Scope
Chapter “The projective loop”, section “The exact result”. This is assertion 1 of 2 in that section.
Expanded claim page · assertion 1 of 2
The exact result
EstablishedAuditor
Follows from declared assumptions and has an inspectable certificate. checks assumptions, certificates, counterexamples and stopping rules.
Exact assertion
An odd three-relation cycle can fail to return on the base configuration while closing on a connected double cover. The placement triangle lifts to a six-cycle, and coherent transport can require twelve steps before every marked datum returns.
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
checks assumptions, certificates, counterexamples and stopping rules.
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 →
- the unique connected double cover of the placement triangle is the six cycle with sideband as deck parityOpen controlling document →
- the graded sideband antiunitary lifts the six cycle to a nested c12 to c6 to c3 transportOpen controlling document →