Diagnosing While Repairing

Restoring a system can destroy evidence

Suppose a device has several faulty components. Resetting one may help restore the device, but it may also erase a distinction needed to tell which fault was present originally. A healthy device and a correct account of its history are different achievements.

This companion manuscript studies that tension in a deliberately small mathematical setting: binary components, silent resets that set one coordinate to zero, specified diagnostic ports, and a controller that can retain its observation history. The original fault label stays fixed while the physical state changes. The proofs depend on this contract; a reset that emits a diagnostic signal or changes another component is a different model.

What the mathematics establishes

For two components, a normal form characterizes exactly which origin labels can be reported after repair. For three components, two overlapping series-health ports give no exact-feasibility advantage to adapting repair order. Changing one port to parallel health creates an adaptive-order separation. Its four-origin and three-component minimality claims apply within the stated binary local-reset class, not to all finite-state machines.

With fresh common binary-symmetric readout noise, the model separates certain restoration from accurate origin reporting. Adaptive repair order can reduce reporting error arbitrarily, while every fixed order retains a positive error floor. Positive full-support noise also forces all three resets when restoration must be certain, changing the cost comparison.

The finite computations then distinguish several questions that should not be conflated: average error under a prior, worst-origin error, randomized acquisition, randomized terminal reporting, and expected observation cost under a statewise error constraint.

What the benchmarks tell us

At readout error probability 1/5 and a hard cap of four readings, the exact worst-origin error is 6353/30625 (about 20.74%) for adaptive repair order and 8011/26075 (about 30.72%) for the best private mixture of precommitted repair orders. These comparator classes and their information access are specified in Section 6. Recalibrating only the terminal report on one fixed acquisition experiment achieves 38/175 (about 21.71%); that is a particular acquisition experiment, not the optimum over every deterministic acquisition policy.

A separate result asks for the least uniform expected number of readings while every origin’s unconditional reporting error is at most 1/4, still with cap four. Its exact minimum is 55/24 readings, or 127/24 total unit actions after including the three required resets. This is one constrained optimum, not the full cost frontier.

These are mathematical benchmark values, not measured device failure rates. They let an implementation be checked against a known model and expose the benefit of acquiring evidence before it is erased. Proposed follow-up benchmarks would compare matched observation access, memory, action budgets and reporting obligations, then vary noise, reset reliability, timing and model mismatch. An explicit self-model should be compared with an equally informed compiled policy and external tracker. Identical behavior would be a useful null result; the label alone supplies no performance advantage. Those broader experiments have not been performed here.

Relation to Being, Becoming and The MIND

The device’s current condition and its retained record are parts of the operational description of Being; repairs and observation-driven updates are forms of Becoming. The mathematics shows why changing the world and improving knowledge about its history can pull in different directions.

This extends the questions in Acquirable Predictive Models to information-changing repairs. For The MIND, it supplies a bounded study of self-diagnosis, retained memory and adaptive control, alongside the matched-policy cautions in Reflective Self-Models. It does not establish subjective awareness, a general theory of consciousness, or physical safety.

Read the paper and its qualifications

Read the complete manuscript online, download the unchanged 46-page PDF, or download the exact LaTeX, bibliography and figures. Release provenance and hashes describe the presentation conversion and archive scope. The source download does not contain the full retained computational and internal review archive cited by historical paths in the paper.

The frozen manuscript documents its assumptions, proofs, computational evidence, simulated AI reviews and source-access limitations. These reviews are internal assessments, not human specialist reports or endorsements. Submission attribution remains undecided. The separate Causal Self-Diagnosis with Noisy Tests v0.3 and all earlier frozen editions remain unchanged.

Post-freeze source note, 8 November 2026: Later examination of Krichen’s distinguishing-machine example reinforces the known antecedents of adaptive versus preset testing. Its exact diagram has not been authenticated. That analysis is outside this frozen edition; a future revision should incorporate the stronger antecedent qualification. Neither the manuscript nor this site entry establishes priority over the general adaptive-testing literature. Original-source and theorem-applicability gaps remain as documented in the paper’s source appendices.

Related fixed-state certificate-risk addendum

A related fixed-state RF-carrier addendum studies certificate coverage under noisy tests. Its conditional-risk bounds and risk/cost frontiers concern exclusion of a static state from declared carriers, not this paper’s origin-label errors or restoration obligations.