The Ledger and the Gate: A Reverse-Derived Möbius Cosmology — Five theses recovered bottom-up from validated engineering invariants — finite channels, relational existence, append-only time, structure as anti-regress guard, and the entitled observer

This paper makes no claim of new physics. Every load-bearing statement in it is either (a) an established result of physics or information theory, (b) a live but respectable interpretation debated inside physics, (c) an active mainstream research program, or (d) an explicit definition. Each of the five theses below carries one of these four status labels, and the label is part of the thesis: quoting a thesis without its label misquotes it. The paper's single original contribution is directional. The earlier Möbius corpus built a cosmology top-down — from a speculative, self-declared poetic origin (Reflective Cosmology R3) downward through a mathematical layer (MUSE) toward engineering. This paper runs the derivation the other way. It starts from three engineering systems that have been built, frozen, measured, and audited, extracts the invariants that make them work, locates each invariant's exact counterpart in established physics, and only then assembles a world picture. A cosmology obtained this way cannot outrun its anchors: it is a selection and organization of known physics, i.e. a world model in the predictive-model sense, not a new theory of the universe. One inference direction is declared forbidden at the outset and again in §6: the engineering successes documented here validate nothing upstream of physics. They do not confirm, support, or even weakly suggest any speculative construct of the prior corpus. The valve points one way. --- AI co-observer: Claude Fable 5 (Anthropic) — drafting and derivation partner; the registered author is the human author alone.