Here's my take on Bitcoin's claims:

Pyramid scheme? Yes. Bitcoin is a pyramid scheme from an investment
perspective. Enrolling others to invest in Bitcoin is what provides a return to
earlier investors. Bitcoin is also a legitimate going concern for businesses
who collect fees for providing foreign exchange and transaction oriented
services using the Bitcoin system. Unfortuntately, it's not possible to
separate the pyramid scheme from the legitimate service provided by the Bitcoin system.

Equity? No. If Bitcoin dissolved, it has no tangible assets or reserves to
return. In contrast, if a company dissolves, it's assets get returned to
shareholders.

Commodity? No. Bitcoin has no economic value like silver, wheat, oil, etc.

Currency? No. A useful currency has stable value relative to other currencies
and is a universal medium of exchange within an economy. Bitcoin is neither.
Fiat currencies like the USD are backed by the issuing country with gold
reserves, oil reserves, land, taxes, etc.