Quantum Structural Theory of Harmony (QSTH X.0) — Entropic Admissibility and Stabilizable Structure From Effective Landscapes to the Separation of Admissibility from Sector Selection

Description QSTH X.0 develops a bounded theoretical audit of entropic admissibility and stabilizable structure. Its central question is whether a nonzero, locally stabilizable branch can exist without its structural or sectoral identity being inserted into the model in advance. Within a one-dimensional even Landau-type witness, the work derives the conditions for the existence of nonzero nondegenerate local minima and separates local stability, metastability, coexistence, and global energetic ordering. It then shows that if the compared sector functionals are identical, amplitude-level admissibility and local stability alone cannot rank sector identities. Physical sector selection therefore requires additional information specified before the outcome, such as a derived coupling, initial or boundary conditions, fluctuation dynamics, or another physically grounded sector-resolving mechanism. This is formulated as a restricted identifiability result, not as a new universal theorem of physics. A second objective is to separate two uses of effective entropy. The phenomenological quantity S_eff(phen) = ΔS_coh − ΔS_red is distinguished from the microscopic signed relative-entropy contrast S_eff,σ(micro) = C_σ − R_σ, defined only within a restricted conditional-expectation framework. No constitutive identification between the two is assumed, and the microscopic quantity is not promoted to a universal force, entropy-production law, or hidden dynamical motor. The work also introduces a strict distinction between Λ_lock(gate), understood as a logical conjunction of closure gates, and Λ_lock(thr), a possible future physical threshold or mechanism that remains to be derived. X.0 can contribute the amplitude-admissibility gate, but it does not by itself close the physical Λ_lock mechanism. An independent numerical recognition protocol (NRP) further shows that a preferred harmonic or multipolar scale is not identical to residual symmetry: characteristic scale and structural identity must be treated as distinct objects. Standard Landau algebra, spontaneous-symmetry-breaking logic, relative-entropy decompositions, and isotropy-subgroup theory are not claimed as new results. The contribution of QSTH X.0 lies instead in the methodological synthesis of these ingredients into an explicit anti-forcing audit: admissibility establishes that a branch may exist; physical identity must still be earned by an independently specified mechanism. The empirical branch X.0B/BASE remains open and separate. Its future outcome must not be used to retroactively tune the theoretical model presented here. Notes Epistemic status: theoretical and methodological audit within a declared model class. Not claimed: a universal law of entropic selection; a universal entropy-production principle; a constitutive derivation of S_eff into the Landau coefficients; a universal sector selector; or a derived physical Λ_lock threshold. Open continuation: X.0B/BASE empirical branch; X.1 phase dynamics and sector stabilization; X.C physical closure of the interface.