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Ben Kaminsky (Jul 21 2026 at 02:11):Conjecture.
Expressiveness/Verifiability/Tractability Trilemma. Every deterministic computational model is fundamentally constrained by a three-way tradeoff among expressiveness (geometric or semantic generality), verifiability (algebraic checkability or formal runtime assurance), and tractability (algorithmic or computational efficiency). These attributes shall satisfy the following trilemma:
No system can simultaneously maximize all three properties. For any given model, at most two of the three can be optimized beyond a critical threshold, while the third must necessarily be sacrificed. Formally, the achievable combinations of these properties are bounded by a 2-dimensional simplex in the space of attributes. The precise tradeoff is determined by the system’s local symmetries and structural constraints.
So I'm developing a conservation law for physical computational behavior. Right, so, uh, basically, this is like the CAP theorem but for programming languages/physical computation. This isn't phrased in particularly categorical language per se right now, but I think people here may appreciate the impulse.
A working version of the paper outlining the thesis can be found here.
I ask people not to share this result outside of this arena for the time being, but I would like to know what people might think about this for the foundations of programming languages/etc. Also. Regarding the fact that parts of this paper can be read as contentious...Topos' stated mission does say:
Pioneer a new mathematical systems science that rigorously addresses fundamental questions about the nature of communication, cooperation, and collective sense-making.
I came up with this a while ago. I was not very familiar with CT at the time when I wrote this down. But I think it does match what people here may be looking for.