Scope
Chapter “The Jordan–Lie hinge”, section “From elimination to symmetry”. This is assertion 2 of 2 in that section.
Expanded claim page · assertion 2 of 2
From elimination to symmetry
EstablishedTranslator
Follows from declared assumptions and has an inspectable certificate. moves a structure between mathematical, physical or ordinary languages.
Exact assertion
For the declared carrier, the closure is ten-dimensional \(\mathfrak{sp}(4,\mathbb R)\). This algebra preserves a nondegenerate oriented-area form on four real phase-space coordinates. A standard low-rank isomorphism identifies its connected group with \(\mathrm{Spin}_0(2,3)\), the double cover of the identity component of SO(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
moves a structure between mathematical, physical or ordinary languages.
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
- peirce schur triple recursion to spin23Open controlling document →
- the gaussian gram selector is the h2r jordan logdet barrier and a peirce slice of the rank three cubicOpen controlling document →