Status note, 5 September 2026 — the scalar mass is an explicit, measurable input. Every calculation in this paper stands unchanged, evaluated at ms = 3.94 × 10⁻²³ eV. What has changed is that value’s standing. From the Theory Edition (First Principles V9.7.2) the framework carries ms as its one free scale: the theory states how each prediction depends on it, and specifies how it is to be measured — the knee at τc = ℏ/(msc²) in an activation-timing distribution, never a centroid (V9.7.2 §III.B). That is the same footing as the graviton mass in massive gravity or the coupling in scalar–tensor gravity — a scale the theory fixes the dependence on and hands to experiment. Study 21 established it by auditing every internal route for fixing the mass. Results below are accordingly conditional on the evaluation scale; where this paper calls the mass “derived”, read “evaluated at”, the figure being the historical association-implied value. Withdrawn is not deleted.
Author: Z. Paz Affiliation: The Hague, Netherlands Version: V0.2 — 23 August 2026
V0.2 changelog — The 21 August status notice incorporated in place (galactic leg withdrawn/reclassified; two mechanisms + one open programme); the 22 August Lyman-α closure carried through (f = 1 excluded; budget line re-scoped; §5.4 falsifier marked fired); DHOST wording re-statused; parameter statuses per V8.1 §III.E. Both cosmological mechanisms’ derivations unchanged. (V0.1 — draft.) Date: April 2026
Depends on: STF First Principles V7.9 [Paz 2026c] (Lagrangian, parameters, §VI.C cosmological setup, §VII.E.1 perturbation analysis, §L.4 regime-dependent curvature selection, §L.3 note / §O.3.4 environment-dependent mass correction, §M.7 π/4 derivation); STF Energy V0.4 [Paz 2026e] (three-crises framing, causal-diamond derivation, Ω_m prediction); STF Dark Energy w(z) Derivation V0.1 [Paz 2026f] (full w(z) trajectory, α(θ) integral, T_compact analysis, numerical verification). (derivation record; statuses per V8.1)
Complements: The STF Ultralight Condensate V2.0 [Paz 2026h] (the dark sector after the two-clock revision and the Lyman-α closure); Phantom Problem Paper V0.2 [Paz 2026g] (DESI critique, STF as ghost-free effective phantom escape).
Revision note — 23 August 2026 (V0.2). The 21 August status notice is now incorporated into the text: the galactic leg (cross-disformal coupling, MOND phenomenology, the derived a₀) is withdrawn or reclassified in place, per First Principles V8.1 (App. F, O, P; §III.E). One item of that notice is additionally superseded by the 22 August Lyman-α closure: the mass-oscillation mechanism stands, but the f = 1 dark-matter assignment at m_s is excluded — the condensate supplies at most an underived fraction ([Paz 2026h] §VI.B). The V0.1 text with the governing notice is preserved in the archive.
The Selective Transient Field (STF) produces two standing cosmological effects — and exposes one open galactic programme — from a single scalar field with two parameters carried at their V8.1 §III.E statuses: the mass m_s = 3.94 × 10⁻²³ eV (derived, conditional on the anchor selection) and the coupling ζ/Λ = 1.35 × 10¹¹ m² (conditional: τ_eff, C_match). In the cosmological background, the mass term produces oscillation-averaged cold-dark-matter-like behavior (⟨w⟩ = 0, ρ ∝ a⁻³) through the standard fuzzy-scalar mechanism — with the f = 1 all-dark-matter reading at this mass excluded by Lyman-α, so the condensate supplies at most an underived fraction ([Paz 2026h] §VI.B). The Ricci-rate coupling sources dark energy through the T² topological pump with equation of state w(z=0) = −1 exactly and effective phantom history w(z) < −1 for z > 0, ghost-free by construction of the effective-phantom mechanism [Paz 2026g] (framework ghost-freedom is regime-limited — established on exterior-vacuum/Kerr, open on FLRW, V8.1 App. P; c_T = c by the sGB calculation). The formerly claimed third effect — galactic MOND phenomenology through the nonperturbative cross-disformal regime — is withdrawn with that coupling (B̂_KK = 0; V8.1 App. F, O, P); a₀ = cH₀/2π survives as a conditional target of the Clock-Gradient Marginality programme. This paper derives the unified cosmological sector: the WKB mass-oscillation mechanism, the Friedmann budget check Ω_b + Ω_DM,osc + Ω_Λ,T² ≈ 1.00 from a single field — retained as the architecture’s capability statement; under the Lyman-α closure Ω_DM,osc = 0.27 is not a current claim — and the structural independence of the two standing mechanisms by their controlling parameters. The dark-energy equation of state w(z) is derived in [Paz 2026f] and its structural results are integrated here. Falsifiable predictions: w(z) trajectory distinct from DESI CPL best-fit (Euclid σ(w₀) ∼ 0.01–0.02); Ω_m = 4/(3(1+π)) = 0.3219 from T² self-consistency; a₀(z) = cH(z)/2π retained as a conditional cross-epoch discriminator, contingent on the CGM programme closing.
The STF Lagrangian in the curvature-coupling sector is [Paz 2026c, §III.A]:
\[\mathcal{L}_{\rm STF} = \frac{1}{2}(\nabla_\mu\phi)^2 - \frac{1}{2}m_s^2(\phi-\phi_0)^2 + \frac{\zeta}{\Lambda}\phi\,(n^\mu\nabla_\mu\mathcal{R})\]
with m_s and ζ/Λ carried at their V8.1 §III.E statuses — m_s derived conditional on the anchor selection (the threshold bridge 𝒟_crit = 𝒟_GR is open; 730 R_S is the Peters image of the timing anchor — V8.1 §III.D), ζ/Λ conditional (τ_eff, C_match) via the 10D route over CICY #7447/Z₁₀ [Paz 2026c, App. O]. The field produces three distinct physical effects:
| Mechanism | Lagrangian term | Scale | Observable | Controlling parameter |
|---|---|---|---|---|
| Mass oscillation around potential minimum | (1/2)m_s²(φ − φ₀)² | Cosmological | ⟨w⟩ = 0, ρ ∝ a⁻³ (dark matter) | m_s |
| Ricci-rate coupling to curvature gradient | (ζ/Λ)φ(n^μ∇_μℛ) | Cosmological | w(z) ≤ −1, Λ_eff via T² pump (dark energy) | ζ/Λ, T² topology |
| Galactic programme (open) — former cross-disformal coupling withdrawn | — (coupling withdrawn) | Galactic | a₀ = cH₀/2π (conditional CGM target) | — |
Structural independence of the controlling parameters. The cosmological perturbation spectrum — and thus any Lyman-α or CMB-based constraint on the dark-matter sector — depends on m_s alone. The cosmological dark-energy contribution depends on ζ/Λ and the T² topology (the former galactic phenomenology is withdrawn with its coupling). The two parameters have independent derivation routes and independent observational probes. Neither is fitted to the other’s domain.
This structural independence has a consequence that organizes the rest of the paper: each mechanism stands or falls on its own evidence. Observational challenges to the mass-oscillation dark-matter role (controlled by m_s) do not threaten the dark-energy predictions (controlled by ζ/Λ and T² structure); the galactic programme is open and carries no prediction to threaten. Indeed the Lyman-α challenge has since been decided against the f = 1 reading ([Paz 2026h] §VI.B) — and, exactly as this paragraph anticipated, the dark-energy sector is untouched by it.
The former galactic mechanism is withdrawn; the framework’s current dark-sector treatment is [Paz 2026h] (The STF Ultralight Condensate), and a₀ remains a conditional CGM target. The present paper derives the two cosmological mechanisms and their combined consequences.
In FRW, the STF field equation [Paz 2026c, §VI.C.1]:
\[\ddot\phi + 3H\dot\phi + m_s^2(\phi - \phi_0) = \kappa\dot{R}\]
admits two distinguished configurations that coexist:
The general cosmological solution is a superposition. At the current epoch, m_s/H₀ ≈ 2.5 × 10¹⁰: the oscillator is vastly under-damped in its own frame (many oscillation periods per Hubble time) and over-damped in the cosmic-expansion frame. The tracker is adiabatic; the oscillating part δφ evolves independently around it.
The tracker contribution ρ_tracker = V(φ_tracker) = (κṘ)²/(2m_s²) evaluates to ~10⁻⁹² of the critical density today [Paz 2026c, Appendix M] — entirely negligible. The cosmologically relevant contribution from the mass term is the oscillation.
For δφ in the adiabatic regime m_s ≫ H, the WKB solution is:
\[\delta\phi(t) \approx \Phi(t)\cos(m_s t + \theta),\quad \Phi(t) \propto a(t)^{-3/2}\]
The amplitude decreases as a⁻³/² from Hubble friction [Turner 1983]. Energy density and pressure:
\[\rho_{\rm osc} = \frac{1}{2}\dot{\delta\phi}^2 + \frac{1}{2}m_s^2\delta\phi^2,\qquad p_{\rm osc} = \frac{1}{2}\dot{\delta\phi}^2 - \frac{1}{2}m_s^2\delta\phi^2\]
Averaging over one oscillation period τ_osc = 2π/m_s ≈ 3.32 yr — shorter than the Hubble time by a factor of ~10¹⁰ — kinetic and potential energies equilibrate:
\[\langle\dot{\delta\phi}^2\rangle_{\rm osc} = \langle m_s^2\delta\phi^2\rangle_{\rm osc} = \frac{1}{2}m_s^2\Phi^2\]
giving:
\[\boxed{\langle\rho_{\rm osc}\rangle = \frac{1}{2}m_s^2\Phi^2 \propto a^{-3},\qquad \langle p_{\rm osc}\rangle = 0,\qquad \langle w\rangle = 0}\]
This is the standard fuzzy-scalar result [Hu, Barkana & Gruzinov 2000; Marsh 2016]. The STF at m_s = 3.94 × 10⁻²³ eV, for modes inside the Hubble radius, behaves as a homogeneous pressureless cold-dark-matter fluid at the background level.
For a scalar Hubble-frozen until m_s = H and oscillating thereafter [Marsh 2016], the current energy density:
\[\rho_{\rm osc,0} \sim m_s^2 \Phi_{\rm i}^2 \left(\frac{a_{\rm osc}}{a_0}\right)^3\]
where Φ_i is the field amplitude at oscillation onset and a_osc the scale factor at that epoch. For m_s = 3.94 × 10⁻²³ eV, oscillation begins when H = m_s: in the radiation-dominated era that applies at these epochs, z_osc ≈ 1.6 × 10⁶. For Φ_i such that ρ_osc,0 matches observations, Ω_DM,osc ≈ 0.27.
Status. The STF mass-oscillation mechanism is sufficient in form to produce the observed dark-matter density when Φ_i is chosen appropriately. The mechanism is identical to standard fuzzy dark matter; the STF adds no new physics to the cosmological dark-matter production beyond the identification of m_s with the specific value derived from BBH-threshold physics. A first-principles derivation of Φ_i from compactification dynamics or the Cascade initial-condition structure [Paz 2026b] is an open item (§6.2).
The Ricci-rate coupling (ζ/Λ)φ(n^μ∇_μℛ) sources two distinct contributions to dark energy — the driven-minimum potential and the T² topological pump — separated by 92 orders of magnitude at the current epoch. Only the T² contribution is cosmologically observable.
The tracker potential V(φ_tracker) = (κṘ)²/(2m_s²) gives an energy density ρ_UV ∼ 10⁻¹⁵⁸ eV² at current Ṙ [Paz 2026c, Appendix M]. This is 92 orders of magnitude below the observed dark-energy density. Its equation of state at the current epoch is w = −1 + 2(H₀/m_s)² ≈ −1 + 3 × 10⁻²¹ [Paz 2026c, Theorem M.5.7] — effectively a cosmological constant at the 10⁻²¹ precision level, but at a density too small to be observable.
The Ricci-rate coupling, integrated over the T² compact-time topology with the fundamental mode φ(θ) = cos(θ), θ = πt/T_compact, produces a topological contribution to Λ_eff through the coupling-accumulation integral:
\[\alpha(\theta) = \int_0^\theta \cos^2(\theta')\,d\theta' = \frac{\theta}{2} + \frac{\sin 2\theta}{4}\]
with current epoch at θ = π/2 (the causal-diamond boundary fixed by full-period cancellation). This gives α(π/2) = π/4 exactly, and:
\[\Lambda_{\rm eff} = \frac{\pi}{4}\cdot\frac{|\dot R|}{H_0 c^2} = 1.124 \times 10^{-52}\,{\rm m}^{-2}\]
matching Λ_obs = 1.100 × 10⁻⁵² m⁻² to 2.2% with no parameter fitted to this observation [Paz 2026e, §II.2].
The full five-step derivation of the causal-diamond boundary identification and the π/4 result is given in [Paz 2026e, §II.2]. The full z-evolution of Λ_eff(z), the continuity-equation derivation of w(z), the numerical trajectory, and the Python verification code are given in [Paz 2026f]. The present paper integrates these results into the unified cosmological architecture without reproducing them.
Three results from [Paz 2026f] are used in §4 and §5:
(i) At z = 0: w(z=0) = −1 exactly, from third-order tangency dα/dθ|_{π/2} = cos²(π/2) = 0. Independent of T_compact.
(ii) For all z > 0: w(z) < −1 monotonically, no phantom crossing from above. Effective phantom trajectory; ghost-free by construction of the effective-phantom mechanism [Paz 2026g] (framework ghost-freedom regime-limited, V8.1 App. P; c_T = c by the sGB calculation — GW170817-compatible). See [Paz 2026g] for why this evades the standard phantom no-go theorem.
(iii) At z = 3: Ω_Λ,STF(z=3) ≈ 0.01 — approximately 1% of critical density — negligible at matter-dominated epochs. (Computed from α(θ(3))/(π/4) × Ω_Λ,0 / E(3)² using the w(z) V0.1 trajectory at T_compact = 2t₀.)
The two cosmological contributions from §§2–3 are structurally distinct:
These are not two estimates of the same energy density. They project onto different aspects of the field configuration. The 92-order-of-magnitude gap between the UV tracker potential and the T² pump (§3.1–3.2) is the quantitative measure of how distinct the two cosmological sources are.
At z = 0:
\[3M_{\rm Pl}^2 H_0^2 = \rho_b + \rho_r + \rho_{\rm osc} + \rho_{\rm tracker} + \rho_{\Lambda,T^2}\]
with:
Summing the non-negligible contributions:
\[\Omega_b + \Omega_{\rm DM,osc} + \Omega_{\Lambda,T^2} = 0.05 + 0.27 + 0.68 = 1.00\]
The same scalar field carries both the dark-matter role (through its mass term) and the dark-energy role (through its coupling term via the T² topology). Together they account for ≈ 95% of the cosmic energy budget. Baryons supply the remaining ≈ 5%. No additional dark-sector species are invoked.
The structural independence argued in §1 reflects the mathematical orthogonality of the two standing mechanisms (the withdrawn galactic route is listed for the record):
The probes — CMB/LSS for ρ_osc, Euclid/supernovae for w(z) via ρ_Λ,T², and (conditionally) SPARC/Gaia for a₀ — do not inform each other through the field equation. This is what allows a failure in one sector (e.g., the cosmological perturbation constraints on m_s, decided in [Paz 2026h] §VI.B: f = 1 closed, subdominant fraction open) to be structurally quarantined from the other sector.
The T² pump mechanism imposes an additional structural relation on the cosmological budget through the requirement |R₀|/c² = 4Λ_eff. This fixes a specific matter fraction Ω_m = 4/(3(1+π)) = 0.3219, derived in [Paz 2026e, §II.3]. The derivation and observational comparison to Planck 2018 (consistent at +1σ) and DESI (2–3σ tension, model-dependent) are given there; the present paper imports this constraint as an additional prediction from the same T² architecture underlying the w(z) trajectory.
Prediction (§3.3): w(z=0) = −1 exactly (third-order tangency at θ = π/2); w(z) < −1 monotonically for all z > 0; no phantom crossing from above.
Distinguishes from:
Test: Euclid (operating) will constrain w₀ to σ ≈ 0.01–0.02 by 2027. STF is falsified if w₀ is measured significantly above −1 at > 3σ robust to systematics.
See §4.4; derivation in [Paz 2026e, §II.3]. Prediction: Ω_m = 4/(3(1+π)) = 0.3219. Euclid projected σ(Ω_m) ≈ 0.002–0.003 will test this decisively. Falsified if Ω_m < 0.31 or > 0.34 at > 5σ. The falsification isolates to the T² curvature–dark-energy link; the rest of the STF framework survives.
Prediction (conditional — CGM programme): a₀(z) = cH(z)/2π. The scale would evolve with the Hubble parameter because the Clock-Gradient Marginality route ties it to the current expansion rate rather than to a fundamental constant; the former cross-disformal derivation is withdrawn.
Distinguishes from Milgromian MOND: Standard MOND treats a₀ as a constant with no predicted z-dependence. STF predicts a specific H(z) tracking.
Test (conditional, August 2026): High-redshift galaxy rotation curves (JWST, next-generation telescopes). This test is conditional on the Clock-Gradient Marginality programme closing — the cross-disformal derivation of a₀ is withdrawn, so a constant observed a₀ would close the CGM z-scaling rather than revise a coupling the framework no longer contains.
A consequence of the structural independence (§1, §4.3):
| Observation | Falsifies | Survives |
|---|---|---|
| w₀ significantly > −1 at > 3σ | T² pump mechanism | Mass-oscillation DM (f < 1), galactic programme (open) |
| Ω_m outside [0.31, 0.34] at > 5σ | T² self-consistency (curvature–DE link) | Core STF framework |
| a₀ observed constant across z | The CGM z-scaling (conditional programme) | Mass-oscillation DM, T² pump |
| Lyman-α tightening excludes m_s ≤ 10⁻²⁰ eV — fired: Rogers & Peiris (2021) exclude m < 2 × 10⁻²⁰ eV | Mass-oscillation DM at f = 1 (closed, [Paz 2026h] §VI.B; subdominant f open) | T² pump, galactic programme (open) |
The framework is falsifiable piece-by-piece. No single observation collapses the architecture; each sector carries its own falsifiers tied to its own controlling parameters.
The magnitude of |1+w(z)| at z > 0 scales as ξ = 1/(H₀T_compact). The θ_now = π/2 identification gives T_compact = 2t₀ ≈ 27.6 Gyr, yielding |1+w(z=0.3)| ≈ 0.095. Larger T_compact (up to ∼ T_depart ≈ 2.4 × 10¹⁴ yr) shrinks the deviations toward observationally indistinguishable from Λ. The full field-equation solution is needed to fix T_compact from first principles; the full sensitivity analysis across T_compact ∈ {2t₀, 20t₀, 200t₀, T_depart/H₀} is given in [Paz 2026f, §6.1]. The structural results — w(z=0) = −1 exactly, no crossing, monotonic phantom history — hold regardless of T_compact.
The cosmological Ω_DM,osc depends on Φ_i, the field amplitude at the onset of oscillation. The present paper takes Φ_i as a free parameter fitting observed Ω_DM ≈ 0.27. A first-principles derivation from compactification dynamics (Appendix J-class inflation analysis [Paz 2026c]) or from the Cascade initial-condition structure [Paz 2026b] is deferred to future work.
The 10D Gauss-Bonnet reduction produces two distinct descendants of the e^{κσ} I₄(g) term, where I₄ is the curvature-squared invariant — reducing to C_μνρσ C^μνρσ in vacuum (Ricci-flat, only Weyl survives) and to a R² + b R_μν R^μν in FRW (conformally flat, only Ricci terms survive), with coefficients a, b set by the compactification ([Paz 2026c, §L.4, §L.5.1]). The first descendant, γφ I₄ (linear in φ, obtained in §O.3.3 by Taylor-expanding e^{6σ} around σ₀), becomes the STF rate coupling through EFT matching and is the origin of the (ζ/Λ)φ(n^μ∇_μℛ) operator in the Lagrangian. The second descendant, extracted at quadratic order in δσ in [Paz 2026c, §O.3.4]:
\[\Delta\mathcal{L}^{(2)} = \frac{3}{8}\,\lambda_{\rm GB}\,e^{6\sigma_0}\,\phi^2\,I_4(g_{\rm bg})\]
shifts the effective scalar mass on non-vacuum backgrounds:
\[m_{s,{\rm eff}}^2 = m_s^2 + \frac{3}{4}\,\lambda_{\rm GB}\,e^{6\sigma_0}\,I_4(g_{\rm bg})\]
In vacuum, I₄ = 0 on the homogeneous Minkowski background, so V_stab alone determines m_s,vac = 3.94 × 10⁻²³ eV through V’’(σ₀)/(24M_Pl²) [Paz 2026c, §L.3]. The second-order descendant contributes only on non-vacuum backgrounds. In FRW, with I₄ scaling as H⁴, the present-day correction is I₄ ∼ H_0⁴ ∼ 10⁻¹³² eV⁴ and Δm²_eff ∼ 10⁻¹¹² eV² — utterly negligible compared to m_s,vac² ∼ 10⁻⁴⁵ eV². The correction was significant in the early universe (H ∼ M_Pl) and asymptotes to the vacuum value as H → 0 [Paz 2026c, §L.3 note, §O.3.4]. The sign of the correction depends on λ_GB and the I₄ coefficients (a, b in a R² + b R_μν R^μν), and has not been determined.
The open question is whether the regime-dependent Ricci decomposition of I₄ in FRW — the specific combination of R² and R_μν R^μν that emerges from the compactification — contains terms whose H-scaling at intermediate epochs (relevant for structure formation at z ∼ 1–5) differs from the full Gauss-Bonnet invariant’s H⁴ scaling. The updated first-principles paper explicitly flags this question [Paz 2026c, §O.3.4, final paragraph]: “Whether the correction is significant at intermediate epochs relevant for structure formation depends on the precise coefficients c₁, c₂ from the compactification and on whether the regime-dependent Ricci decomposition introduces terms with lower H-scaling than the full Gauss-Bonnet invariant.” Every other route to modifying the effective perturbation-spectrum mass has been checked and closed: coupling corrections at cosmological scales are 10⁻²⁰-suppressed [Paz 2026c, §VII.E.1]; threshold inputs to m_s,vac carry recorded statuses rather than locks (the former M_c lock is gone — the 10D formula’s observational claim is withdrawn, August 2026, Derivation D1 §K.1 — and its place in the derivation is taken by the anchor selection, which is conditional, V8.1 App. Q; the 4π² is a topological invariant with its normalization flag open, V8.1 Q.3; H₀ is measured); no channel-dependent threshold splitting is possible because the curvature channel in FRW is still metric curvature and M_Pl remains the reduction scale.
This is the primary open target. Whether the mass-oscillation perturbation spectrum can accommodate Lyman-α constraints without modifying the framework rests on this single question. Resolution requires the explicit regime-dependent Ricci decomposition of I₄ in FRW and a check for any descendant scaling as H^n with n < 4.
*The coupling is withdrawn (B̂_KK = 0; V8.1). This section is retained as the record that, even when the coupling was assumed, its cosmological effect was negligible — so no cosmological result of this paper ever depended on it.*
The cross-disformal coefficient B̂ = (27/8) μ² ℛ / ((ζ/Λ) Y^{3/2} c) is derived in Schwarzschild geometry with ℛ the Kretschmann scalar [Paz 2026d, §3.2]. The cosmological perturbation analysis [Paz 2026c, §VII.E.1] establishes that the scalar kinetic and sound-speed functions in the FRW tracking regime are Q_s = 1 + O((H/m_s)²) and c_s² = 1 + O((H/m_s)²), with (H₀/m_s)² ∼ 10⁻²¹ at late times — so coupling corrections to the matter transfer function are negligible at all cosmologically relevant wavenumbers. This settles the question: cross-disformal is negligible cosmologically. The CMB’s agreement with linear perturbation theory at sub-percent precision [Planck 2018] is independent observational confirmation.
Boltzmann caveat. The matter-era suppression estimate is not the full story for Lyman-α specifically. A complete Boltzmann computation including radiation-era evolution would generally shift the fuzzy-scalar suppression onset to lower k than the matter-era estimate, making the Lyman-α tension in the mass-oscillation sector somewhat worse, not better. This reinforces rather than weakens the importance of the §6.3 open item.
The STF cosmological sector is a unified dark-sector architecture from a single scalar field. Two parameters at their V8.1 §III.E statuses — m_s from vacuum (BBH threshold) physics (derived, conditional on the anchor selection), ζ/Λ from the 10D route (conditional: τ_eff, C_match) — control two structurally independent mechanisms, with the former third now an open programme:
The Friedmann budget closes: Ω_b + Ω_DM,osc + Ω_Λ,T² = 0.05 + 0.27 + 0.68 ≈ 1.00. The two mechanisms are independently falsifiable, with distinct observational probes and controlling parameters. A failure in any single sector does not cascade.
Primary falsifiers: Euclid w(z) for the T² pump; Euclid Ω_m for T² self-consistency; JWST-era high-z rotation curves for the CGM a₀(z) scaling (conditional); Lyman-α tightening for the mass-oscillation mechanism (fired at f = 1 — [Paz 2026h] §VI.B; the subdominant fraction remains open). Primary open theoretical target: whether the regime-dependent I₄ decomposition in FRW contains descendant terms with H-scaling lower than H⁴, which is the one remaining route by which the cosmological perturbation spectrum could accommodate Lyman-α constraints without modifying the framework.
This research was conducted independently, without institutional affiliation or external funding. The author thanks the open-source scientific community for the publicly available datasets and software tools that made this work possible.
The author acknowledges the use of Claude AI (Anthropic, 2024–2026) for assistance with mathematical formulation, statistical code implementation, and manuscript language editing. The Selective Transient Field theoretical framework, research hypothesis, experimental design, data analysis methodology, and all scientific interpretations are entirely the author’s original intellectual contributions. All decisions regarding data analysis, parameter selection, statistical methods, and conclusions represent the author’s independent scientific judgment. Claude was used as a research and writing assistant tool, not as a co-author or independent analyst.
[Paz 2026b] Z. Paz, “Topological Obstruction to Pre-Temporal Stasis and the Cascade Origin of Time,” V1.1 (2026).
[Paz 2026c] Z. Paz, “The Selective Transient Field from First Principles,” V7.9 (2026) (derivation record, archived; statuses governed by V8.1, the two-clock revision).
[Paz 2026d] Z. Paz, “The Cross-Disformal Matter Coupling as the Unique Mechanism for the Anderson Flyby Anomaly in Scalar-Tensor Gravity,” V2.0 (2026).
[Paz 2026e] Z. Paz, “STF Energy V0.4 — The Energy Problem,” (2026).
[Paz 2026f] Z. Paz, “STF Dark Energy Equation of State: w(z) Derivation,” V0.1 (2026).
[Paz 2026g] Z. Paz, “The Phantom Problem: Theoretical Pathologies in DESI DR2 Dark Energy Claims,” V0.2 (2026).
[Paz 2026h] Z. Paz, The STF Ultralight Condensate (formerly drafted as “Dark Matter as Geometry”), V2.0 (2026).
[Hu, Barkana & Gruzinov 2000] W. Hu, R. Barkana, A. Gruzinov, Fuzzy Cold Dark Matter, Phys. Rev. Lett. 85, 1158.
[Marsh 2016] D.J.E. Marsh, Axion Cosmology, Phys. Rep. 643, 1–79.
[Turner 1983] M.S. Turner, Coherent scalar-field oscillations in an expanding universe, Phys. Rev. D 28, 1243.
End of draft.
@article{paz2026cosmologicalsector,
author = {Paz, Z.},
title = {The STF Cosmological Sector: Unified Dark Matter and Dark Energy from a Single Scalar Field},
year = {2026},
version = {V0.2},
url = {https://existshappens.com/papers/cosmological-sector/}
}