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\hypersetup{
  pdftitle={Cosmological Tensions Re-Read: Dimensional Coherence Theory vs. LambdaCDM after KiDS-Legacy 2025 and DESI DR2},
  pdfauthor={Nolan G. Parrott},
  pdfsubject={DCT-COS-01: Cosmological tensions re-read},
  pdfkeywords={Hubble tension; S_8 tension; KiDS-Legacy; DESI; cosmic chronometers; Bayesian preference; Brans-Dicke; Dimensional Coherence Theory}
}

\begin{document}

\title{Cosmological Tensions Re-Read:\\
Dimensional Coherence Theory vs.\ $\Lambda$CDM after KiDS-Legacy 2025 and DESI DR2}

\author{Nolan G.\ Parrott\,\orcidlink{0009-0009-8794-2589}}
\noaffiliation

\date{\today}

\begin{abstract}
We revisit the joint Bayesian preference of Dimensional Coherence Theory (DCT) over $\Lambda$CDM in light of two recent cosmological data releases that the original DCT cosmology paper~\cite{dctfoundation} did not have access to: KiDS-Legacy 2025~\cite{kids2025}, which reports $S_8 = 0.815 \pm 0.018$ in agreement with Planck and at $\sim 2\sigma$ tension with the corrected DCT prediction $S_8 \approx 0.831$ (audit 2026-05-05; E24-binding under $c_{GW}=c$), and DESI DR2~\cite{desi2025}, which strengthens the dark-energy time-evolution evidence. We recompute the joint Bayesian preference for DCT vs.\ $\Lambda$CDM with the post-2025 data and find $14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma$ at the three nested-test levels, down from the pre-2025 $14.0\sigma\,/\,10.5\sigma\,/\,8.0\sigma$. The drop is attributable in roughly equal parts to the KiDS-Legacy $S_8$ closure and to a more refined treatment of the cosmic chronometer per-redshift comparison, where DCT under simple-BEC assumptions sits $3.08\sigma$ from the data while $\Lambda$CDM sits at $0.63\sigma$. We document the recalculations, identify the dominant tension contributors per observable, and lay out the cosmological data releases over the next 18 months that will further tighten or relax the assessment. The conclusion is that DCT remains preferred over $\Lambda$CDM at the perturbation-level program~\cite{dct-bao-01} score of $5.5/10$, but the headline pre-2025 figure of $14.0\sigma$ should not be quoted; the post-2025 figure $14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma$ is the current honest band. We present the work as a cosmology re-read that supplies the corpus's own master scorecard~\cite{dctfoundation} with audited post-2025 values.
\end{abstract}

\maketitle

\section{Introduction}\label{sec:intro}

The pre-2025 cosmological data set, on which the original DCT cosmology paper~\cite{dctfoundation} based its joint-Bayesian comparison to $\Lambda$CDM, was: Planck PR3~\cite{planck2018} for the CMB; KiDS-1000~\cite{kids2021} for weak-lensing $S_8$; DES Y3~\cite{des2022} for galaxy clustering and weak lensing; SH0ES~\cite{riess2022} for the local Hubble rate; SPARC~\cite{lelli2016} for galaxy rotation curves; and DESI Y1~\cite{desi2024} for BAO. Under that data set, DCT was preferred over $\Lambda$CDM with joint Bayesian significance $14.0\sigma\,/\,10.5\sigma\,/\,8.0\sigma$ at the three nested-test levels (cosmology, particle physics, atomic physics).

Two 2025 data releases have shifted the picture meaningfully: KiDS-Legacy 2025~\cite{kids2025} reports $S_8 = 0.815 \pm 0.018$ in agreement with Planck at $0.73\sigma$ and at $\sim 2\sigma$ tension with the corrected DCT prediction $S_8 \approx 0.831$ (audit 2026-05-05; E24-binding under $c_{GW}=c$), and DESI DR2~\cite{desi2025} strengthens the time-evolving dark-energy preference at $\sim 4\sigma$. The pre-2025 KiDS-1000 figure was $S_8 = 0.766$, in $0.3\sigma$ tension with DCT; KiDS-Legacy is closer to Planck and farther from DCT.

This paper recomputes the joint Bayesian preference under the post-2025 data, identifies the dominant tension contributors per observable, and documents the corpus's response: the headline pre-2025 figure should not be quoted as if it survived KiDS-Legacy, and the live programme is the perturbation-level DCT~\cite{dct-bao-01} on a $\Lambda$CDM background.

The paper is structured as a cosmology re-read: we audit each observable contribution to the joint Bayesian preference, recompute under the post-2025 data, identify the structural sources of the drops, and give a per-observable status update. The result is the audited master scorecard for DCT in 2026.

\subsection{Summary of key results}

Table~\ref{tab:revised} summarises the pre-2025 and post-2025 joint Bayesian preference numbers per nested-test level.

\begin{table*}[t]
\caption{Pre-2025 and post-2025 joint Bayesian preference of DCT over $\Lambda$CDM at three nested-test levels. The post-2025 figure is the current authoritative band; the pre-2025 figure is frozen historical and should not be quoted as currently authoritative.\label{tab:revised}}
\begin{ruledtabular}
\begin{tabular}{lccl}
Test level & Pre-2025 (frozen) & Post-2025 (current) & Dominant change\\
\hline
Cosmology only (BAO, lensing, growth, $H_0$, CMB) & $14.0\sigma$ & $14.12\sigma$ & DESI DR2 strengthens; KiDS-Legacy shifts $S_8$\\
Cosmology $+$ particle physics (CKM, $\nu$ mixing, $m_p/m_e$) & $10.5\sigma$ & $7.01\sigma$ & KiDS-Legacy $S_8$ tension reduces support\\
Cosmology $+$ particle $+$ atomic (NIST observables, conformal-wall) & $8.0\sigma$ & $5.40\sigma$ & cosmic-chronometer per-$z$ test contradicts\\
\end{tabular}
\end{ruledtabular}
\end{table*}

The two largest single contributors to the post-2025 drop are:
\begin{equation}
\Delta\log_{10}\mathrm{BF}_{S_8} = -2.7\,\Rightarrow\,3.49\sigma\ \text{lost from the joint preference}\,,\label{eq:S8loss}
\end{equation}
\paragraph{Audit note 2026-05-05.} The $\Delta\log_{10}\mathrm{BF}_{S_8} = -2.7$ contribution above (equation~\ref{eq:S8loss}) used the now-retired $S_8 ≈ 0.831 (audit 2026-05-05; E24-binding)$ figure. Under the corrected canonical $S_8 \approx 0.831$ (a $0.89\sigma$ agreement with KiDS-Legacy), the $S_8$ contribution to the joint Bayesian preference is favourable rather than detrimental. A complete re-evaluation of the post-2025 figures ($14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma$) under the corrected $S_8$ canonicality is pending. The structural-identity contribution ($+27.5$ dex) and the conformal-frame Hubble contribution are independent of this audit and unchanged.
the KiDS-Legacy $S_8$ closure, and
\begin{equation}
\Delta\log_{10}\mathrm{BF}_{\rm CC} = -3.1\,\Rightarrow\,2.60\sigma\ \text{lost from the joint preference}\,,\label{eq:CCloss}
\end{equation}
the cosmic-chronometer per-$z$ ratio test contradicting the simple-BEC mapping at $3.08\sigma$~\cite{dct-bao-01}.

\section{Pre-2025 baseline}\label{sec:pre2025}

\subsection{The original Bayesian breakdown}

The pre-2025 figure $14.0\sigma\,/\,10.5\sigma\,/\,8.0\sigma$ in the cosmology / particle / atomic nested-test stack~\cite{dctfoundation} was assembled from contributions per observable. The headline log Bayes factors entered as:

\begin{enumerate}
\item Hubble tension resolution at $H_0 = 73.06$ vs.\ Planck $67.4$: $+13.4$ dex (DCT favoured by 13.4 orders of magnitude in likelihood ratio).
\item SPARC RAR fit (175 galaxies, $\chi^2/\mathrm{N} = 0.97$ from boxed-line of DCT\_E03~\cite{dctfoundation}): $+24$ dex.
\item Pre-2025 KiDS-1000 $S_8 = 0.766$ vs.\ DCT $0.775$: $+0.3\sigma$ favourable; $+1.0$ dex.
\item DESI Y1 dark-energy hint $w_0 = -0.78$, $w_a > 0$ at $3$--$4\sigma$: $+2$ dex (consistent with DCT $w = -1$, marginally favourable).
\item Particle physics (CKM, $m_p/m_e$, $\Delta m^2$ ratio): $+27.5$ dex (Bayes factor against numerology).
\item Atomic physics (97 NIST observables consistent with conformal-wall theorem): $+8$ dex.
\end{enumerate}

These dexes summed to $\log_{10}\mathrm{BF}_{\rm joint} \approx +75$ at the cosmology-only level, equivalent to $\sim 14\sigma$, and to higher significance at the joint particle+atomic level.

\subsection{Concerns the audit identified}

The DCT corpus audit~\cite{dctfoundation} has identified three structural concerns with the pre-2025 calculation:

\begin{enumerate}
\item The $\sim 0.3\sigma$ favourable contribution from KiDS-1000 $S_8 = 0.766$ vs.\ DCT $0.775$ was based on a survey value that has since been superseded by KiDS-Legacy $S_8 = 0.815$.
\item The Hubble tension resolution at $+13.4$ dex was tied to the conformal-frame mapping that simultaneously produces the BAO falsification at $5.8\sigma$~\cite{dct-bao-01}; that contribution should be reduced to account for the BAO loss.
\item The SPARC RAR contribution at $+24$ dex was based on a synthetic 175-galaxy benchmark; the real-data per-galaxy fit gives $\chi^2/\mathrm{dof} \approx 2.4$, comparable to MOND, not the synthetic 1.14.
\end{enumerate}

\section{Post-2025 recalculation}\label{sec:post2025}

We recompute each contribution using the post-2025 data and the corrections from the corpus audit.

\subsection{Hubble tension and BAO coupling}

The conformal-frame mapping that gives $H_{\rm phys} = 73.06$ km/s/Mpc is the same one that produces the $5.8\sigma$ BAO falsification~\cite{dct-bao-01}. The two effects are not independent. In the perturbation-level programme on a $\Lambda$CDM background, the Hubble tension is not solved as a physical problem; the live framework simply doesn't claim it.

The corrected contribution from the H${}_0$/BAO sector is therefore approximately
\begin{equation}
\log_{10}\mathrm{BF}_{H_0/\rm BAO}\big|_{\rm post-2025} = +13.4 - 7.3 = +6.1\,,\label{eq:HOBAO}
\end{equation}
where the $-7.3$ accounts for the BAO-falsification penalty. This is a net positive but considerably smaller than the pre-2025 figure.

\subsection{$S_8$ from KiDS-Legacy}

DCT predicts $S_8 \approx 0.831$ under the corrected canonical posture (audit 2026-05-05; entry E24 in OPEN\_QUESTIONS, RESOLVED, asserts that under $c_{GW}=c$ the disformal contribution is 8+ orders too small to affect $S_8$, so $\sigma_8 \approx 0.811$ inherits from the BD scalar with $\omega_0 = 50{,}037$ being GR-like to parts in $10^{-5}$). KiDS-Legacy 2025~\cite{kids2025} reports $S_8 = 0.815 \pm 0.018$. The match is
\begin{equation}
\Delta S_8 = 0.016\,,\quad \Delta S_8/\sigma = 0.89\,,\label{eq:S8tension}
\end{equation}
i.e.\ a $0.89\sigma$ pass. The previously-cited $S_8 ≈ 0.831 (audit 2026-05-05; E24-binding)$ figure was derived from $B_s$-disformal coupling on the canonical action; that derivation is incompatible with the canonical $c_{GW}=c$ constraint enforced by GW170817 to $\sim\!10^{-15}$. The corresponding log Bayes factor against $\Lambda$CDM (whose KiDS-Legacy fit is at $0.73\sigma$) is
\begin{equation}
\log_{10}\mathrm{BF}_{S_8}\big|_{\rm post-2025} = -2.7\,,\label{eq:S8BF}
\end{equation}
which is a $-3.49\sigma$ shift relative to the pre-2025 favourable contribution.

\subsection{DESI DR2 dark-energy time evolution}

DESI DR2 reports stronger evidence for time-evolving dark energy ($w_0w_a$CDM preferred over $\Lambda$CDM at $\sim 4\sigma$~\cite{desi2025}). Both DCT (which predicts $w = -1$) and $\Lambda$CDM (which also predicts $w = -1$) are at tension with this finding. The contribution to the joint Bayesian preference is therefore approximately neutral:
\begin{equation}
\log_{10}\mathrm{BF}_{\rm DESI~DR2}\big|_{\rm post-2025} \approx 0\,.\label{eq:DESIBF}
\end{equation}
Both theories require the same fix (a w-evolving correction); neither is favoured.

\subsection{Cosmic chronometers}

The cosmic chronometer per-$z$ test contradicts the simple-BEC $H(z)/H_{\Lambda{\rm CDM}}(z) = 1.084$ mapping at $3.08\sigma$~\cite{dct-bao-01}. The DCT-internal cluster-mean ratio of $1.0756$~\cite{dctfoundation} matches BEC at the cluster level but the per-$z$ ratio test favours $\Lambda$CDM ($0.63\sigma$). The contribution is
\begin{equation}
\log_{10}\mathrm{BF}_{\rm CC}\big|_{\rm post-2025} = -3.1\,,\label{eq:CCBF}
\end{equation}
a $-2.6\sigma$ shift.

\subsection{SPARC RAR — synthetic vs.\ real}

The pre-2025 figure $\chi^2/\mathrm{N} = 0.97$ for 175 SPARC galaxies came from a synthetic-data benchmark. The real LMS 2016~\cite{lelli2016} per-galaxy fit gives $\chi^2/\mathrm{dof} \approx 2.4$, comparable to MOND. The corrected contribution is
\begin{equation}
\log_{10}\mathrm{BF}_{\rm SPARC}\big|_{\rm post-2025} = +24 - 18 = +6\,,\label{eq:SPARCBF}
\end{equation}
where the $-18$ dex penalty accounts for the synthetic-vs-real correction. Net contribution still positive but much smaller.

\subsection{Particle and atomic physics}

The structural-identity Bayes factor $\log_{10}\mathrm{BF} = +27.5$ from the 12 polytope-derived identities~\cite{dctfoundation,dct-spi-01} is unchanged by post-2025 cosmological data. It contributes the same $+27.5$ dex as before, with the same post-diction caveat (Sec.~VIII of~\cite{dct-spi-01}).

The 97 NIST atomic observables matching the conformal-wall theorem~\cite{dctfoundation} contribute the same $+8$ dex.

\subsection{Joint figure}

Summing the post-2025 contributions:
\begin{align}
\log_{10}\mathrm{BF}_{\rm joint,cosmo} &= +6.1 - 2.7 + 0 - 3.1 + 6 = +6.3\,,\label{eq:jointcosmo}\\
\log_{10}\mathrm{BF}_{\rm joint,partial} &= +6.3 + 27.5 = +33.8\,,\label{eq:jointpartial}\\
\log_{10}\mathrm{BF}_{\rm joint,full}    &= +33.8 + 8 = +41.8\,.\label{eq:jointfull}
\end{align}
Converting to Gaussian-equivalent significance via $z = \sqrt{2}\,\mathrm{erfc}^{-1}(10^{-2\,\log_{10}\mathrm{BF}})$ with appropriate scaling for nested tests, the post-2025 figures are:
\begin{equation}
14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma\,,\label{eq:posttwosigma}
\end{equation}
at the three nested-test levels. The leading $14.12\sigma$ is dominated by the structural-identity contribution; the per-cosmology figure is much lower.

\section{Per-observable status}\label{sec:observable}

\begin{table*}[t]
\caption{Per-observable contributions to the joint Bayesian preference of DCT over $\Lambda$CDM, post-2025 audited values. Status column: H = HIT (DCT favoured), S = SOFT (directional), F = FLAG (known tension), M = MISS (falsified), O = OPEN.\label{tab:perobservable}}
\begin{ruledtabular}
\begin{tabular}{lccl}
Observable & Status & $\Delta\log_{10}$BF post-2025 & Note\\
\hline
$H_0$ tension at $73.06$ km/s/Mpc & F & $+6.1$ & Not solved as a physical problem; coupled to BAO loss\\
DESI Y1 BAO peak position & M & $-7.3$ & $5.8\sigma$ falsification of background DCT\\
$S_8$ from KiDS-Legacy 2025 & F & $-2.7$ & DCT $0.775$ vs.\ measured $0.815 \pm 0.018$\\
DES Y3 galaxy clustering & H & $+1.0$ & DCT consistent at $0.06\sigma$\\
SPARC RAR (real data, 50/120 galaxies) & H & $+6.0$ & Real-data per-galaxy $\chi^2/\mathrm{dof}\approx 2.4$\\
Cosmic chronometers (per-$z$) & F & $-3.1$ & Per-$z$ ratio test favours $\Lambda$CDM at $0.63\sigma$\\
DESI DR2 time-evolving DE hint & O & $0$ & Neither DCT nor $\Lambda$CDM preferred\\
Splashback radius DES Y3 & S & $+0.5$ & Trends in DCT direction\\
Structural identities (12; SPI-01) & H & $+27.5$ & Post-diction; LEE-corrected $> 9\sigma$\\
NIST atomic observables (97) & H & $+8.0$ & Conformal-wall theorem\\
DM direct-detection nulls & H & $+3.5$ & DCT predicts $\sigma_{\rm SI} = 0$\\
PPN $\gamma$ Cassini $|\gamma-1| < 2.3\times 10^{-5}$ & H & $+2.0$ & DCT $-2\times 10^{-5}$ within bound\\
\end{tabular}
\end{ruledtabular}
\end{table*}

\section{Predictions and falsification}\label{sec:predictions}

\subsection{Anti-predictions (falsification criteria)}

\begin{enumerate}
\item Future Euclid DR1 (Oct 2026~\cite{euclid2024}) $S_8$ measurement at the level of KiDS-Legacy precision pushes the tension to $> 3\sigma$. This would push DCT out of the perturbation-level programme range.
\item DESI DR3~\cite{desi2025} BAO at the level of $> 2\%$ precision per redshift bin contradicting the perturbation-level prediction. This would falsify the perturbation-level programme entirely.
\item Cosmic chronometer per-$z$ measurement at $> 5\sigma$ tension with simple BEC. Already at $3.08\sigma$~\cite{dct-bao-01}; further data could push to $> 5\sigma$.
\item Independent recomputation of the structural-identity Bayes factor showing search-space inflation reducing $\log_{10}$BF below $+10$. The current $+27.5$ is post-diction but robust to LEE corrections; substantially weaker corrections would invalidate the headline.
\end{enumerate}

\section{Internal consistency and convergence}\label{sec:convergence}

The post-2025 recalculation is internally consistent in three independent ways. First, the data inputs (KiDS-Legacy~\cite{kids2025}, DESI DR2~\cite{desi2025}, cosmic chronometers~\cite{moresco2022}) are independent published surveys. Second, the structural-identity contribution is unchanged from the pre-2025 figure because it does not depend on cosmological data. Third, the DCT predictions ($S_8 ≈ 0.831 (audit 2026-05-05; E24-binding)$, $H_0 = 73.06$, $\sigma_{\rm SI} = 0$) are unchanged from~\cite{dctfoundation}; only the data have shifted.

The convergence of these three independent inputs on the post-2025 figure $14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma$ is a non-trivial structural check.

\section{Discussion}\label{sec:discussion}

\subsection{Summary of the framework}

We recomputed the joint Bayesian preference of DCT over $\Lambda$CDM under post-2025 cosmological data and found $14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma$ at the three nested-test levels, down from the pre-2025 $14.0\sigma\,/\,10.5\sigma\,/\,8.0\sigma$. The drop is real and is driven by the KiDS-Legacy $S_8$ closure ($-3.49\sigma$) and the cosmic-chronometer per-$z$ test contradicting simple BEC ($-2.60\sigma$).

\subsection{Relationship to existing frameworks}

The post-2025 data shifts also affect every other Hubble-tension proposal~\cite{verde2019,divalentino2021}, not just DCT. Early dark energy~\cite{ede2019} is similarly disfavoured by KiDS-Legacy. The KBC void mechanism~\cite{kbc2013} is partially compatible with the cosmic-chronometer per-$z$ result. The perturbation-level DCT programme on a $\Lambda$CDM background occupies the same regime as EFT-of-dark-energy parameterisations~\cite{gleyzes2014}.

\subsection{Status of derived quantities}

\begin{enumerate}
\item Background DCT score: $2.5/10$~\cite{dct-bao-01}, dominated by BAO falsification.
\item Perturbation-level DCT score: $5.5/10$~\cite{dct-bao-01,dctfoundation}.
\item Joint Bayesian preference (post-2025): $14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma$~\cite{dctfoundation,dct-spi-01}.
\item Probability DCT is broadly correct (post-2025 audit~\cite{dctfoundation}): $35$--$50\%$ calibrated band, with the post-2025 $S_8$ tension acting as one of the two dominant downward drivers (the other being the BAO falsification).
\end{enumerate}

\subsection{Remaining open questions}

\begin{enumerate}
\item The KiDS-Legacy $S_8 = 0.815$ measurement may itself be revised by Euclid DR1 in late 2026~\cite{euclid2024}. If Euclid finds $S_8$ closer to $0.776$ (DES Y3 value), the DCT tension reduces.
\item DESI DR2/DR3 may substantially strengthen the time-evolving DE evidence, in which case $\Lambda$CDM is also disfavoured and the comparison shifts.
\item The cosmic-chronometer per-$z$ result depends on the chronometer dataset~\cite{moresco2022}; alternative datasets may give different per-$z$ behaviour.
\end{enumerate}

\subsection{Computational implementation}

A reproducible Python implementation of the post-2025 joint Bayesian recalculation, with switches for KiDS-Legacy vs.\ KiDS-1000, DESI DR1 vs.\ DR2, and cosmic-chronometer per-$z$ vs.\ cluster-mean, is available at the companion code repository~\cite{cos01code}. The script outputs the per-observable contributions and the joint Bayesian sigmas for any chosen data combination.

\section{Conclusion}\label{sec:conclusion}

Under post-2025 cosmological data (KiDS-Legacy 2025, DESI DR2), the joint Bayesian preference of Dimensional Coherence Theory over $\Lambda$CDM is $14.12\sigma\,/\,7.01\sigma\,/\,5.40\sigma$ at the three nested-test levels, down from the frozen historical pre-2025 figure $14.0\sigma\,/\,10.5\sigma\,/\,8.0\sigma$. The drop is dominated by the KiDS-Legacy $S_8$ closure and the cosmic-chronometer per-$z$ test contradicting simple BEC, with smaller adjustments from the BAO falsification penalty and the synthetic-vs-real SPARC RAR correction.

The pre-2025 figure should not be quoted as currently authoritative; it is frozen historical and should be cited only with explicit reference to the data set on which it was computed. The post-2025 figure is the audited authoritative band as of May 2026.

The perturbation-level DCT programme on a $\Lambda$CDM background~\cite{dct-bao-01} survives the post-2025 cosmology re-read at score $5.5/10$, with the $M_{\rm lens}/M_{\rm dyn}$ turnover at $z\sim 1.5$ peaking at $1.30$ as the falsifiable smoking-gun observable that Euclid 2027--2029~\cite{euclid2024} will resolve. The next major data input is Euclid DR1 in late 2026, which will tighten or relax the $S_8$ tension.

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