Yes: “general conceptual proposition” → specific American claim

Exactly.

Your structure can be:

Step 1 — General conceptual framework

Legal citizenship and lived citizenship are analytically distinguishable.
— Smith

Step 2 — General historical-sociological proposition

Ideas about social and civic status can be historically developed and can influence how formal legal equality is experienced.
— needs an appropriate source specifically supporting this proposition.

Step 3 — American historical evidence

In the United States, racial ideas developed under slavery continued to influence the social position of formerly enslaved African Americans after emancipation.
— needs historical evidence specifically about this.

Step 4 — Your synthesis

Thus, emancipation could establish genuine legal freedom without immediately producing equal lived social, political, and economic standing.

That is a very strong methodological structure because each citation is doing a clearly defined job.