Retractions and corrections
Retractions and corrections to the published Foundation paper
Items in Dimensional Coherence Theory: Unifying Quantum Mechanics, General Relativity, and the Standard Model (Zenodo 10.5281/zenodo.18703512, 19 February 2026) that have been refined, reconciled, or updated.
This page lists items that appeared in the published Foundation paper at 10.5281/zenodo.18703512. The cluster paper set linked from /papers/ carries the corrected values where they differ.
| Was | Now | Kind | Reason |
|---|---|---|---|
| §XIII.A "no tension exceeding 2σ" headline | Per-tension empirical status table on /scorecard/ | framing | The headline phrasing was internally inconsistent with §XIII.D's listing of open cosmological items. The cluster papers carry the per-tension status row by row. |
| KiDS-1000 \(S_8 = 0.766\) cited (Heymans 2021) | KiDS-Legacy 2025 \(S_8 = 0.815 \pm 0.018\); DCT canonical \(S_8 \approx 0.831\) gives 0.89σ agreement | data update | KiDS-Legacy 2025 was published after the v1 deposit. The canonical DCT prediction \(S_8 = \sigma_8 \sqrt{\Omega_m/0.3}\) is unchanged; only the comparison data has been updated. |
| \(\delta_{CP} = 2\pi/3 = 120^{\circ}\) | \(\pi/3 = 60^{\circ}\) | sharpened | Spinorial half-angle lift of \(C_3 \subset {\rm SO}(3)_L \subset {\rm SO}(4) \subset H_4\) to Spin(4) selects the \(\pi/3\) branch; both branches give the same Jarlskog \(J\). Detail: DCT-SM-01. |
| \(\sin\theta_{13}\) deviation stated as 15% | 0.3% (after the \((1-1/\varphi^4)/240\) ansatz) | numerical | v1 stated 15% deviation; the closed-form \((1 - 1/\varphi^4)/240 = 0.003559\) matches the PDG central value at 0.3%. |
| "629+ matched observables" headline | 141-row closed observable ledger with 117 HIT / 14 SOFT / 0 FLAG / 0 MISS / 10 OPEN | recharacterised | The 629 figure conflated parallel chains as independent observables. The structured row-level ledger separates evidence kinds (sharp predictions, exact theorems, structural identities, qualitative). |
| Background BAO Δχ² ≈ 33.6 cited as a tension | Photon-null cancellation: homogeneous \(P(t)\) drops out of \(d\chi/dt = 1/a\) | geometry | The cited Δχ² came from rescaling \(D_M \to D_M/\sqrt{P_0}\), which is not what null geodesics do under a homogeneous \(P(t)\). Background BAO is ΛCDM-degenerate. Detail: DCT-BAO-01. |
| "\(10^{24}\sigma\) margin" / "zero contradictions" maximalist phrasings (in popularisation drafts) | Per-tension empirical-status table on /scorecard/ and Bayesian preference figures with explicit caveats | framing | The maximalist headline-σ figures and "zero contradictions" phrasing are retracted. The zero-free-parameter framing is canonical and is not retracted. |
What was not retracted
- Zero free parameters. The Foundation paper claims zero free parameters; this is canonical and unchanged. Every numerical prediction reduces to a combination of icosahedral primitives.
- The mathematical framework. The canonical action, the McKay 2I → E₈ derivation of the Standard Model gauge group, the master identity 2ω₀ + 3 = cBD·P₀² = 100,077.
- The 32 positive predictions and 12 anti-predictions in the published paper. These are the row content of the predictions and tests pages.
Items that pre-dated v1 and never appeared in it
For completeness, a few items widely discussed in pre-publication drafts but never in the published paper:
- The functional form \(\omega(P) = (c \cdot P^{5/2} - 3)/2\) was a pre-publication exploration; the published paper already uses \(\omega(P) = (c_{BD} \cdot P^2 - 3)/2\) with \(c_{BD} = 138{,}189\).
- Popularisation-pipeline names \(\Lambda_P\), \(P_\eta\), \(N_0\), \(P(N) = 1 - \exp(-N/N_0)\) appear only in pre-publication drafts; they were never canonical.
Source: DCT-FND-V1 (Zenodo); cluster papers under /papers/.