Admissibility frontier · Edition 3

Expanded claim page · assertion 3 of 6

Three local motion types

EstablishedTranslator

Follows from declared assumptions and has an inspectable certificate. moves a structure between mathematical, physical or ordinary languages.

Exact assertion

The quarter-turn and mirror do more than name two endpoints. When they anticommute on the same typed plane they generate Cl(1,1), equivalently the full real two-by-two matrix algebra. Their equal and opposite mixtures are two square-zero directed rungs: the dual-number branch is therefore the null seam between compact rotation and noncompact squeeze, not an unrelated third metaphor. The traceless closure is the local Spin(2,1) algebra; lifting it to the corpus's Spin(2,3) architecture still requires a source-native carrier, action and held-out record.

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

Scope

Chapter “The admissibility frontier”, section “Three local motion types”. This is assertion 3 of 6 in that section.

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

  1. Recover the declared objects and assumptions from the controlling documents.
  2. Check the calculation, construction, obstruction or stopping rule on those same objects.
  3. Compare the source conclusion with the exact assertion above; do not strengthen its verbs or enlarge its domain.
  4. 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