Narrative analysis
PT means Perseroan Terbatas, which translates to "Limited Liability Company" in Indonesian. Untaian means "strings", and is refering to the "silk" theme.
PT Untaian is the company responsible for the invention of Mycele, a silk-derived space material, which is used to build the space elevator in the set.
"Life's building blocks" indicates that this is the first corporation to build space materials out of organic matter.
"The Looming future" is a play on words with "Loom", the equipement used to weave textiles, while implicitely evocating words like "glooming" (this is a corporation after all) or "blooming" (still in the plant theme)
The illustration shows a HQ made with Mycele, and appears "woven" into construction. I think you can also see the foundation of the space elevator in the background.
The effect lets you "grow" your cards over time, rather than producing them through industrial means, adding to the "building through organic components" theme rather well. As for the hand limit condition, I think Jinteki associates hand-trashing with a theme of "Natural selection", and "Bio-engineering through culling of the weak". This would mean that, to achieve "organic self-growth", PT Untaian has to maintain a certain level of "biological purity" in their product, requiring frequent "genetic selection".
Pretty straightforward design, but very elegant !