Scope
Chapter “The Jordan–Lie hinge”, section “Why ten generators are a real gate”. This is assertion 1 of 1 in that section.
Expanded claim page · assertion 1 of 1
Why ten generators are a real gate
EstablishedAuditor
Follows from declared assumptions and has an inspectable certificate. checks assumptions, certificates, counterexamples and stopping rules.
Exact assertion
Four real coordinates do not automatically imply \(\mathfrak{sp}(4,\mathbb R)\). A pair of ordinary oscillators can explore only a three-generator squeezing/rotation subalgebra. Reaching ten requires independently available anisotropies and shears. Generator rank is therefore a kill test: if commutators close at three, the model is a lower-rank control, not hidden full Spin(2,3).
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
- a three generator jordan furey recursion closes all of sp4 but requires the furey channel rotation as a continuous flowOpen controlling document →
- full sp4 closure requires addressed anisotropy which is control data not cycle symmetryOpen controlling document →