Finite Noisy Audits

Learning the baseline is part of the problem

Repeated checks can reduce noise, but diagnosing a change also depends on how well the baseline is known. This technical addendum to Reflective Self-Models makes that dependence exact in a finite experiment.

Six local response bits and two interaction bits are unknown. The experiment observes two baseline contexts and two audit contexts, then predicts at four other contexts. Its response equalities and noise law are supplied. Here, an audit means prespecified cross-context calibration and diagnosis. It does not independently validate the assumed structure, and every nominal response parameter needed for final prediction is measured somewhere.

What the finite model establishes

With three observations per block and fresh independent bit-flip noise of probability 1/5, the optimal final normalized Hamming risk is 0.104. Each interaction diagnosis has error 0.186368. The distinction matters: an accurately predicted response need not reveal whether its baseline or its interaction produced it.

The memory minimum depends on the answers required. Under the fixed blocked schedule, public time index and terminal-state-only readout, simultaneously attaining the specified optimal prediction and interaction decisions requires 384 peak data states. Prediction alone requires 96. These correspond to nine and seven register bits; the clock is charged separately. They are not memory lower bounds for arbitrary suboptimal prediction or for a redesigned acquisition task.

A matched compiled controller retains the same sufficient statistic. The two supplied implementations serialize to identical 22,689-byte ROMs. This is a reproducible simulation result, not evidence that architectural labels determine performance or that the encoding is the smallest possible program or hardware design.

A controlled example of what the audit cannot see

One extension permits a bit that flips only the first response at context 010. Its location and form are known, but none of the permitted observations reveals its value. For that explicitly enlarged family, allowing a fresh independent fair output bit gives exact randomized minimax Hamming risk 0.137. The nominal learner instead has risk 0.17 when that defect is present.

The fair output bit is an additional resource, not part of the original deterministic ROM. This result covers the declared defect family, not arbitrary model failures. Likewise, the paper’s fixed 44-sample comparison demonstrates a better allocation than one fixed-baseline choice, without claiming a globally optimal sample frontier.

Place in the research line

The addendum preserves the matched-controller null from Reflective Self-Models: names such as explicit self-model and compiled controller do not create an advantage when the information and decision rule are matched. Its contribution is the integrated finite benchmark and accounting contract, using established inference, indistinguishability and finite-state methods.

It complements Acquirable Predictive Models by emphasizing noisy evidence and output-dependent memory. It does not import a new general learning principle or establish subjective awareness, physical validity or publication priority.

Read and reproduce

Read the complete manuscript online, download the unchanged six-page PDF, or download the complete original public release. The archive includes the exact text source, original reading copies, bibliography, claim ledger, public review material, standard-library Python checkers and finite ROM/data files. Public provenance and hashes distinguish original artifacts from site presentation.

All three portable checkers were rerun during site preparation. The fresh checks reproduced 65,536 block-count tuples, independently evaluated 65,536 truth/error-mask pairs, propagated 783,360 weighted ROM transitions, and regenerated both ROMs byte-for-byte. These are exact compressed mathematical computations, not physical experiments or a literal enumeration of every observation word.

Two independent internal AI reviewers completed proof and hostile review rounds, followed by rereading the actual final manuscript. Their supported precision and framing objections were incorporated, and neither final reread found a remaining major or minor mathematical repair. The public review summary and responses to reviewers describe that scope. Internal AI review is not human specialist peer review or a proof-assistant certificate. No individual byline is inferred from the source.

Final-file review update

On 9 November 2026, two new independent internal AI reviewers each read the complete exact final source and computed its SHA-256. The proof and adversarial passes found no supported fatal, major or required minor mathematical correction. The dated final-file review supplement and hash-bound receipt describe the independent checks, resolved prior requests and limits. No manuscript, PDF or original archive revision was required. This is internal AI review; external human specialist review and historical priority remain open.