# V131 Cosmology — Unified Causal Field Applications

**Organization:** Milkyway Center | **Contact:** yuanjimaster@gmail.com | **Site:** https://milkyway.center

**PDF reports:** [English](/assets/V131_Cosmology_Final_EN.pdf) | [中文](/assets/V131_Cosmology_Final_ZH.pdf)

> Astrophysical consequences of the Route-B field equations (`00_Final_RouteB_EN.md`). Full derivations: `04_宇宙学应用.md`;
> numerical engines: `engine/v131_cosmos.py`, `v131_torsion_core.py`, `v131_wz.py`, `v131_halo_core.py`.
> Labels: **[EST]** = established mainstream/semi-mainstream physics inherited by V131; **[V131]** = framework-specific interpretation or prediction; **[SPEC]** = qualitative narrative, not quantitatively closed.
> Data baselines: Sgr A\* (GRAVITY 2019), shadow (EHT 2022), $\Lambda$ (Planck 2018), $w_0w_a$ (DESI DR2 2025).

---

## 0. Key Findings & Predictions (calibrated summary)

> This section follows the framework's own calibration principle: reported confidence = measured hit rate. "Calibration" and "prediction" are kept strictly apart; known tensions are stated up front.

**Findings (theory aligned with existing observations)**

1. **The end of the black-hole singularity** [EST+V131]: the center of a black hole is not a divergent singularity but a **torsion core** held up by spin–torsion repulsion — for Sgr A\* about **47 nm** (neutron-borne baseline); the exterior returns to GR, with a computed shadow diameter of 52.1 μas vs the EHT-measured 51.8±2.3 μas (within 1σ). *Note: the singularity-free torsion bounce itself is an established Einstein–Cartan result; V131's contribution is the 9-D information-geometric embedding, the propagating-torsion ξ factor, and the concrete astrophysical numbers.*
2. **Two mysteries, one field** [V131]: dark energy and dark matter are two faces of the same S01 field — **dark energy = its potential** (the unfixed causal residual), **dark matter = its gradient** (the gradient halo).
3. **Dark energy reinterpreted and calibrated** [V131]: the cosmological constant is re-read as the residual of incomplete causal fixing, with its characteristic scale **calibrated** to 2.25 meV against Planck 2018 — a calibration, not a prediction; the actual predictions live in the w(z) trajectory and the phantom kill-line (below).
4. **The Donato universal law, structurally a theorem** [V131]: in the core column density $\Sigma_0=a_*/16\pi G$, $v_{\rm flat}$ and $r_c$ cancel exactly — **the universality (independence of every galaxy property) is a zero-parameter theorem**; the absolute value, after a single $O(1)$ calibration $\zeta=1.5$, lands on the measured central value $141^{+82}_{-52}\ M_\odot/\mathrm{pc}^2$.
5. **Core–cusp dissolved** [V131]: the fixing-gate threshold naturally yields a two-state distribution — **cored galaxies, NFW-like clusters** — matching the observed situation and answering CDM's small-scale difficulty head-on.

**Predictions (falsifiable, aimed at future data)**

1. **Hard bound on propagating torsion**: $\alpha<10^{-6}\ \mathrm{m}^2$ (every known black hole must bounce sub-Planckian).
2. **Thawing trajectory + phantom kill-line**: $w(z)$ frozen at $-1$ at high redshift, thawing away late, with $w\ge-1$ always — a confirmed phantom crossing ($w<-1$) at DESI DR3+ kills the dark-energy sector outright.
3. **Countdown to the cosmic endgame** (under the DESI best-match calibration $\psi_i=1.0\,M_{pl}$): the universe has completed **38%** of its causal fixing; in about **16 Gyr** dark energy is exhausted, expansion turns around, and the universal wavefunction undergoes its final collapse.
4. **Rigid galactic-dynamics relations**: $r_c\propto v_{\rm flat}^2$ (log-log slope exactly 2) and $\Sigma_0$ strictly identical for all galaxies — directly decidable with SPARC-class samples.

**Known tensions (stated up front)**: solar-circle dark-matter density off by +23%; the DESI central values contain a phantom crossing that thawing cannot in principle reach; $a_*$ differs from MOND's $a_0$ by a factor of ~8 (common origin unexplained).

---

## 1. Overview: one equation per cosmic mystery

| Equation | Structure | Mystery | Status |
|---|---|---|---|
| (2b′) torsion equation | spin–torsion repulsion at high density | **singularity → Galactic-center core** | computed |
| (1′) $\lambda(\Psi_{S01}-\Phi_{fixed})$ | unfixed causal residual | **dark energy / $w(z)$** | computed |
| (2a′) $\beta\,\Theta^{[S01]}_{\mu\nu}$ | S01 gradient-halo stress | **dark matter / rotation curves / core–cusp** | computed |
| (3′) info transition + $h(\tau)$ | axial torsion bias | baryon asymmetry | SPEC |
| (4′) torsion holonomy | geometrized information storage | BH information paradox | narrative closed |
| (2b′) bounce cosmology | collapse → bounce | Big Bang origin / initial low entropy | SPEC |

**The single lever**: V131's (2b′) is an Einstein–Cartan (EC) torsion equation — fermion spin density sources torsion, which feeds back as a **repulsive** effective energy density $\propto n^2$: invisible at low density (all GR tests pass), inevitably overtaking gravity in a collapsing core. Fifty years of mainstream groundwork (Hehl–von der Heyde–Kerlick 1974; Trautman; Popławski 2010–2016); V131 plugs it into a 9-D information-geometric frame and lets torsion **propagate** via the $\alpha T^2$ term.

---

## 2. The Galactic-center core: main computation

### 2.1 Exterior check [EST]

Sgr A\* ($M=4.154\times10^6M_\odot$, $D=8.178$ kpc): $r_s=2GM/c^2=1.23\times10^{10}$ m $=0.082$ AU; shadow angular diameter

$$\theta_{\rm sh}=2\sqrt{27}\,GM/(c^2D)=\mathbf{52.1\ \mu as}\quad\text{vs EHT}\ 51.8\pm2.3\ \mu\text{as}.$$

The GR limit passes — interior modifications never touch the observationally pinned exterior.

### 2.2 Torsion bounce [EST] → core size [V131]

EC effective energy density for a Weyssenhoff spin fluid, and the bounce criterion:

$$\varepsilon_{\rm eff}=nmc^2-\frac{\pi G\hbar^2}{2c^2}n^2=0\ \Longrightarrow\ n_b=\frac{2mc^4}{\pi G\hbar^2},\qquad r_{\rm core}=\Big(\frac{3M}{4\pi\rho_b}\Big)^{1/3}\propto M^{1/3}m^{-2/3}.$$

| Spin carrier | $\rho_b$ (kg/m³) | **Sgr A\* core radius** |
|---|---|---|
| electron | $5.7\times10^{51}$ | $7.0\ \mu$m |
| **neutron (baseline)** | $1.9\times10^{58}$ | $\mathbf{47\ nm}$ |
| constituent quark | $2.5\times10^{57}$ | $92$ nm |

**4.16 million solar masses held up by torsion in a virus-sized nugget**; $\rho_b$ sits **38 orders of magnitude below** the Planck density (no quantum gravity required); $r_{\rm core}/r_s\approx4\times10^{-18}$ (exterior indistinguishable from Kerr). Scaling: $10M_\odot$ BH → 0.63 nm, M87\* → 0.54 μm.

### 2.3 Propagating-torsion correction: shape factor $\xi$ [V131, computed]

For $\alpha\neq0$ torsion obeys a screened equation (propagation length $\ell_T=\sqrt\alpha$); the uniform-core analytic solution gives

$$\xi(x)=1-\frac{3(1+x)e^{-x}(x\cosh x-\sinh x)}{x^3},\quad x=\frac{R}{\ell_T};\qquad \rho_b=\frac{\rho_b^{(0)}}{\xi},\quad r_{\rm core}=r_{\rm core}^{(0)}\xi^{1/3}$$

(finite-difference check at the $10^{-3}$ level; the self-consistent fixed point $x^*=(R_0/\ell_T)\xi^{1/3}$ is unique). Two regimes: **locked** ($\ell_T\ll R_0$, $\xi\to1$, algebraic EC values intact) and **leaking** (torsion escapes the core, $r_{\rm core}=\tfrac25R_0^3/\ell_T^2$, collapse deepens toward Planck failure).

![Propagating-torsion shape factor and core correction curves](/assets/v131_torsion_core_en.png)

| Object | $R_0$ | $\ell_{1\%}$ | $\ell_{\rm crit}$ ($\rho_b\to\rho_{\rm Pl}$) |
|---|---|---|---|
| stellar $10M_\odot$ | 0.63 nm | 4.2 pm | **1.0 mm** ← tightest |
| Sgr A\* | 47 nm | 0.31 nm | 7.5 cm |
| M87\* | 0.54 μm | 3.6 nm | 0.87 m |

**First bound on $\alpha$**: demanding every known black hole bounces sub-Planckian ⇒ $\boxed{\alpha<10^{-6}\ \mathrm{m}^2}$ (a pure self-consistency bound; experiment barely constrains propagating torsion at all).

**V131-specific reading**: the horizon cuts off Fisher-information exchange ($\Delta E\to0\Rightarrow\tau_{\rm fix}\to\infty$) — core matter stays permanently in the unfixed phase $\Theta<\pi/3$: the core is the universe's largest reservoir of uncollapsed wavefunction.

---

## 3. Dark energy = unfixed causal residual: explicit $w(z)$ dynamics

### 3.1 Calibration [V131]

The term $-g_{\mu\nu}\lambda(\Psi_{S01}-\Phi_{fixed})$ in the (2a′) source is precisely the shape of a cosmological constant: $\Lambda_{\rm eff}=\kappa\beta\lambda\langle\Psi_{S01}-\Phi_{fixed}\rangle$. Against Planck 2018: $\varepsilon_\Lambda=5.3\times10^{-10}$ J/m³, characteristic scale $(\varepsilon_\Lambda\hbar^3c^3)^{1/4}=2.25$ meV. Reframing: not "why is vacuum energy small" but "why has cosmic fixing already completed down to this residual" (each fixed bit releases Landauer heat $\ge kT\ln2$ — 163 μeV at CMB temperature).

### 3.2 Dynamics [V131, computed]

Taken at face value the S01 term is **linear-potential quintessence** $V(\psi)=\lambda\psi$ — no tuning freedom. RK4 integration, shooting to $\Omega_\psi^0=0.69$:

| $\psi_i$ ($M_{pl}$) | 30 | 3 | 1.5 | 1.2 | 1.0 | 0.9 | $\le0.85$ |
|---|---|---|---|---|---|---|---|
| $w_0$ | $-1.000$ | $-0.984$ | $-0.926$ | $-0.869$ | $-0.770$ | $-0.636$ | **not viable** |
| $w_a$ | $-0.000$ | $-0.024$ | $-0.108$ | $-0.191$ | $-0.340$ | $-0.546$ | (fixing completes before today) |

![w(z) dynamics vs DESI DR2](/assets/v131_wz_en.png)

1. **Direction (honestly logged: corrects the draft guess)**: a linear potential is **thawing** — frozen at $w=-1$ at high redshift, thawing **away from** $-1$ late (the draft guessed the opposite; the computation stands).
2. **Against DESI DR2**: the V131 trajectory sits **1.7–2.4σ** from the three data combinations (diagonal χ²), while ΛCDM sits **4.2–5.8σ** — if the DESI drift holds up, this sector decisively beats a bare Λ.
3. **Hard falsification line**: the minimal S01 sector has $w\ge-1$ always; a confirmed phantom crossing at the true-likelihood level kills the sector outright.
4. **Anthropic window**: universes with $\psi_i\lesssim0.85M_{pl}$ complete fixing before today and recollapse early ⇒ our existence bounds $\psi_i\gtrsim0.9$.

**Best-match calibration** ($\psi_i=1.0M_{pl}$): the universe has completed **38%** of its causal fixing ($\langle\psi\rangle_0=0.62M_{pl}$); $\lambda^{1/3}=2.4\times10^{-13}$ eV; **fixing completes = dark energy exhausted = expansion turnaround: ≈16 Gyr from now** — the final collapse of the universal wavefunction.

---

## 4. Dark matter = S01 gradient halo + fixing-gate core

### 4.1 Gradient halo [V131, computed]

$\Psi_{S01}=q\ln(r/r_0)$ (the natural massless-scalar solution around a point source) ⇒ $\rho=q^2/(2c^2r^2)$, an isothermal halo ⇒ **flat rotation curves for free**: $v_{\rm flat}^2=2\pi Gq^2/c^2$. Calibrating $q$ to the Milky Way's $v_{\rm flat}=220$ km/s **predicts** the solar-circle density $9.5\times10^{-22}$ kg/m³ vs the measured $7.1\times10^{-22}$ (0.4 GeV/cm³) — one parameter, 35% off (narrowing to +23% after regularization). **One field: dark matter is its gradient, dark energy its potential** — two mysteries, one field.

### 4.2 Fixing gate ⇒ core–cusp resolved [V131, computed]

**[Proposal]** Causal fixing fires where the information rate is high: $a_{\rm bar}(r)>a_*\equiv\zeta cH_0$ ($cH_0=6.5\times10^{-10}$ m/s², $\zeta=O(1)$) ⇒ the inner gradient is erased (core) while the outer halo survives. Regularized profile and rotation curve:

$$\Psi'=\frac{qr}{r^2+r_c^2},\qquad \rho=\frac{q^2r^2}{2c^2(r^2+r_c^2)^2},\qquad r_c=\frac{v_{\rm flat}^2}{a_*}.$$

**Main result — the Donato universal law becomes a theorem**: in the core column density, $v_{\rm flat}$ and $r_c$ **cancel exactly**:

$$\boxed{\ \Sigma_0\equiv\rho_{\rm max}r_c=\frac{a_*}{16\pi G}=140\ M_\odot/\mathrm{pc}^2\ (\zeta=1.5)\ }\quad\text{vs observed } \rho_0r_0=141^{+82}_{-52}\ M_\odot/\mathrm{pc}^2$$

(Donato et al. 2009, universal across 14 magnitudes) — independent of every galaxy property, zero tuning.

![Fixing-gate core regularization: profiles, rotation curves, universal column density](/assets/v131_halo_core_en.png)

Consistency: at the Milky Way's $r_c=1.6$ kpc the baryonic acceleration is $8.2\times10^{-10}$ vs $a_*=9.8\times10^{-10}$ (ratio 0.83 — the gate boundary is self-locating); halo contribution at 8 kpc is 172 km/s, the remainder belonging to disk/bulge (standard decomposition).

**Falsifiable predictions**: **P1** $\Sigma_0$ identical for all galaxies; **P2** $r_c\propto v_{\rm flat}^2$ (slope exactly 2, SPARC-testable); **P3** no $r^{-1}$ cusp in any DM-dominated galaxy (head-on split from CDM N-body); **P4** clusters have $a_{\rm bar}<a_*$, gate shut ⇒ **cored galaxies, NFW-like clusters** — a two-state prediction matching the observed situation and partially answering the Bullet cluster.

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## 5. Speculative sectors (not quantitatively closed)

- **Baryon asymmetry [SPEC]**: torsion couples axially to Dirac fermions (Hehl–Datta), opposite sign for particles/antiparticles; early high-torsion background biases fixing probabilities via $h(\tau)$. Needs the early-universe $\tau(s)$ solution (open).
- **BH information paradox [V131]**: no singularity (§2) + entanglement stored geometrically in torsion holonomy $\mathrm{Hol}(C)=\exp(i\oint\mathcal T)$ + a Landauer ledger — the paradox becomes bookkeeping. Page curve open.
- **Big Bang = the previous bounce [SPEC]**: BH and cosmological singularities are removed by the same torsion term; the bounce resets $\Theta$ into the symmetric phase ⇒ **initial low entropy = a global information-phase reset**, not fine-tuned initial conditions. Spectral index $n_s$ open.

## 6. Falsification table

| # | Prediction | Test | Failure kills |
|---|---|---|---|
| F1 | $w\ge-1$ always; thawing track $w_a\approx-1.58(1+w_0)$ | DESI DR3+ / true likelihood | S01 dark-energy sector |
| F2 | $\Sigma_0=a_*/16\pi G$ universal | larger rotation-curve samples | gate model |
| F3 | $r_c\propto v_{\rm flat}^2$ (slope 2) | SPARC regression | gate criterion |
| F4 | cluster centers NFW-like (no core erasure) | cluster strong lensing | gate direction |
| F5 | Landauer heat $\ge kT\ln2$ per fixing event | quantum-thermodynamics experiments (B9 target) | info-dynamic fixing |
| F6 | BH exteriors exactly Kerr ($r_{\rm core}/r_s\sim10^{-18}$) | EHT/GRAVITY precision | — (consistency) |
| F7 | Leggett–Garg violations scale as $\tau_{\rm fix}=\frac{\pi/3}{2}\hbar/\Delta E$ | micro-to-mesoscopic interferometry | fixing law (3′) |

## 7. Honest boundaries

1. This document is **consequence-mining of a speculative framework**, not consensus physics; the [EST] ingredients (EC bounce, linear-potential quintessence, screened-sphere solutions) each have mainstream literature — V131's contribution is organizing them in one information-geometric frame with a unified reading.
2. Known order-of-magnitude tensions: solar-circle density +23%; $a_*$ vs MOND's $a_0$ differ ×8 (different quantities, common origin unexplained); DESI's central phantom crossing is unreachable for thawing.
3. Main open items: deriving $\zeta$ from B9, true DESI likelihood, quantitative lensing/Bullet, $\eta_B$, $n_s$, Page curve.
4. The C2 draft guess was corrected by computation and the correction is kept on record — the framework's calibration principle (reported confidence = measured hit rate) applies to itself.

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**One-sentence summary**: one set of equations — torsion repulsion replaces the Galactic-center singularity with a **47 nm torsion core** ($\alpha<10^{-6}$ m² bound), the potential and gradient of $\Psi_{S01}$ deliver **dark energy** (thawing $w(z)$, 1.7–2.4σ from DESI vs 4.2–5.8σ for ΛCDM) and **dark matter** (Donato's universal $140\,M_\odot$/pc² becomes a theorem), and the exterior spacetime returns to GR (52.1 vs 51.8±2.3 μas). Seven falsification lines, all on the table.