Submitted to Foundations of Physics, March 20, 2026 The identification of quantum vacuum energy density ρ_vac with the cosmological constant Λ, proposed by Zel'dovich in 1967, has produced a discrepancy of 55–120 orders of magnitude between theoretical estimates and observational bounds. This paper reviews and synthesizes five independent theoretical frameworks in which Λ and ρ_vac are treated as physically distinct entities. The approaches surveyed include: (i) geometric reformulations of general relativity in which Λ emerges as an integration constant (trace-free/unimodular gravity, Codazzi-equation formulations, conformal Killing gravity, Kaloper–Padilla vacuum energy sequestering); (ii) thermodynamic and condensed-matter analogies (Volovik) showing that vacuum energy is governed by macroscopic boundary conditions rather than zero-point fluctuations; (iii) renormalization-group methods demonstrating that ρ_vac runs dynamically with the Hubble rate (Solà Peracaula and collaborators); (iv) the Quantum-Kinetic Dark Energy (QKDE) effective-field-theory framework (Brown, IJMPD 2026), in which a time-dependent scalar kinetic normalization K(χ) carries all dark-energy phenomenology while the Einstein–Hilbert metric sector and the Planck mass remain unmodified (α_B = α_M = α_T = 0, α_K > 0); and (v) conceptual and foundational analysis of the assumptions underlying the Zel'dovich identification (Rugh–Zinkernagel). The paper develops key mathematical results including: a proof that Λ arises as an integration constant in trace-free gravity; the demonstration that QKDE preserves GR-like linear phenomenology (Φ = Ψ, μ = Σ = 1, c²_s = c²_T = 1); a discussion of Weinberg's no-go theorem and how the reviewed approaches sidestep it; and a synthesis theorem assembling the five lines of evidence into a unified logical structure. Falsifiable null predictions are identified: any statistically significant detection of μ ≠ 1, Σ ≠ 1, nonzero gravitational slip, or non-luminal tensor propagation at late times would lie outside the QKDE baseline. This is Paper #1a in the research program "What If the Vacuum Gravitates Locally? Separating Cosmic Expansion from Quantum Vacuum Energy" (Institute of Integrative and Interdisciplinary Research, Toronto / Information Physics Institute, Gosport). Recommended for submission to Foundations of Physics. KEYWORDS:cosmological constant; vacuum energy; quantum field theory; general relativity; effective field theory of dark energy; running vacuum; unimodular gravity; QKDE; Kaloper-Padilla sequestering; degravitation; Hubble tension LICENSE:Creative Commons Attribution 4.0 International (CC BY 4.0) RELATED IDENTIFIERS:• References: DOI 10.1142/S0218271826500069 (Brown, QKDE, IJMPD 2026) — is cited by this upload• References: DOI 10.1140/epjc/s10052-024-13694-4 (Feng & Chen, EPJC 2024) — is cited by this upload• References: DOI 10.1140/epjc/s10052-022-10920-1 (Moreno-Pulido & Solà Peracaula, EPJC 2022) — is cited by this upload COMMUNITIES:Astronomy and Astrophysics; Cosmology; Theoretical Physics GRANTS:No external funding. ADDITIONAL NOTES:The QKDE framework of D. Brown is incorporated with the author's permission (personal communication, 2026). AUTHORS:Kriger, Boris (ORCID: 0009-0001-0034-2903)