Artian Inertial Mass Operator and Three-Readout Spectral Equivalence Theorem

When does the coefficient in Newton's second law become a finite spectrum rather than an inserted input? The paper constructs a positive finite source operator from funded completed-event classes. For a finite region \( R\), \[ BR = ∑_{p∈ PR} ι_p\!({ Qᵛⁱˢ_p}{2π}), 0 BR | PR|\, I. \] The quotient set \( PR\) counts funded physical completions once. Copying a record does not change the operator. An observed mass can test an eigenvalue after construction; it cannot create one. For a source eigenstate \(|b\), the source rest branch is \[ H_b( p) = √c^2| p|^2+b^2E_*^2, . ∂^2H_b/∂ p_i∂ p_j |ₚ₌₀ = {δᵢⱼ}{b m_*}. \] Its inverse curvature therefore supplies the inertial coefficient rather than presupposing it: \[ F=bm_*\, a+O(v^2/c^2). \] The same A1 source action in a weak external lapse gives \[ L_b = -bm_*c^2 +12bm_*v^2 -bm_*Φ+⋯, Mₚₐₛₛ=Mᵢₙ=bm_*. \] With the independently declared A2 endurance-source map, the central three-readout identity is \[ { B = { Hᵣₑₛₜ}{E_*} = { Mᵢₙ}{m_*} = { Mₚₐₛₛ}{m_*} = { Mactive}{m_*} = t\,ΓA2 }. \] For a full interacting state, binding energy is transported through all three mass readouts with one sign: \[ Δ Mᵢₙ = Δ Mₚₐₛₛ = Δ Mactive = {Δ Ebind}{c^2}. \] The action ledger is explicitly typed. A degree-one canonical phase turn and one positive A6 capacity token are related but are not the same object: \[ Scan=2πν, C_A=∑_j|ν_j|. \] The theorem also fixes its own boundary: A6 and A7 define the admissible finite operator class, but do not by themselves choose the complete particle-mass population. That remaining sector-population problem is exposed as a typed theorem interface rather than hidden in a fitted coefficient. Machine certificate: 11/11 deterministic checks pass, including the funding quotient, finite spectrum, free-branch Hessian, weak-lapse equality, binding transport, local-versus-extensive ceiling, constructor firewall, typed action/capacity distinction, and nine negative mutations. Stable anchors: paper concept DOI; Main Book v10.01; Inertia Theorem lexicon entry; Derivation Atlas; source/readout ontology.