V131 Cosmology — Sgr A* Torsion Core, Dark Energy w(z) vs DESI

One Set of Field Equations, Nine Cosmic Mysteries (v2)

Galactic-Center Core • Dark Energy w(z) • Dark Matter Core–Cusp • Baryogenesis ⇔ Neutrino Masses • 11 Falsification Lines

Planck-density torsion core inside Sgr A* (~4×10⁻²¹ m, universal curve)  |  shadow 52.1 vs EHT 51.8±2.3 μas  |  Σ₀ = cH₀/32G = 146 M☉/pc² (zero-parameter, v2.1)  |  w(z): 2.3–3.5σ from DESI DR2 (ΛCDM: 3.0–4.5σ, correlated likelihood)  |  Σm_ν = 0.059 eV point prediction (v2.1 finalized)

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. Balancing it against the n^4/3 energy of relativistic degenerate matter gives a bounce point containing only G, ħ, c — a mass-independent theorem: ρ′ = 5.1 ρ_Pl (honest band [5, 20] ρ_Pl), in the same order as Popławski's published relativistic treatment (~15 ρ_Pl, arXiv:1105.6127).

Erratum (v1 superseded): v1 used the dust criterion (ε = nmc²), giving carrier-dependent cores (47 nm for Sgr A*, neutron-borne) at a sub-Planckian density; the dust approximation is valid only ~40 orders of magnitude below its own solution point, so v2 replaces it. Structural bonus: the carrier ambiguity disappears.

Core size [V131, v2]: one universal curve, no fermion-species freedom:

r_core = 2.6×10⁻²³ m × (M/M☉)^1/3

4.16 million solar masses held up by torsion in a core 10¹⁴ Planck lengths across. A core collapses to the Planck length only for M < 21 M_Planck ≈ 5×10⁻⁷ kg — the finite, singularity-free core survives for every astrophysical black hole. r_core/r_s ≈ 3×10⁻³¹: the Kerr exterior is even safer than in v1. Honest downgrade: at Planck-order density, classical EC results are order-of-magnitude estimates.

Propagating torsion [V131, computed; under re-review at the v2 core scale]: 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). Re-derived at the Planck-core scale (v2.1, criterion: leakage must not push the bounce beyond the honest band), the bound tightens to α < 2×10⁻⁴⁵ m² — 38 orders beyond the earlier 10⁻⁶ m².

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.

5. (v2) Hubble-tension verdict: anchoring on the CMB acoustic scale, every viable trajectory gives H₀ ≤ the ΛCDM value (68.0 down to 63.4) — thawing worsens the tension, and a three-wall no-go theorem (reservoir lock 10⁻⁹; both fixing-rate choices 10⁻⁴⁶/10⁻⁸; FIRAS/ΔN_eff/ω_m block any tuned escape) closes every early-universe rescue within the equations. The stake is placed: H₀=73 confirmed systematics-free kills this sector; 67–69 leaves it fully consistent.

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) = cH₀/32G = 146 M☉/pc² — identical for every galaxy, zero parameters (v2.1: ζ = π/2 derived)

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.

A speculative, conditional prediction — deliberately kept outside the seven kill-lines above. It rests on a collapse mechanism that is currently left open (see the field-equations note), plus a Born–Markov approximation; a firm version requires the torsion spectral density, which is not yet computed.

Prediction (conditional; v2.1 note). If causal fixing is driven by the propagating-torsion sector (treated as an intrinsic decohering bath), decoherence acquires a threshold at the torsion mass scale Mc² = ħc/√α. v2.1 update: with the tightened bound α < 2×10⁻⁴⁵ m², the threshold moves from the v2 value (≳0.2 meV) to ≳4×10⁶ GeV — far above any laboratory scale, so the low-energy suppressed-collapse signature is withdrawn; the conditional extension survives only as a formal statement.

Why it is distinctive. Neither standard quantum mechanics nor the mass-scaled objective-collapse models (GRW, Diósi–Penrose) carry a meV energy threshold. Decidable with low-temperature superconducting-qubit and cold-molecule interferometry — no black holes required.

Status: [SPEC] speculative. Depends on an unproven torsion-bath mechanism and a Born–Markov approximation. The threshold is a lower bound (α is only bounded above), so the true scale may be higher. This is a conditional extension, not one of the seven falsification lines.

The three sectors first left qualitative are now quantitatively addressed:

• Black-hole information — explicit Page curve [computed]. No singularity means information is stored in the torsion holonomy; the unitary radiation entropy S_rad = min(S_thermal, S_BH) rises to the Page point (half-entropy, peak S_rad/S₀ = 0.500 at t/t_evap = 0.646) then falls back to zero — all information returns. The turnover is enforced by the holonomy correlations.
• Baryon asymmetry η_B [v2.1 — closed at theorem level]. The torsion self-energy bias becomes self-consistently unstable above T_c = 2.1×10¹⁸ GeV — a post-bounce chiral-condensate phase whose sign is set by the bounce arrow (CP phase O(1), no tuning); the only surviving latch is ΔL=2 Majorana washout. v2.1 completes the flavor-resolved constraint chemistry (hypercharge-neutrality + inertness theorems, spectator-protected fixed point, super-gauge-equilibrium epoch structure with boson underpopulation) — the framework's own overproduction wall forces m₁ < 10 meV and the production-limited solution lands at m₁ consistent with zero: Σm_ν = 0.059 eV, normal ordering, Majorana, m_ββ = 1.5–3.7 meV — five finalized observables, no survey input anywhere.
• Bounce spectral index n_s [computed; v2 survival audit passed]. Dust-dominated contraction gives n_s ≈ 1.000, matching Planck's 0.9649 to 3.5%, avoiding the pure-torsion blue-tilt pathology. v2 audit: observable modes exit ≥22 orders below the dust-validity bound (Δn_s ≤ 10⁻¹⁵) — the index survives the Planck recalibration; reheating moves to 0.6–0.9 E_Pl, 1+z_b ≈ 10³², now matching Popławski's published a_min.
• (v2.1) Primordial magnetic fields — unconditional. The comoving horizon caps B_eff@Mpc ≤ 2.3×10⁻¹⁹ G (chiral instabilities blocked by a parameter-free inequality, 2.6 < 54; CPI door shut). v2.1 closes the last exit: the condensate branch is analytically dead (BCS gap Δ/E_F ~ e^−2.6×1012 at sub-Planck Fermi surfaces). Single-valued prediction: no observable primordial field. A confirmed volume-filling helical field ≥10⁻¹⁶ G falsifies the sector outright, no fallback.
• (v2) Lithium-7 — formally disclaimed, with a consistency dividend. All three V131 levers at BBN are ≤10⁻³¹ of the required effect — V131 cannot eat the lithium excess and does not claim to; the same numbers mean the D/H (1%) and Y_p (0.5%) gates, where most modified-gravity models die, pass automatically.

The predictions are pinned to live experiments. Honest record of whether the newest 2025 data pushes each toward support or falsification:

• 🔴 Dark energy w(z) (F1) — under pressure. DESI DR2 (2025) shows a 2.8–4.2σ preference for evolving dark energy; its best-fit w(z) crosses below −1 at higher redshift (a phantom crossing) — squarely on V131's hard kill-line F1 (thawing quintessence has w ≥ −1 always and cannot cross). DR2 pushes F1 toward falsification. We flagged this in 09.3; w₀ > −1 today is still consistent, and the past-crossing's reality is itself debated.
• 🟡 Black-hole shadow (F6) — neutral, by design. EHT's 51.8±2.3 μas stands (2024 added magnetic-field imaging, no new size). V131's exterior is exactly Kerr (r_core/r_s~10⁻³¹ after the v2 recalibration — even safer), so EHT cannot distinguish the core — a consistency check, not a discriminator.
• 🟢 (v2.1) Baryogenesis ⇔ neutrino masses (F9/F10) — sharpest target, finalized. Σm_ν = 0.059 eV sits at the normal-ordering theoretical floor, inside the DESI 2024 bound (<0.072 eV); a measurement resolving Σm_ν significantly above 0.065 eV, an inverted ordering, or 0νββ above 4 meV kills the pipeline.
• 🟡 (v2) Hubble tension (F8) — self-limiting, early escape closed. CMB-anchored H₀ ≤ ΛCDM with every early-universe escape closed by a three-wall theorem. No position taken on SH0ES systematics; the stake cannot be adjusted after the fact.
• 🟢 Nonsingular torsion bounce (C1/C6) — supported. Popławski is actively publishing V131's exact core mechanism in 2024–2025 (torsion repulsion → nonsingular bounce → "universe in a black hole") — C1/C6 are mainstream-adjacent and live. A 2025 JWST analysis found ~⅔ of early galaxies spin clockwise, read by some as evidence the universe sits inside a rotating black hole — a new (if debated) observational hook.

Bottom line: the foundation (nonsingular torsion bounce) is gaining real-world footing; the dark-energy prediction is being squeezed by the newest data. That is the system working as intended — one sector supported, one under pressure, exactly as the falsification table anticipated.

V131 claims no singularity — so Penrose's rigorous results (his 2020 Nobel was for the singularity theorems) are the natural reference point. Graded honestly:

• 🟢 Penrose–Hawking singularity theorem — strongest. V131's torsion core doesn't violate it; it sits in the precise gap where a premise fails. The theorem assumes no torsion, and Einstein–Cartan torsion adds an anti-convergence term to the Raychaudhuri equation that un-traps the surface at ρ_b. Not "Penrose was wrong" — "V131 lives in the loophole Penrose's own assumption leaves open."
• 🟢 Diósi–Penrose objective collapse — genuine. The (3′) causal-fixing rule is a cousin of DP, but triggered by a Fisher information angle (a critical Θ) rather than gravitational self-energy — which is exactly why the DP γ-ray bound (Donadi 2021) does not constrain V131.
• 🟡 Weyl Curvature Hypothesis / CCC — analogy. "Initial low entropy = information reset" and "Big Bang = previous bounce" run parallel to Penrose's WCH / Conformal Cyclic Cosmology — but the mechanisms differ (information phase transition vs conformal geometry); analogy, not identity.

4D landing: V131 is 9D but reduces to 4D (3+1) GR as τ→0; the Penrose / conformal 4D spacetime is its GR limit. V131 doesn't replace 4D GR — it contains it as a limit.

（v2）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 4×10⁻²¹ 米的挠率芯（普朗克长度的 10¹⁴ 倍，零承载歧义普适曲线； v1 的"47 纳米"来自尘埃判据，已勘误），反弹密度为普朗克量级（与 Popławski 相对论性处理一致）；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； 附单向哈勃预言 H₀ ≤ ΛCDM、无早期逃生门），梯度 = 暗物质（平坦旋转曲线自然出现； 固定闸门抹除核区尖峰，Donato 柱密度成为零参数常数 cH₀/32G = 146 M☉/pc²——闸门系数已推导 ζ = π/2）。（v2.1 定稿）普朗克反弹的冻出把重子不对称闭合为 五条定稿中微子可观测量：最轻中微子与零一致、Σm_ν = 0.059 eV（正常序理论下限·点预言）、 正常质量序、Majorana、m_ββ = 1.5–3.7 meV。

十一条证伪线全部列明（F1–F11）。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、已知张力与历次勘误 （含 v1 核洞数值的当日更正）均在完整报告中注明。

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

Archived & citable — Zenodo (CERN), priority date 2026-07-03, now v2.1:
Concept DOI: 10.5281/zenodo.21153115 (resolves to latest)  |  v2.1: 10.5281/zenodo.21180901

NEW — Quantum Foundations & Measurement Sector Supplement (v2.3-QFound):
two postulates (π/2 threshold + GKSL fixing), everything else theorems — QSL bound τ_fix ≥ πħ/4ΔE, no-record theorem (zero intrinsic decoherence at any mass), Born rule derived, torsion↔QGT two-channel dictionary, energy-gap division of labor; v2.3: ensemble-calorimetry protocol for the F5′ Landauer-ledger kill line (measure-and-keep heat-floor audit, full Holevo heat–information curve, feasible with current calorimetry) + complete 9-dimensional ε-dual index decomposition.
↓ QFOUND SUPPLEMENT (PDF)
DOI: 10.5281/zenodo.21193722 (concept: 10.5281/zenodo.21184136, supplement to the cosmology record)

Calculation engines: v131_cosmos.py • v131_torsion_core.py • v131_wz.py • v131_halo_core.py • v131_cx.py • (v2) v131_hz.py • v131_fpsi.py • v131_core_planck.py • v131_c6_planck.py • v131_c4_freezeout.py • v131_c10_planck.py • v131_li7.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.