3738 — A Jointly Faithful Ubermonitor Terminates the Relative Diagnostic Tower
Relative termination theorem
For the frozen four-bit health object , one sixteen-outcome syndrome instrument is injective. Its kernel pair is diagonal, and every higher Čech object contains only constant tuples. Diagnostic descent therefore terminates immediately after the jointly faithful monitor.
One physical monitor does not mean one bit: the sixteen outcomes retain four bits of information.
The terminal sign-contrast bit is not faithful. Its kernel pair has 226 elements, and its Čech tuple counts grow from 226 at arity two to 759376 at arity five.
Ontology boundary
Adding one fresh unobserved failure bit enlarges the health object to 32 states and gives the old ubermonitor a 64-element kernel pair. The tower reopens. Termination is therefore exact relative to the declared ontology, never an absolute finite-ontology claim.
Physical realization additionally requires source-authorized joint legs and the correct coefficient system. A rationally faithful section need not define an integral physical monitor.
Evidence
research/strominger/a-jointly-faithful-ubermonitor-terminates-the-relative-diagnostic-tower.md;research/strominger/checkers/ubermonitor_cech_termination_checks.py;research/strominger/results/ubermonitor_cech_termination_checks.json.
The exact checker passes 10 of 10 gates and verifies Čech levels through arity
seven. Checker SHA-256:
7c30aed33661f5c6035dddcb82efb7b2aea8acbcf946da8e5f375bd53992cd7a.
Allocator claim: seqclaim-e417ccf80bbf7113594dc073.