AbstractWe live in four dimensions. We always have. We prove that no observer can know this from within.Within the K₅ programme, every physical system — every atom, every observer — is an integral part of a four-dimensional simplicial substrate, the pentachoron Δ⁴. We model the observer not as a fragment of the pentachoron but as a viewpoint: a vertex w of Δ⁴ — the present — from which the perceived world is the full subcomplex Δ_{V{w}} spanned by the four remaining vertices. The observer is complete; its blindness is perspectival, not structural.Three algebraic results then follow. Simplicial Blindness (Theorem 4): the perceived dimension is exactly min(n−1, 3), saturating at three. Informational Isolation (Theorem 8): the closed star of the viewpoint vertex has empty intersection with the perceived world; the chain complex C*(Δ_S) receives zero information from w. No inference of the four-dimensional structure is possible from within. Symmetry Indistinguishability (Theorem 10): the automorphism group S₅ acts transitively on equal-size vertex subsets, making all perceived worlds isomorphic to Δ³. An internal observer cannot determine which vertex is the viewpoint, nor even that one is the viewpoint. A fourth result, Invariant Opacity (Theorem 13), shows that every standard computable simplicial invariant — f-vector, Euler characteristic, Betti numbers, graph Laplacian spectrum — is identical across all five perceived worlds.Together these results establish that three-dimensional perception is not a biological adaptation, a compactification artefact, or an anthropic selection effect: it is a theorem of simplicial topology. The limitation is not in our eyes or our brains — it is in the algebraic structure of what it means to observe from within rather than from outside. The 16 invisible simplices (those touching the viewpoint) equal exactly 5² − 3²: the Pythagorean deficit between the whole (K₅) and the part (the observer), identifying the kernel of perception with the gravitational exponent derived in P23. All results are verified by an exhaustive companion script (134 tests, 0 failures).