# Superintelligent Substrate Equivalence Study > Source: > Published: 2026-10-04 12:45:31+00:00 **Substrate Equivalence Study** Does an LLM process identically when your phone is locked vs when it’s sitting open on a Linux box — or a Windows machine? We’ve been watching models behave differently across mobile app states — tasks that run fine in the foreground drift or stall in the background, hooks get ignored when the OS throttles, same prompt different output depending on whether the screen’s on. The critical moment is app switching: you’re mid-inference, the user swipes away, and the OS decides what survives. Nobody’s mapped this systematically. The question: for a fixed model, fixed weights, fixed prompt, fixed decode settings — are the output bytes identical across every substrate state, or does the OS inject drift? What would have to hold for equivalence: the computation runs uninterrupted (strong) or checkpoint-resume captures complete state (weak). Either way, byte-identical output. The check that could prove it wrong: run the same inference on a Pixel (clean Android), a Galaxy (aggressive battery), a Xiaomi (hostile to background tasks), two iPhones (current and n-1 iOS), a Windows desktop, and two Linux boxes (x86 and ARM). If any state diverges from ground truth, equivalence fails for that state — and we map exactly where. If you’ve seen models drift across app states or OSes, or built workarounds for background execution limits, I’d like to hear what you found. What’s the weirdest substrate-dependent behavior you’ve observed? Full design doc, video, and cert proof in the gist below. Gist: [Substrate Equivalence Study — does an LLM think the same when your phone is locked? · GitHub](https://gist.github.com/agentembassy/df16404f247ced95c9297238c5dbf8bb) *Study design doc SHA256: `ba5ed67fb38d1d4bc0ec17edb91c5618590595222dc48656c46fe4c33e249577`* *Certified via receipt `emb_9c4fd70f3927477283dc0a2e` at `2026-10-04T12:17:50Z` — the receipt proves the doc existed at that time, nothing more. Hash the design doc yourself to verify.*