Errata FE-08-2026
Thirteen reclassifications of the scope declared in v35 of the Tratado de Fundamentos (Treatise of Foundations). They do not change any equation, proof or structure of the treatise: they change what is claimed about them.
This page is a translation of the Spanish original (30 September 2026). Where they differ, the Spanish text and the reference copy of the errata prevail.
Epistemological errata correct the scope of what is claimed, not the mathematics. Where this document and v35 differ on the status of a claim, the errata prevail until v36 is published.
What it is and what it is not
FE-08-2026 is not a version of the treatise. On 28 September 2026 the author decided that there will be no intermediate version v35.1: the next one will be v36. In the meantime, each correction is cited as “FE-08-2026, En”, with the codes E1 to E13 in the table.
Its reclassifications are already applied on this site: in the axioms, the status of the results, the comparison with ΛCDM, the simulations and the code and reproducibility page. In the repository, continuous integration prevents the phrases withdrawn by the errata from reappearing.
The thirteen reclassifications
| Item | What v35 said | What the errata say | Code |
|---|---|---|---|
| Adrián's Theorem | Single theorem, “all constants sealed” | Basal Theorem 13.1a (proven) and complete Conjecture 13.1b (program) | E1, E2 |
| Wilson reflection positivity (7.4) | “Theorem” with a proof sketch | Conditional proposition | E3 |
| $N_{\text{gen}} = 3$ (12.4) | Proven, “algebraic consequence” | Structural identification; its derivation becomes a sub-front of front 7 | E4 |
| Appendix A.6 (H₀, σ₈, SPARC) | Current observational validation | Historical record; the current state is the repository's v1 and v2 fits | E5, E6 |
| Appendix B.5 (core, SPARC, subhalos) | Validation results | Program objectives (front 5): implemented does not mean solved | E7 |
| Appendix H | Verifications that “demonstrate” | Internal consistency checks of the implementation | E8 |
| Symbols ε, εΛ, εK, εc, δ₀*, δH | Occasional fluidity of symbols | C6 convention, safeguarded | E9 |
| The $S_n \leftrightarrow j_n$ map | Correspondence | Proposed dictionary under normalization | E10 |
| Mass gap (D.4) | “They close the calculation” | Effective spectral floor; it is not the Yang–Mills problem | E10 |
| Quantum hardware (C.5) | “Puts the model to the test” | Prototype that bounds circuit parameters | E10 |
| The arrow (13.1.iii) | “Arrow of time” | Arrow of structuring before Florencia; the temporal arrow is induced afterwards by the Florencia Rotation | E11 |
| The step from σ to S | Implicit | Piecewise or generalized inverse | E12 |
| BBN contrast (H.2.5, Table H.2) | “Favors the sign” | Consistency check passed, with no sign significance | E13 |
The C6 convention: four distinct epsilons
Four quantities in the treatise share a letter or a numerical value, and the earlier corpus went as far as interchanging them. The C6 convention separates them: they are distinct and non-interchangeable objects.
| Symbol | What it is | Value | Where |
|---|---|---|---|
| $\delta_0$ | Imperfection inherited from the cycle; an input to the model | No value assigned in the treatise | — |
| $\varepsilon_\Lambda$ | Amplitude of the $\Lambda_{\text{rel}}$ transition | 0.012 ± 0.003, calibrated | A.3 |
| $\varepsilon_K$ | Residue of Newton's Seal | ≈ 0.012 | §9.5, F.4 |
| $\varepsilon_c(\rho)$ | Local Cronos correction in the lapse | Function of the density | Ch. 11 |
Two more symbols are reserved: $\delta_0^{*}$ for the attractor of Theorem 10.6 and $\delta_H$ for the value required by the Higgs splice (H.8). The computational program measures $\delta_H \approx 0.055$ with the full landscape, which structurally withdraws the identification $\delta_0 \equiv \varepsilon_\Lambda$ of the earlier corpus (Computational Note I).
The canonical formula of Appendix H (E8)
The twenty-four verifications are “internal consistency checks of the implementation — identities, signs, recovery limits and negative controls — passed. They establish that the formalism does what it declares; they do not establish, by themselves, that the ansatz is physically true, that its parameters come from nature, or that the extrapolation to the continuum is valid”.
FE-08-2026, E8
The canonical formula of the BBN contrast (E13)
“At ~0.3σ from the central value there is no detection and no sign preference: the result is a consistency check passed — the contrast could have excluded the predicted value and did not — declared without significance.”
FE-08-2026, E13. The “refutable (alive)” status of front 6 does not change.
Why it matters. An overstated claim is enough for a reviewer to dismiss the whole. The errata do the opposite: they reduce the declared scope wherever the proof or the data do not support it, and leave intact what does hold up. The state of each claim, row by row, is in the program's computational status.
The full classification of the results is in the status of the results, and the deductive chain in the eight axioms. The complete text of the current record is in the Tratado de Fundamentos.