Simplicial blindness: Three-dimensional perception as a combinatorial theorem of the pentachoron

We 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 as the full subcomplex Δ_S induced by a proper vertex subset S ⊂ V, |S| < 5. Three algebraic results then follow. Simplicial Blindness (Theorem 1): the perceived dimension of Δ_S is exactly min(n−1, 3), saturating at three. Informational Isolation (Theorem 2): the closed star of every absent vertex has empty intersection with Δ_S; the chain complex C*(Δ_S) receives zero information from the missing vertices. No inference of the four-dimensional structure is possible from within. Symmetry Indistinguishability (Theorem 3): the automorphism group S₅ acts transitively on equal-size vertex subsets, making all four-vertex subcomplexes isomorphic to Δ³. An internal observer cannot determine which vertex is absent, nor even that one is missing. 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 be a part rather than the whole. All results are verified by an exhaustive companion script (75 tests, 0 failures).