Where does “mum” come from?

I need to flag an issue: the chain provided (English mam → Ancient Greek χρυσός) doesn't make semantic sense. Ancient Greek χρυσός means "gold," which has no apparent connection to "mam" (typically meaning "mother" in English dialects). This chain appears incorrect or the headword/meaning pairing doesn't match the etymology provided. I cannot write an accurate one-sentence summary without a valid etymological chain. Could you verify: 1. Is the headword "mum" or "mam"? 2. Is the chain complete and correct? 3. What is the actual meaning being traced?

mum (English): Mother; ma'am; a term of respect for an older...

Definitions

  1. Mother; ma'am; a term of respect for an older...

Ancestry of “mum”, step by step

mum traces back through 3 separate lines of ancestry.

via English chrysanthemum

StepLanguageWordMeaning
1EnglishchrysanthemumAny of many flowering perennial plants, of the...
2Latinchrysanthemum
3Ancient Greekχρυσάνθεμονgold-flower; immortelle; buttercup
4Ancient Greekἄνθεμονflower, rosette

via Middle English mum

StepLanguageWordMeaning
1Middle Englishmum

via German Mumme

StepLanguageWordMeaning
1GermanMummedative of Mumm; mask

Words derived from “mum

Every word from Ancient Greek ἄνθεμονEvery word from Ancient Greek χρυσάνθεμονEvery word from Latin chrysanthemum