Code and Reproducibility
The computational program of the model: what can be run, with which dependencies, and how to verify the results independently.
A cosmological proposal that cannot be run cannot be refuted. The computational program exists so that any team can reproduce the complete chain without depending on the author's good faith: clone, install, download, and verify.
The Repository
The public repository of the computational program, in Python (3.10 or higher) and under the Apache 2.0 license. It contains the implementation (the executable deductive chain, the cosmological background and the fits, Cronos v3, the lattice block, and the qudit), the canonical claims registry, and a dated results folder for each experiment, including those with an unfavorable outcome.
The registry has seventy rows. Each one declares the derivation, the implementation, the test, the data, the falsifier, and the status of a claim, and a “—” marks a real gap instead of hiding it. The test suite runs in continuous integration (Python 3.10, 3.11, and 3.12), together with language guards that prevent the phrases withdrawn by the errata FE-08-2026 from reappearing.
The production variant Gadget-4-Cronos (octree, MPI, and boxes from 512³ to 1024³, Appendix B.4) is not in the repository and has not been run; its configurations are. What the repository runs is a minimal particle-mesh scheme, sufficient for collapse pairs with identical seed, not for the production boxes.
The Reproducibility Chain
The repository fixes the seeds of each run and verifies each downloaded dataset by its SHA-256 checksum. What it does not yet have is a tagged version or a DOI of its own for the software: it is cited by its address and by the DOI of the treatise, as its citation file indicates.
The comparisons with the standard model are made with pairs of runs with identical seeds, so that no difference can be attributed to the particular realization of the initial conditions. For the production boxes, the treatise plans to generate the conditions with Music or N-GenIC from the power spectrum of modified Boltzmann solvers, with the growth factor under the model's metric.
The Current Scheme: Cronos v3
The current numerical scheme is the one corrected in Chapter 11 of the treatise. It incorporates the gate friction (active only while the region collapses, switched off upon virialization), the corrected exponent, and the force term from the gradient of the Cronos correction.
$$\Delta t_i = \frac{\eta}{\sqrt{|\vec{a}_i|\,a}}\left[1 + \frac{1}{\alpha_{cr}}\left(\frac{\rho_i}{\rho_c}\right)^{3/2}\right]^{-1}, \qquad \eta = 0{,}025$$
The entropic step. The sign is the one corrected in Remark 11.4, which replaces that of the old scheme.Version notice. Any result obtained with earlier schemes must be reproduced with Cronos v3 before being considered valid. The treatise itself classifies the execution of the production simulations with the corrected scheme as one of its seven open fronts: it is pending, not taken for granted.
In the treatise's design, the overhead of the adaptive step stays below 1% and the parallelization does not break, because the global synchronization keeps the usual bitmask scheme in powers of two. It is a design property of the production variant: it will be measured when that variant is run.
The Lattice Gauge Block
It complements the N-body and responds to a need of the formalism itself: Wilson's reflection positivity that Chapter 7 requires needs a lattice in which to be formulated. That positivity is today a conditional proposition (FE-08-2026, E3).
The coupling is not free but a function of the structuring variable, so that the scale of the strong interaction emerges precisely when space reaches its first genuinely three-dimensional extension. The strength of the gauge interaction recalls, in that sense, the tensorial rigidity of the stretch that precedes it.
| Parameter | Value |
|---|---|
| Gauge groups | SU(3), SU(5), SU(10), SO(10) |
| Grid size | L = 50–250 |
| Spacing | ~5×10⁻³ – 10⁻² |
| Tensional term | Discrete jumps in the structuring variable |
The Map to Loop Quantum Gravity
By equating the minimum area variation with that of structuring, the four seals of the Law of the Decade are associated with the first four half-integer spin multiplets. The Immirzi parameter is fixed by the Bekenstein–Hawking entropy and a count of microstates; in loop quantum gravity its value depends on the chosen counting scheme.
$$S_1 = 0{,}009 \leftrightarrow j_1 = \tfrac{1}{2}, \quad S_2 = 0{,}099 \leftrightarrow j_2 = \tfrac{3}{2}, \quad S_3 = 0{,}999 \leftrightarrow j_3 = \tfrac{5}{2}, \quad S_4 = 1{,}001 \leftrightarrow j_4 = \tfrac{7}{2}$$
With the Immirzi parameter set at 0.274. The errata FE-08-2026 (E10) specifies its status: it is a proposed dictionary under normalization, not an established correspondence.The Quantum Integration
The history of the universe is encoded in a five-level qudit, whose computational basis is the five ontological phases: from the dimensionless support to the effective spacetime. The tension accumulated before each collapse is represented by a diagonal Hamiltonian, and the dimensional progress is monitored with an operator whose expectation value tracks the count of emerged dimensions.
Each collapse is a conditional unitary that is activated only when the corresponding threshold is exceeded, and the four gates fire exactly at the thresholds of the Law of the Decade. The circuit uses three registers: the ontological state, a tensorial ancilla that represents the conversion channel, and a polarizable latent one.
From this comes a concrete signature of the circuit: a decreasing pattern of fidelities along the chain of collapses, with the maximum superposition in the intermediate phase of the conversion. It can be tested in quantum simulation and, in principle, compiled on hardware. The errata FE-08-2026 (E10) specifies its scope: the circuit is a prototype that bounds parameters of the circuit itself; running it on hardware does not put the model to the test.
What Can Be Verified Today
With the repository, an independent team can repeat today the contrasts with data and the numerical experiments of the program. Each one points to a dated folder in results/ with its report, its seed, and, when there are data, its SHA-256 verification. The main ones, with the status that the claims registry assigns them:
| Contrast | Data | Outcome |
|---|---|---|
| Production fits v1 and v2 (10 August) | 31 cosmic chronometers, 6 BAO, and 1371 supernovae (n = 1408); v2 adds the compressed CMB and 11 fσ8 (n = 1422) | Negative result: they favor ΛCDM (ΔBIC +14.50 and +14.60); ε compatible with zero |
| DESI DR2 BAO (18 August) | 13 DR2 components, with the likelihood validated against Cobaya 3.6.2 | Negative result: it favors ΛCDM in all eight configurations (ΔBIC between +4.47 and +4.90); ε cannot be probed by BAO in this parametrization |
| Residues via BBN (14 September, preregistered) | Primordial abundances YP and D/H, transcribed from their publications | Outcome A: the prediction and zero both fall within the interval; a bound without identification, not a detection |
| Isolated halo of front 5 (September, preregistered) | Numerical experiments, no observational data | Indeterminate: the instrument does not converge in the interior of the halo |
| SPARC and Sculptor profile (front 5E) | Catalogs not available from the execution environment | Not run: frozen preregistration, no verdict |
Historical record. The three validations that the treatise attributed to the N-body—the 2.3 kpc core in an isolated halo, the drop in the root-mean-square error on SPARC from 12% to 4.5%, and the 45% reduction in subhalos above $10^8\,M_\odot$—are not reproducible results today. Since the errata (E7), they are targets of front 5, pending reproduction with the corrected scheme.
What is not yet closed, and the treatise declares it, is the execution of the production simulations with the gate friction and the verification of the bound on the Cronos amplitude. That is the point where the model exposes itself to failure most directly.
The complete numerical scheme is in simulations, the comparison with the standard model in MCMC versus ΛCDM, and the status of each result in what is proven and what is not. The versioned deposits are in publications.