Computational Blocks of the MCMC
The Multiple-Collapse Cosmological Model is structured into 5 computational blocks that describe the evolution of the universe from the primordial state to observable physics.
Reference implementation in Python, with the claims registry and the dated results
Overview
Each block represents a stage of cosmic evolution and contains the corresponding equations, parameters, and simulations.
Primordial State
Initial configuration of the universe with maximum tension between Primordial Mass and Primordial Space.
Pre-geometry
Collapse rate k(S) and entropic integral that determines the mass→space conversion.
Cosmology
Modified Friedmann equations with the Λrel(z) correction.
N-body
Halo simulations with entropic friction, generating Burkert profiles.
Lattice-Gauge
Yang-Mills theory on a lattice with MCMC beta function and mass gap.
The Structuring Variable S
The MCMC organizes cosmology around a structuring variable S: a dimensionless, monotonically non-decreasing index, defined as accumulated entropy production, that measures tensional reconfiguration. It is not physical time, nor does it have an upper bound fixed in advance. The working gauge unit is ΔS = 10⁻³, a choice of units and not a new physical constant.
S ∈ [0, 1.001) — No classical spacetime
S ≥ 1.001 — Observable cosmology
Note on earlier versions. Earlier formulations of the model described S as a parameter bounded in the interval from 0 to 100, with a calibrated value of about 95 and a current epoch close to 90. The Tratado de Fundamentos (v35) does not contain that parametrization, and those values are withdrawn.
Pre-Geometric Phase: Collapses and Seals
The pre-geometric phase is structured into four Collapse-Seal cycles that make dimensions emerge progressively: V₀D → V₁D → V₂D → V₃D → V₃₊₁D.
| S value | Type | Dimension | Emergent Attribute |
|---|---|---|---|
| 0 | Root | — | Formless dual Mp/Ep unit |
| 0.001 | Collapse C₀ | V₀D start | Embryonic gravity |
| 0.009 | Seal C₀ | V₀D sealed | Planck (~10¹⁹ GeV) |
| 0.010 | Collapse C₁ | V₁D start | PP/AP, motion, U(1) |
| 0.099 | Seal C₁ | V₁D sealed | GUT (~10¹⁶ GeV), c fixed |
| 0.100 | Collapse C₂ | V₂D start | Turn, rotation |
| 0.999 | Seal C₂ | V₂D sealed | EW (~246 GeV), c² calibrated |
| 1.000 | Collapse C₃ | V₃D start | 3D volume |
| 1.001 | Seal C₃ | V₃₊₁D | BIG BANG (~200 MeV) |
Post-Big Bang Cosmological Epochs
The entropy-redshift mapping S(z) = S_geom + (S₀ - S_geom) / E(z)² defines the observable epochs. (Note: S values are effective/interpolated, not canonical)
| Epoch | S value | Redshift z | Description |
|---|---|---|---|
| Big Bang | 1.001 | ∞ | Start of the observable universe |
| Recombination | 1.08 | 1100 | Decoupling (CMB) |
| Early galaxies | 2.5 | 10 | First stellar systems |
| Stellar peak | 47.5 | 2 | Maximum star formation |
| SNe Ia reference | 65.0 | 1 | Supernova standardization |
| Dark energy | 84.2 | 0.5 | Dominant accelerated expansion |
| Current epoch | ~90 | 0 | Stratified present (effective Sext) |
| Asymptotic limit | 100.0 | — | de Sitter boundary |
Structuring sequence
The 5 blocks describe the sequential evolution of the universe:
Primordial State
The universe begins with all the potential mass concentrated (Mp₀ = 1) and minimal space (Ep₀ ≈ 0). The polarization P_ME ≈ +1 indicates total dominance of mass.
Pre-geometry
The collapse rate k(S) governs the gradual conversion of mass into space. The entropic integral ε(S) accumulates the transitions.
Cosmology
The modified Friedmann equations describe the expansion of the universe with the Λ_rel(z) correction that distinguishes the MCMC from the standard model.
N-body
Entropic friction modifies structure formation, generating halos with Burkert profiles instead of the cuspy NFW ones.
Lattice-Gauge
Lattice Yang-Mills field theory connects with particle physics; the mass gap of the QCD vacuum is treated as an effective spectral floor, not as the Yang–Mills problem (FE-08-2026, E10).