V131 Cosmology — Torsion Core of Sgr A*, Dark Energy w(z), Dark-Matter Cores

V131 UNIFIED CAUSAL FIELD — COSMOLOGICAL APPLICATIONS | JULY 2026

09. COSMOLOGY — UNIFIED CAUSAL FIELD APPLICATIONS

One Set of Field Equations, Six Cosmic Mysteries

Galactic-Center Core • Dark Energy w(z) • Dark Matter Core–Cusp • 7 Falsification Lines

47 nm torsion core inside Sgr A* | shadow 52.1 vs EHT 51.8±2.3 μas | Σ₀ = 140 M☉/pc² (Donato law derived) | w(z): 1.7–2.4σ from DESI DR2 (ΛCDM: 4.2–5.8σ)

Honest framing. V131 is a speculative theoretical framework, not consensus physics. Every claim below carries one of three labels: [EST] = established published physics that V131 inherits (Einstein–Cartan torsion bounce, linear-potential quintessence, screened-sphere solutions); [V131] = framework-specific prediction or interpretation; [SPEC] = qualitative narrative, not yet quantitatively closed. All numerical results are reproducible from the open calculation engines listed at the bottom. Where a computation contradicted an earlier guess, the correction is kept on record.

09.0 KEY FINDINGS & PREDICTIONS (CALIBRATED)

WHAT WE FOUND — aligned with existing data

1. No singularity: black-hole centers are torsion cores — Sgr A* ≈ 47 nm; exterior returns to GR (shadow 52.1 vs EHT 51.8±2.3 μas, within 1σ). The bounce itself is established Einstein–Cartan physics; V131 adds the embedding, the ξ factor and the numbers.

2. Two mysteries, one field: dark energy = the S01 field's potential (unfixed causal residual); dark matter = its gradient (halo).

3. Dark energy reinterpreted: Λ = residual of incomplete causal fixing, calibrated (not predicted) to 2.25 meV against Planck 2018.

4. Donato law, structurally a theorem: universality of Σ₀ = a_*/16πG is zero-parameter (v_flat cancels exactly); the absolute value lands on 141⁺⁸²₋₅₂ M☉/pc² after one O(1) calibration (ζ=1.5).

5. Core–cusp dissolved: cored galaxies, NFW-like clusters — a two-state prediction matching observations.

WHAT WE PREDICT — falsifiable, future data

1. Torsion bound: α < 10⁻⁶ m² (all known black holes bounce sub-Planckian).

2. Phantom kill-line: w(z) is thawing and w ≥ −1 always — a confirmed phantom crossing at DESI DR3+ kills the sector outright.

3. Cosmic endgame (DESI best-match calibration): the universe is 38% causally fixed; in ≈16 Gyr dark energy is exhausted and expansion turns around.

4. Rigid relations: r_c ∝ v_flat² (slope exactly 2) and Σ₀ identical for all galaxies — SPARC-decidable.

Known tensions, stated up front: solar-circle density +23%; DESI's central phantom crossing unreachable for thawing; a_* vs MOND a₀ differ ×8.

09.1 OVERVIEW — ONE EQUATION PER MYSTERY

Equation	Structure	Mystery	Status
(2b′) torsion equation	spin–torsion repulsion ∝ n²	singularity → Galactic-center core	COMPUTED
(1′) λ(Ψ_S01−Φ_fixed)	unfixed causal residual	dark energy / w(z)	COMPUTED
(2a′) βΘ^[S01]	S01 gradient-halo stress	dark matter / rotation curves / core–cusp	COMPUTED
(3′) info transition + h(τ)	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

09.2 THE GALACTIC-CENTER CORE: 47 NANOMETERS

Exterior check [EST]: for Sgr A* (M = 4.154×10⁶ M☉, D = 8.178 kpc, GRAVITY 2019) the framework's GR limit gives r_s = 1.23×10¹⁰ m = 0.082 AU and a shadow angular diameter of 52.1 μas vs EHT-measured 51.8 ± 2.3 μas. Interior modifications never touch the observationally pinned exterior.

Torsion bounce [EST]: in Einstein–Cartan gravity, fermion spin density sources torsion, which feeds back as a repulsive energy density ∝ n². Collapse halts at n_b = 2mc⁴/(πGħ²) — 38 orders of magnitude below the Planck density. No quantum gravity required.

Core size [V131]: r_core = (3M/4πρ_b)^1/3 ∝ M^1/3m^−2/3

Spin carrier	Bounce density ρ_b (kg/m³)	Sgr A* core radius
electron	5.7×10⁵¹	7.0 μm
neutron (baseline)	1.9×10⁵⁸	47 nm
constituent quark	2.5×10⁵⁷	92 nm

4.16 million solar masses held up by torsion in a virus-sized nugget. r_core/r_s ≈ 4×10⁻¹⁸ — the exterior is indistinguishable from Kerr. Scaling: a 10 M☉ black hole → 0.63 nm; M87* → 0.54 μm.

Propagating torsion [V131, computed]: V131's αT² term lets torsion propagate over a length ℓ_T = √α. The screened-sphere shape factor ξ(R/ℓ_T) was solved analytically and verified by finite differences (10⁻³). Demanding every known black hole bounces sub-Planckian yields the first bound on the torsion coupling: α < 10⁻⁶ m².

Propagating-torsion shape factor and core-radius correction curves for Sgr A*, stellar black holes and M87* — Shape factor ξ(x) with locked/leaking asymptotes (left); self-consistent core radius r_core(ℓ_T) for three black holes, × = Planck-failure points (right).

09.3 DARK ENERGY = UNFIXED CAUSAL RESIDUAL: w(z)

Taken at face value, the S01 constraint term in the action is linear-potential quintessence V(ψ) = λψ — zero tuning freedom [EST dynamics, V131 reading]. Explicit integration (RK4, shooting to Ω_ψ = 0.69):

1. Thawing: frozen at w = −1 at high redshift, thawing away from −1 late. (The draft guessed the opposite direction; the computation corrected it and the correction is on record.)

2. Against DESI DR2 (2025): the V131 trajectory sits 1.7–2.4σ from the three data combinations, while ΛCDM sits 4.2–5.8σ away. If the DESI drift holds, this sector decisively beats a bare Λ.

3. Hard falsification line: the minimal sector has w ≥ −1 always. A confirmed phantom crossing kills it outright.

4. Calibration: best match at ψ_i = 1.0 M_pl: the universe has completed 38% of its causal fixing; λ^1/3 = 2.4×10⁻¹³ eV; fixing completes — dark energy exhausted, expansion turns around — ≈16 Gyr from now.

Thawing w(z) curves and the V131 trajectory in the w0-wa plane against DESI DR2 constraints — Thawing w(z) family (left); V131 single-parameter trajectory vs DESI DR2 baselines and ΛCDM in the (w₀, w_a) plane (right).

09.4 DARK MATTER: GRADIENT HALO + FIXING-GATE CORE

Gradient halo [V131]: Ψ_S01 = q ln r gives an isothermal ρ ∝ r⁻² halo — flat rotation curves for free. Calibrating q to the Milky Way's 220 km/s predicts the solar-circle dark-matter density to +23% (measured 0.4 GeV/cm³). One field: dark matter is its gradient, dark energy its potential.

Fixing gate [V131, proposal]: causal fixing fires where baryonic acceleration exceeds a_* = ζ·cH₀ (ζ = O(1)) — erasing the inner gradient (core) while the outer halo survives. In the core column density, v_flat and r_c cancel exactly:

Σ₀ = a_*/(16πG) = 140 M☉/pc² — identical for every galaxy

vs the observed universal core column density ρ₀r₀ = 141⁺⁸²₋₅₂ M☉/pc² (Donato et al. 2009, universal across 14 magnitudes). One of the most mysterious empirical laws of dark matter becomes a theorem. The cusp–core problem dissolves: no r⁻¹ cusp in any DM-dominated galaxy, while clusters (gate shut) stay NFW-like — a two-state prediction matching observations.

Density profiles, halo rotation curves and the universal core column density against the Donato 2009 band — Fixing-gate cored profile vs SIS/NFW/Burkert (left); halo rotation curves (center); universal Σ₀ vs the Donato band (right).

09.5 FALSIFICATION TABLE — SEVEN WAYS TO KILL THIS

#	Prediction	Test	Failure kills
F1	w ≥ −1 always; thawing track w_a ≈ −1.58(1+w₀)	DESI DR3+ true likelihood	S01 dark-energy sector
F2	Σ₀ = a_*/16πG universal	larger rotation-curve samples	gate model
F3	r_c ∝ v_flat² (slope exactly 2)	SPARC regression	gate criterion
F4	cluster centers NFW-like (no core erasure)	cluster strong lensing	gate direction
F5	Landauer heat ≥ kT ln2 per fixing event	quantum thermodynamics	info-dynamic fixing
F6	BH exteriors exactly Kerr (r_core/r_s ~ 10⁻¹⁸)	EHT / GRAVITY precision	— (consistency)
F7	Leggett–Garg violations scale as τ_fix = (π/6)ħ/ΔE	micro-to-mesoscopic interferometry	fixing law (3′)

09.6 中文摘要 (CHINESE SUMMARY)

一套统一因果场方程组的宇宙学推论：挠率排斥消解奇点——银心 Sgr A*（416 万倍太阳质量）中心不是奇点，而是一颗半径约 47 纳米的挠率芯，反弹密度低于普朗克密度 38 个量级；外部时空退回广义相对论（阴影角径 52.1 微角秒，对 EHT 实测 51.8±2.3）。

同一个场 Ψ_S01：位势 = 暗能量（thawing 型 w(z)，距 DESI DR2 数据 1.7–2.4σ，而 ΛCDM 为 4.2–5.8σ；宇宙已完成约 38% 的因果固定，约 160 亿年后固定完成、膨胀转折），梯度 = 暗物质（平坦旋转曲线自然出现；固定闸门 a > ζcH₀ 抹除核区尖峰，Donato 普适柱密度 140 M☉/pc² 从拟合变成定理）。

七条证伪线全部列明（F1–F7）。本框架为推测性理论，全部数值可由公开计算引擎复现；诚实边界与已知张力（太阳圈密度 +23%、 DESI 中心值的幻影穿越不可达等）均在完整报告中注明。

09.7 FULL REPORTS & REPRODUCIBILITY

Complete derivations, honest-boundary lists and all numerical tables:

↓ FULL REPORT (ENGLISH, PDF) ↓ 完整报告（中文，PDF）

Calculation engines: v131_cosmos.py • v131_torsion_core.py • v131_wz.py • v131_halo_core.py
Established-physics ingredients: Einstein–Cartan spin-fluid bounce (Hehl–von der Heyde–Kerlick 1974; Popławski 2010–2016), linear-potential quintessence, screened-sphere solutions. Data: GRAVITY 2019, EHT 2022, Planck 2018, DESI DR2 2025, Donato et al. 2009.

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