3733 — Exact Component Diagnosis Needs Four Binary Monitors, Not Three
Global diagnostic lower bound
Three additional observation rows repair the linearized rank defect found in Entry 3731. They do not diagnose arbitrary simultaneous binary failures.
For four component-health bits, terminal contrast is their logical AND. Only the ideal state has contrast one; fifteen nonideal states share contrast zero. Three additional binary monitors provide only eight codes on that blind fiber and cannot be injective. Four binary monitors provide sixteen codes and direct component-health readouts distinguish all sixteen configurations.
Thus three monitors suffice for tangent-carrier rank closure, while four are necessary and sufficient for exact binary-subset diagnosis. Fewer nonbinary ports could suffice only if their combined blind-fiber output has at least fifteen distinct values.
Evidence
research/strominger/exact-component-diagnosis-needs-four-binary-monitors-not-three.md;research/strominger/checkers/exact_component_diagnosis_lower_bound_checks.py;research/strominger/results/exact_component_diagnosis_lower_bound_checks.json.
The exhaustive checker passes 10 of 10 gates over all sixteen health states.
Checker SHA-256:
b793006eae41897d2a3c343324333c33dea9c437abf583f735227bbf56355af7.
Allocator claim: seqclaim-3ffe0425976467c5d538f165.