What is proven, what is conditional, what remains open
Epistemic status of each result of the model, according to the classification that the Tratado de Fundamentos (Treatise of Foundations) itself establishes in its validation appendix.
This page is a translation of the Spanish original (30 September 2026). Where they differ, the Spanish text and the Tratado de Fundamentos prevail.
A non-standard cosmological model must be judged by the same criteria as any other: mathematical consistency, covariance, stability, recovery of the established limits, parameter identifiability, reproducibility and an honest statistical comparison with ΛCDM on the same data. This page applies that criterion to the model itself and states, result by result, how far it goes.
The classification is neither a concession nor a list of apologies. It is taken from the treatise, with the reclassifications of the errata FE-08-2026, and from the claims registry of the code repository. The treatise subjects each part to twenty-four internal consistency checks of the implementation—identities, signs, recovery limits and negative controls—all of them passed: they establish that the formalism does what it declares, not that the ansatz is physically true (E8). It then deliberately separates what holds up from what does not yet. That separation is part of the method, not a courteous add-on.
It follows from the axioms through a chain of results without circularity. It is an internal theorem: it does not by itself amount to an empirical confirmation.
It holds under explicit hypotheses not yet verified.
Reduced to a concrete calculation or to a pending observational test.
A test executed with a contrary or null outcome, published as such.
A structural identification without proof or a dedicated test, or a figure from the earlier corpus without current support.
The fine-grained classification, with the eight categories of the claims registry—among them three distinct negative ones: negative result, non-derived claim and non-executed experiment—is in the computational status, row by row.
C6 convention: four distinct epsilons. $\delta_0$ is the cycle's inherited imperfection, an input of the model with no value assigned in the treatise; $\varepsilon_\Lambda = 0.012 \pm 0.003$ is the calibrated amplitude of the $\Lambda_{\text{rel}}$ transition; $\varepsilon_K \approx 0.012$ is the residue of Newton's Seal; and $\varepsilon_c(\rho)$ is the local Cronos correction. The numerical coincidence between $\varepsilon_\Lambda$ and $\varepsilon_K$ does not imply identity. $\delta_0^{*}$ denotes the Victoria attractor and $\delta_H \approx 0.055$ the value measured by the Higgs splice (FE-08-2026).
The figures for $\delta_0$, $H_0$, the mass gap or the size of the cores that appear on pages marked as historical belong to the earlier corpus and are not current values.
Structural results
Time is not postulated: it emerges. At the Florencia threshold a single generator changes norm, $\gamma^0 \equiv i\gamma_S$, and the signature goes from Euclidean to $(-,+,+,+)$. Reflection positivity on the Florencia slice enables the Osterwalder–Schrader reconstruction, which yields a positive-norm Hilbert space with Hamiltonian $\hat{H} \geq 0$ and unitary evolution. The positivity of the spinor sector (Wilson) is a conditional proposition (E3).
The arrow of structuring is a theorem and not a postulate: the Path Monotonicity Theorem deduces it from the dissipative structure of the flow. The temporal arrow is induced afterwards by the Florencia Rotation (E11).
There is no singularity because there is no instant zero to start from. The primordial state is atemporal by construction—Axiom 6 establishes that before the final threshold there are only correlations ordered by structuring—and the Dimensional Orthogonality Lemma shows that the internal duality is consistent on a zero-dimensional support. What in the standard model is a divergence is here simply the stretch prior to the birth of geometry.
The treatise identifies the three generations with the dimension of the spinor module of the Chain of Algebras in the $V_{3+1D}$ stretch (Prop. 12.4). The errata FE-08-2026 (E4) reclassifies that proposition: it is a structural identification, not a proven consequence, and its derivation becomes a sub-front of front 7.
In the claims registry it appears as a declared gap: it does not yet have a dedicated test. An explicit construction with $N_{\text{gen}} \neq 3$ in the same algebra would refute it.
The four collapse thresholds—$0.009$, $0.099$, $0.999$ and $1.001$—reduce to three pieces of data: the Decade ratio, the gauge unit and the one-quantum rule. It is an exact arithmetic reduction, not a numerical coincidence.
With the caveat that the ratio $\lambda = 10$ itself is calibrated and not derived; deciding whether it is physics or gauge convention is the second open front.
The smallness of the neutrino masses emerges as a seesaw induced by the hierarchy of seals, with the ontological reading that the neutrino is the mode whose survival through the seals is maximal—it barely couples—and therefore the lightest. The treatise describes it as structural: a consequence of the ontology, not an added parameter. Its predictive character is not established, because the mass program on which it depends is calibrated.
Cosmological phenomenology
A distinction that is easily lost is in order here. That a model fits some data and that it predicts them are different things, and the treatise marks the difference in each case.
The Bayesian production fits have already been run, and their outcome is unfavorable to the model. Re-run on 10 August 2026 with the corrected background normalization, they favor ΛCDM: ΔAIC = +4.00 and ΔBIC = +14.50 in the v1 fit (1408 data points), and ΔAIC = +4.08 and ΔBIC = +14.60 in the v2 fit (1422 data points, with compressed CMB and fσ₈). The transition amplitude, ε, is compatible with zero, and the citable value from the v2 run is H₀ = 68.19 ± 0.40 km s⁻¹ Mpc⁻¹: the model recovers ΛCDM with no advantage and does not relieve the Hubble tension. The test against DESI DR2 gives the same verdict, uniformly in favor of ΛCDM, with ΔBIC between +4.47 and +4.90 across eight configurations.
The value “between 69 and 70 km s⁻¹ Mpc⁻¹”, previously presented as a direction consistent with the relief, comes from the corpus (Appendix A.6) and remains as a historical record (FE-08-2026, E5/E6). The full CMB spectrum and weak lensing are left out of these fits.
The citable value from the corrected v2 run is σ₈ = 0.799 ± 0.029, obtained in the same fit that favors ΛCDM (ΔBIC = +14.60) and with ε compatible with zero: the fit does not support a relief of the tension in S₈.
The earlier trend, a “slightly reduced” σ₈, comes from the corpus and remains as a historical record (FE-08-2026, E5/E6).
The earlier corpus presented a cored profile that emerged from the mechanism without baryonic feedback, and an improvement in the rotation curves of the SPARC catalog. The errata FE-08-2026 (E7) reclassifies it as an objective of the program (front 5): that the mechanism is implemented does not mean that the problem is solved.
In the repository, the collapse gate is reproduced, but the core has not been produced: it remains indeterminate because of resolution (2 August) and also indeterminate at Level A (17 and 18 September, with the instrument not converged). The SPARC catalog could not be ingested, so that improvement has no support today. The corpus figures remain as a historical record.
The earlier corpus presented a reduction in the number of subhalos relative to ΛCDM, attributed to the same mechanism as the cores. With the E7 reclassification it also becomes an objective of the program (front 5).
That reduction comes from the corpus runs. The production variant that could reproduce it, Gadget-4-Cronos, has its configurations prepared but has not been run; the earlier figure remains as a historical record.
Dark energy appears as an emergent vacuum channel and not as a rigid constant, and the effects attributed to dark matter as a consequence of entropic friction. The construction is coherent and recovers ΛCDM in the limit in which the tension switches off; the parameters of the two channels are calibrated and, in the production fits, the transition amplitude is compatible with zero.
The pending closure that the treatise itself points to in this sector is the constraint algebra of Gea, the strong-coupling regime of the Atlas mode and the derivation of the tensional term from the potential. The stability of that mode is among the conditional results.
The mass program
This is the section where the treatise is most severe with itself, and that severity is worth reproducing without softening it.
The expression $m_H = \sqrt{2\beta_3}\,v_3$ gives 125.3 GeV against the measured 125.25 ± 0.17 GeV, an agreement to 0.04%. But the treatise itself includes a circularity audit that has to be taken seriously: that expression is exactly the Standard Model identity with $\lambda_H = \beta_3$, so any value of $\beta_3$ fitted to the Higgs mass reproduces the Higgs mass.
The result will have predictive content if and only if $\beta_3$ is derived from the splice conditions of the potential without using $m_H$ as an input. That independent derivation is declared in the open program.
The corpus table reproduces eleven masses with deviations between 0.04% and 6%. The form of the Path Functional, which writes each mass as a weighted sum of the seal scales, is structural. The weights, on the other hand, are pending an explicit WKB calculation.
The treatise's formulation is literal: if that calculation is completed with values derived from first principles, the Path Functional would constitute the first derivation of the Yukawa constants from a cosmology; until then, the spectrum is a successful fit whose predictive character remains to be established.
The lattice gauge block estimates, by spectral diagonalization, an effective spectral floor in the model's emergent gauge theories, and entropic quantization ties it to the fundamental mass scale. v35 said that this calculation “is closed”; the errata FE-08-2026 (E10) corrects the scope: it is an effective spectral floor on the lattice.
It is not a resolution of the open Yang–Mills problem in the strict mathematical sense, and the two should not be allowed to be confused. A spectral floor that disappeared on refining the lattice would refute it.
The seven open fronts
The open program is not a list of gaps but a map of bifurcations: each front admits several ways out, and the model's ontology predicts what its reading would be in each case. Each one is reduced to a concrete calculation or to an observational test.
| Front | What resolves it | Status as of 30 Sep 2026 |
|---|---|---|
| Complete reflection positivity | Work out in detail the positivity of the spinor sector without doublers and extend it to non-stationary couplings. It decides whether time can be born on rules that are still changing. | Toy model: specularity is sufficient, without proof that it is necessary. Wilson positivity remains open and is currently a conditional proposition (FE-08-2026, E3). |
| Derivation of $\lambda$ | Integrate the flow functions of the Basal potential and read off the shift of the discriminant, to decide whether $\lambda = 10$ is physics or gauge convention. | Two published negative results: the Fokker–Planck β (outcome A at the preregistered point) and the preregistered screening of 28 September (147 runs, no crossing of the discriminant) do not derive the Decade. $\lambda = 10$ remains calibrated. |
| The closure of Gea | Close the constraint algebra with local lapse, resolve the strong-coupling regime of the Atlas mode and derive the tensional term from the potential. | Newton's Seal is exact in the suite and the Atlas channel is derived from the action (internal check, E8); the preferred-frame PPN bounds set $\alpha_a \le 8\times10^{-7}$. Atlas remains conditional. |
| The Return of Victoria | Calculate from the microdynamics the sign of the Lydia exponent and the Ceiling, and estimate the attractor. On this depends whether the cosmos is fertile or whether there is a terminal cycle without offspring. | The circle of $\delta_0$ reduces to a single number, the required Ceiling: $W_{\max} \approx 1.87\times10^{-4}$ with the fiducial shapes. The sign of $\nu$ remains conditional. |
| Cronos v3 in production | Run the simulations with the gate friction and verify the bound $\alpha_0^{-1} \lesssim 10^{-6}$. | No production: the core has not been produced. Level A, the Cronos–Jeans criterion (rounds 1 and 2) and the halo and shell series return INDETERMINATE. The vertical kinematics of the solar neighborhood (Oort–$K_z$) excludes, in the plane, the amplitude calibrated in Sculptor ($A \lesssim 0.06\,A_{\text{Sculptor}}$ with the declared slab). SPARC and the Sculptor profile, not ingested. |
| The Residues contrast | Confront $G_{\text{cosmo}}/G_N - 1 \approx -1.8\,\%$ with the bounds from primordial nucleosynthesis and the CMB against laboratory measurements. | Primordial nucleosynthesis, preregistered: consistency check passed at 0.32σ, with no sign significance (E13); the front remains refutable. Data transcribed from the publications, provisional on provenance grounds. |
| The Path Functional | WKB calculation of the weights and independent derivation of $\beta_3$. | The C¹ splice measures $\delta_H \approx 0.055$ without circularity (distinct from $\delta_0^{*}$, C6 convention); $\beta_3$ remains conditional and the mass spectrum, calibrated. $N_{\text{gen}} = 3$ becomes a sub-front (E4). |
In sum, the model puts itself on the line on three concrete empirical fronts: the comparison between the cosmological gravitational constant and the laboratory one, the collapse gate in virialized halos, and the bound on the Cronos amplitude. As of 30 September 2026 none has yielded a favorable outcome: the Residues contrast is consistent without detection, the gate is implemented but without production, and the Cronos amplitude calibrated in Sculptor is excluded in the solar plane, conditional on the declared slab and on the weak form of the law.
The recovery limits
An extension of known physics is only acceptable if it can give it back. The model gives it back in three explicit limits, and this is indeed proven: when the imperfection tends to zero, the eternal inertia of the perfect state is recovered; when the couplings of the foliation reach their fixed point, general relativity is recovered through Newton's Seal; and when the Cronos correction vanishes, the standard Friedmann–Robertson–Walker geodesic is recovered.
There is also a proposition of complete recovery: if the ontological tension switches off and the conversion rates tend to zero, the Relative Dual Metric collapses to FRW, the propagation speeds tend to unity, the latent channel is absorbed into a constant and the tensional Friedmann equation reduces to the equation with constant $\Lambda$, with a growth prediction that coincides with that of ΛCDM.
Why this page exists. It is easier to publish a list of solved problems, and that is what almost all alternative proposals do. The reason for not doing so is practical as well as honest: a specialist reviewer spots an overstated claim within seconds, and a single one is enough for them to discard the whole without reading the rest. Stating precisely how far one gets is what allows what does hold up to be read with attention.
The invitation to the reader with training in the field is concrete: examine the sector closest to your specialty. A precise objection, a relevant comparison or the identification of a decisive falsification test is worth more than a general endorsement.
The complete deductive chain is in the eight axioms, the primordial state in The Root and the sequence of thresholds in foundations. The full text, with the proofs and the validation appendix, in the Tratado de Fundamentos. The deposits and their chronology, in publications.