Heavy-Quark Effective Theory as Nyquist–Shannon Aliasing: The Strange-Sector Hadron Spectrum from a Discrete Substrate

Audit note. The K^*/K mass-difference match at 398. 0 MeV is exact only conditional on the choice of light-quark orbital geometry. This paper identifies that geometry as the ``C₈ P₇ Dirichlet collapse'' for K^* and P₂ for K, justified structurally by the requirement that pseudoscalar-to-vector spin-flips emerge natively from substrate topology without ad-hoc angular-momentum operators. The geometric assignment is a single point in a discrete topology space of \!3--4 available pinned-walk adjacency choices (P₂, P₅, P₆, P₇, P₈ and variants) ; the formula freedom is bounded but non-trivial. Per §16. 3 classification, the result sits as a tight match conditional on a discrete topological choice, not as a fully zero-degree-of-freedom prediction. The strength of the result lies in the simultaneous locking of both K and K^* geometries by the uniform +28 MeV offset --- a constraint that In continuum quantum field theory, Heavy-Quark Effective Theory (HQET) is a mathe- matical 1/mQ expansion that becomes accurate when mQ ≫ΛQCD. On a discrete substrate, HQET is a hard physical limit: when a quark’s chiral phase rotation frequency exceeds the lattice clock rate, the Nyquist–Shannon sampling theorem dictates that the signal aliases, adiabaticity breaks, and the wavefunction is forced into Anderson localization on a single Q3 matter cell. We apply this identification to the canonical Holographic Circlette substrate Z3 ⊗Q3 on the 4. 8. 8 Archimedean tiling and obtain the strange-sector hadron spectrum at zero free parameters. Anchoring the static strange defect mass via the η (548) at L= 1 pseu- doscalar s¯ sstring, with the previously-derived string tension σ= (4/3) ΛQCD (the substrate analytical value), gives Ms = 52. 55 MeV. Three further observables follow without additional parameters: K± at L= 1 asymmetric hybrid via a P2/Dirichlet pinned walk (522 MeV, +28 MeV vs experiment) ; K∗ (892) via a C8 matter-octagon orbital collapsing to P7 adjacency at the strange-defect Dirichlet vertex (920 MeV, +28 MeV) ; ϕ (1020) at L= 2 static s¯ s (990. 5 MeV, −29 MeV). The decisive consistency check is the K∗/K mass difference: predicted √2 (2 cos (π/8) −1) ΛQCD = 398. 0 MeV vs experimental 892−494 = 398. 0 MeV — exact to the rounding of the inputs. The uniform +28 MeV over-prediction across both heavy-light states (with the symmetric vector under-predicting by−29 MeV) is therefore not a geomet- ric error but a substrate-level kinematic offset: the finite-mass recoil correction softening the rigid-Dirichlet boundary. We identify this∼28 MeV as a discovered universal coupling con- stant of the framework, structurally distinct from any fitted parameter. The charmonium spectrum — which fails the same string-ladder formula for J/ψ— is explained by ANCHOR §9. 7’s silver-ratio band cutoff Emax = δ4 S /4·ΛQCD ≈2820 MeV, above which states enter a topologically smeared regime distinct from the macroscopic gauge-string ladder.