Logo family for a construction group — parent + 2 divisions

We run brand and document production for a US construction group: a general-contracting parent, a division that builds hyperscale AI data centers, and a division that manufactures steel and post-frame buildings. The group is retiring its current mark. We need one logo family across the three brands. Most of the identity work is already done. You are designing the marks. Already locked (do not re-explore) Color palettes per brand, with hex values Typography: Archivo family across the group All three websites are built; staging links provided Names are final. You receive them after a short NDA. The job Design the shared root symbol and the rule by which it varies per division, then draw all three marks from it. The three symbols must read as one family at a glance, and each must survive at 16 px in one color. This contract: $500 fixed Three distinct directions, one of them a stretch. For each direction: The idea in one sentence, and the variation rule in one sentence Parent: symbol + horizontal lockup in full color, one-color, and reversed, with a scale row from 16 to 256 px Both divisions: symbol + lockup in one color All three symbols side by side at 24 px A short rationale paragraph To apply — required; proposals missing any of these are skipped Link one identity system you designed where a parent and at least one sub-brand share a root mark. State that system's variation rule in one sentence. Link one mark of yours that holds at 16 px in one color. Confirm the structure: boards only in this round; masters and IP transfer in the production contract. NO AI GENERATED MARKS