Scope
Chapter “The Standard-Model seam”, section “Three generations and the index”. This is assertion 1 of 2 in that section.
Expanded claim page · assertion 1 of 2
Three generations and the index
ConditionalBuilder
Works after a named field, coefficient, boundary condition or control is supplied. constructs a model, mechanism, calculation, protocol or intervention.
Exact assertion
An index is a robust signed count of zero modes, rather like counting unmatched left-moving and right-moving lanes after paired lanes cancel. The selected-projector completion canonically pulls back the anticanonical line on \(\mathbb{CP}^{1}\) to O(3), giving Dirac index three for every spectator Standard-Model multiplet.
What this commits us to
The construction is admitted only after the named additional input is supplied. The page records the dependency instead of hiding it inside the conclusion.
Logical anatomy
Evidence posture
Identify the named external input and verify that the construction follows after it is supplied.
Research move
constructs a model, mechanism, calculation, protocol or intervention.
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
Show that the named input is inconsistent, insufficient, unavailable, or fails to imply the claimed construction.
Source map
Controlling documents
- the completion cp1 canonically inherits o3 and index three but no current action makes it the fermion family dirac spaceOpen controlling document →
- the o3 twisted cp1 operator has exactly three universal chiral zero modes but its minimal local six dimensional parent is anomalousOpen controlling document →