional rows of the finite formulation. The 599-variable floating-point LP is a cross-check, not the proof of exact equality. The episode-only comparator deliberately fails the stronger conditional contract; its recorded violations are expected.

The AI review and response record and source/proof ledger state what was checked and what remains open. Internal AI review is not external specialist endorsement. Historical priority, unknown or dependent noise, physical interventions and longer-horizon claims remain outside this release.