Why Nontrivial\, [formula in source] is necessary.
note carrier rigidity lean4
Without the non-triviality hypothesis the rank-3 slogan would be false: for [formula in source] the spaces [formula in source] and [formula in source] are both zero, the contraction [formula in source] is trivially bijective, both operational predicates hold vacuously, but [formula in source] . The transparency theorem finrank_E_eq_zero_or_three (v9) records the unconditional disjunction [formula in source] ; the ran
Opening source excerpt. Formulas and the full argument remain in the original document.
Source location and explicit evidence links
documents/experiments--lean4-carrier-rigidity--note_carrier_rigidity_lean4/sections/004-section-interface-table-tfpt-paper-2-texorpdfstring-left.tex · lines 135 to 146
These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.
- explicit file citation AuditContract.lean
literal source filename/path in TeX
- explicit script identifier v9_neutrino_texture.py
literal short identifier uniquely resolves in local script registry
- cross reference join YukawaStageDExistence.lean
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
- explicit lean symbol YukawaTrilinearForm.lean
exact texttt symbol under explicit Lean/theorem context