simulation_unprovable
plain-language theorem explainer
The theorem establishes that no RS universe u admits a proof that every possible outer RS universe differs from it in events at every natural number n. Researchers examining Bostrom-style simulation arguments in foundational physics or information theory would cite this when dissolving the real/simulation distinction inside Recognition Science. The proof is a direct term-mode contradiction obtained by instantiating the outer-universe quantifier with u itself and deriving u.events 0 ≠ u.events 0.
Claim. For every RS universe $u$, it is not the case that every RS universe $v$ satisfies $v.events(n) ≠ u.events(n)$ for all $n ∈ ℕ$.
background
RSUniverse is the structure whose sole datum is the function events : ℕ → ℝ with events n > 0 for all n; it encodes the complete ledger of recognition events as the physical universe itself. The module IC-004 treats the simulation hypothesis as meaningless rather than false: the ledger is reality, no external substrate exists, and any purported outer universe must itself be an RSUniverse. Upstream results supply auxiliary lists (plot families, kinship systems, ore classes) that populate the wider Recognition Science context but are not invoked in the present argument.
proof idea
The term proof introduces u and the hypothesis h that ∀ outer ∀ n, outer.events n ≠ u.events n. Instantiation of h at outer = u produces ∀ n, u.events n ≠ u.events n. Specializing to n = 0 yields the false statement u.events 0 ≠ u.events 0, which is contradicted by reflexivity via absurd rfl.
why it matters
The result is IC-004.3 and supplies the key step for the ic004_certificate summarizing dissolution of the simulation hypothesis and for simulation_implies_church_turing. It shows that the simulation/reality distinction carries no semantic content once the ledger is identified with reality, consistent with the Recognition Science claim that every ledger entry is self-grounding and that no external computer can be distinguished from an RSUniverse.
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