Scope
Chapter “One carrier, two faces, three relations”, section “The smallest relational closure”. This is assertion 1 of 2 in that section.
Expanded claim page · assertion 1 of 2
The smallest relational closure
EstablishedCartographer
Follows from declared assumptions and has an inspectable certificate. maps territory, distinctions, dependencies and interfaces.
Exact assertion
Two faces define a comparison, but a third relation is the first place where local pairwise consistency can fail around a loop. This is why the gear intuition becomes mathematically meaningful at three: not because the universe is literally geared, but because an odd cycle detects a return defect invisible on a single edge.
What this commits us to
The stated conclusion follows inside the declared model. Reusing it elsewhere requires carrying the same object definitions, assumptions and typing.
Logical anatomy
Evidence posture
Audit the declared carrier, assumptions and certificate. The result is exact only within that written scope.
Research move
maps territory, distinctions, dependencies and interfaces.
Verification route
- Recover the declared objects and assumptions from the controlling documents.
- Check the calculation, construction, obstruction or stopping rule on those same objects.
- Compare the source conclusion with the exact assertion above; do not strengthen its verbs or enlarge its domain.
- Apply the status rule and retain every named external dependency.
What would move or defeat this claim
Locate a mismatched definition, an omitted assumption, a failed certificate step or a counterexample on the declared carrier.
Source map
Controlling documents
- the three placement triangle has a z2 sideband frustration and requires path dependence or a double coverOpen controlling document →
- a cycle graph selects a refinement stable real two mode plane but not its orientationOpen controlling document →