# L9: CHARM QUARK CUBIC — THREE-ROOT VERIFICATION

**Category:** library_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING

## Prompt

CHARM QUARK CUBIC — THREE-ROOT VERIFICATION
Per v1.27.5 fix: the charm cubic should yield exactly 3 roots. Using SymPy, solve the charm sector cubic and verify output: Root 1: 46.73558181, Root 2: 1720.952951, Root 3: 176875.3257. Confirm no fused/split rendering artifact. Identify which root corresponds to m_c = 1273 MeV physical mass after RG running. #SuperGrokTOE #CharmCubic #v1275fix