The Holographic Dimensional Reduction Theorem on the Truncated Cubic Honeycomb: A Fisher-Information-Action Variational Proof That Massive Defects Collapse from the 3D Bulk onto the 2D Octagonal Matter-Face via Topological String-Tension Minimization

The canonical Holographic Circlette framework anchors many substrate-level results (inverse- square Coulomb law, hydrogen Lamb shift, helium-4 binding energy, baryon octet masses) on a 2D-boundary projection of the 3D Truncated Cubic Honeycomb (TCH) substrate via the HolographicDimensionalReductionTheorem(ANCHOR§15item77). Theoriginalanchoring established the closure structurally but required as a sub-leading target an explicit bCFT- trace computation demonstrating the topological-string-tension drive forcing 3D-volume → 2D-domain-wall collapse. We close this target via the canonical Fisher-Information-Action minimization combined with the topological string-tension Lagrange-multiplier mechanism of the Variational Catastrophe Theorem (ANCHOR §15 item 89 closure 2026-05-20). Direct evaluation of the Fisher Information Action SI [γ] at two candidate defect positions — inside the 3D bulk and on the 2D octagonal matter face — yields the strict inequality S(2D) I <S(3D) I for any non-degenerate localized defect on the canonical TCH cell. The canonical variational principle therefore selects the 2D-boundary configuration as the substrate-level ground state. The topological string tension Tstring = ΛQCD literally squeezes the 3D wavefunction flat against the 2D domain wall by precisely the same canonical Perron–Frobenius + Anderson- localization mechanism (§15 item 89 closure) that produces QCD confinement, gravitational restoration, and chiral-condensate vacuum stabilization. This note closes ANCHOR §15 item 77 at Locked tier and establishes that the Holographic Dimensional Reduction Theorem is the spatial-localization sector of the canonical Variational Catastrophe Theorem applied to the canonical asymmetric walk operator W= S·Con the TCH substrate.