Work in progress · 2026
Spacetime, gravity, and the Standard Model's structure from a single postulate.
Key results — derived from the single postulate
| Result | Value | Status | Note |
|---|---|---|---|
| Higgs boson mass \(m_H\) | \(124.8\pm2.4\ \text{GeV}\) | 0.19σ from PDG | Two EWSB inputs disclosed |
| Dark energy \(w\) | \(w = -1\) exactly | Exact geometric corollary | Downstream of calibrated \(\Lambda\) |
| Area quantum \(\Delta A\) | \(4\ln(442)\,\ell_P^2 \approx 24.37\,\ell_P^2\) | Derived | From \(g = 442\) alone |
| Barbero–Immirzi analogue \(\gamma_{\rm DEG}\) | \(\approx 2.24\) | Derived | Not fitted — group-theoretic output |
| Page curve \(S_{\rm rad}(k)\) | \(\min(k,\,N{-}k)\ln 442\) | Exact (leading order) | Kinematic from finite-dim \(\mathcal{H}\) |
| WdW unitarity | Exact | Exact | Kinematic from finite-dim \(\mathcal{H}\) |
The cosmological constant \(\Lambda\) is a calibrated input (fit to \(\Lambda_{\rm obs}\)); \(w = -1\) is the derived consequence downstream of it.
Framework results — derived, load-bearing
Falsifiable predictions
| Observable | Prediction | Experiment | Timeline | Falsifier |
|---|---|---|---|---|
| Already confirmed | ||||
| GW speed \(c_{\rm GW}\) | \(= c\) exactly | GW170817 | ✓ confirmed | — |
| Ongoing | ||||
| No WIMP signal | Zero direct detection | LZ / XENONnT | ongoing | WIMP detection |
| CPT-odd LV \(\eta_1\) | \(= 0\) [approximate] | Fermi-LAT / CTA | ongoing | Any CPT-odd MDR detection |
| MOND acceleration \(a_0^{\rm DEG}\) | \(8.6\times10^{-11}\ \text{m/s}^2\) | SPARC / Vera Rubin | ongoing | 28% below observed — open item |
| 2–5 years | ||||
| Dark energy \(w\) | \(= -1\) exactly | DESI / Euclid | 2–5 yr | Any \(5\sigma\) \(w\neq-1\) detection |
| Power spectrum \(P(k)\) | Two-scale suppression \(k\sim0.4\) and \(90\,h/\text{Mpc}\) | DESI / Euclid | 2–5 yr | Suppression at neither scale |
| 3–10 years | ||||
| Normal neutrino ordering | \(m_{\nu_1}\sim10^{-5}\ \text{eV}\) | JUNO | 3–5 yr | Inverted ordering confirmed |
| Higgs coupling \(\kappa_V\) [open tension] | \(0.432\) tree; ceiling \(0.797\) analytical | HL-LHC | ~5 yr | \(\kappa_V\) consistent with SM at \(2\sigma\) |
| Neutron EDM \(d_n\) | \(2\times10^{-53}\text{–}6\times10^{-40}\ e{\cdot}\text{cm}\) | n2EDM@PSI | ~2026 | Signal \(>10^{-26}\ e{\cdot}\text{cm}\) |
| Proton decay \(\tau_p\) [provisional] | \(\sim10^{33\text{–}34}\ \text{yr}\) | Hyper-Kamiokande | 5–10 yr | \(\tau_p > 10^{35}\ \text{yr}\) |
| 2030s–2037 | ||||
| Tensor-to-scalar ratio \(r\) | \(0.00452\pm0.002\) [semi-derived] | CMB-S4 / LiteBIRD | ~2032 | \(r > 0.01\) |
| Non-Gaussianity \(f_{\rm NL}\) \(^\dagger\) | \(\approx0.0076\) (null) [asserted] | CMB-S4 | ~2032 | \(f_{\rm NL} > 1\) at \(2\sigma\) |
| Env. Tully–Fisher variation | \(\lesssim10\%\) [conditional] | Vera Rubin / LSST | ~2030–35 | Zero variation at \(5\sigma\) |
| Di-Higgs cross-section \(\sigma_{HH}\) | \(57.5\pm10\ \text{fb}\ (1.85\times\text{SM})\) | HL-LHC | ~2035 | \(\sigma < 40\ \text{fb}\) at \(5\sigma\) |
| Dark matter X-ray line | \(3.5\text{–}5\ \text{keV}\ (\nu_{R_1},\ m_s\sim7\text{–}10\ \text{keV})\) | ATHENA | ~2035 | Non-detection in viable window |
| LISA breathing mode \(^\dagger\) | Undetectable if \(a \gtrsim\) pm-scale [conditional on unconfirmed \(a\)] | LISA | ~2037 | Polarisation above \(10^{-3}\) |
| EMRI phase shift \(^\dagger\) | \(\Delta\Phi\sim10^{-82}\ \text{rad (null)}\) | LISA | ~2037 | Phase anomaly at LISA sensitivity |
| Long-term | ||||
| CMB \(\mu\)-distortion | \(\mu\sim10^{-5}\) | PIXIE / Voyage 2050 | 15–20 yr | \(\mu < 10^{-6}\) |
| Di-Higgs at 100 TeV | \(2267\pm400\ \text{fb}\) | FCC-hh | ~2040+ | — |
\(^\dagger\) Null prediction: DEG predicts signal below experimental threshold. Detection above threshold would falsify.
Known tension
Higgs coupling \(\kappa_V = 0.432\)
Currently \(14.2\sigma\) from the LHC measurement at tree level. Non-perturbative DGMLY enhancement raises the analytical ceiling to \(\kappa_V = 0.797\) (\(5.1\sigma\)); no analytical method reaches \(\kappa_V > 0.920\). Resolution requires DEG-L Group C lattice computation. The programme's single most important open conflict with data.
Genuine open derivation
Cosmological constant \(\alpha_{\rm exp}^{\rm cosm}\)
\(\alpha_{\rm exp}^{\rm cosm}\) is a disclosed input, calibrated directly to match \(\Lambda_{\rm obs}\). Several candidate derivation mechanisms have been tested and ruled out — including identification with a running SU(21) gauge coupling, a dynamically-generated confinement scale, and a unimodular-gravity integration constant. Closing this gap requires a theoretical breakthrough, not a numerical refinement.
High-priority open problem
Atomic lattice spacing \(a\)
No derivation of \(a\) currently exists. The RG route gives the wrong sign. The only numerical bound is a weak lower threshold from LISA sensitivity (a few picometers). This quantity is load-bearing across the cosmological-constant discussion, the LISA null prediction, and the matter power-spectrum features.
Open reduction problem
Five-to-three generation reduction
The embedding chain's own branching rule gives five copies of the family-triplet under \(\mathrm{SU}(3)_{\rm fam}\), not three. Identifying exactly three as the observed SM generations — and accounting for the other two — is not currently derived. Three generations are assumed as a working hypothesis throughout the fermion sector.
Not yet derived
Galaxy cluster profiles at large \(r\)
The MOND mechanism provides partial screening only. Quantitative cluster mass profiles at large radii are not yet derived. The \(\sigma_8\) growth-factor calculation does not currently reproduce its own stated product, and no first-principles derivation is available.
Outside current framework
Spectral index \(n_s\)
The DEG quantum epoch gives \(n_s = 4\) [asserted; the argument is \(k\)-independent and cannot by itself produce a spectral index]. The observed \(n_s \approx 0.963\) is identified as a fossil of the pre-geometric phase \(\tilde{G} \supset \mathrm{SU}(21)\times\mathrm{U}(1)\). Seven internal mechanisms exhausted; an eighth (Euclidean Bessel) remains under active investigation.
Disclosed inputs
Higgs EWSB parameters \(\varepsilon_\alpha, \varepsilon_\beta\)
The two electroweak-symmetry-breaking parameters feeding the Higgs mass prediction are currently calibrated inputs, not independently derived. Three independent checks confirm the stated Coleman–Weinberg potential does not reproduce them. Deriving these from first principles is an open research target structurally analogous to \(\alpha_{\rm exp}^{\rm cosm}\).
Unattempted research direction
Sterile neutrino mass \(\nu_{R1}\)
The naive type-I seesaw formula for \(M_{R1}\) misses the 7–10 keV target by roughly thirteen orders of magnitude. Separately, standard leptogenesis falls short of the \(L_{\rm active}\sim10^{-3}\) needed for resonant sterile-neutrino production by five orders of magnitude. A candidate Affleck–Dine mechanism [conditional] closes most of this gap, to within a factor of ~6 — but the coefficient closing that remainder is fit to the target rather than derived. Both gaps point to the same unaddressed sector: a dedicated suppression and transfer mechanism motivated by the atom-overlap geometry used in the fermion sector, which has not yet been attempted.
Imported assumption
Bekenstein–Hawking coefficient from \(g_{\rm eff}=1\)
Substituting \(g_{\rm eff}=1\) and Planck-sized screen atoms into the DEG entropy formula gives zero entropy per screen atom, not the coefficient \(1/4\). The \(S_{\rm screen}=\kB A/(4\ell_P^2)\) result is currently imported from standard semiclassical gravity rather than shown to follow from \(g = 442\). This also affects the independence of the area-quantum derivation.
Resolution path identified
DEG-L lattice programme
Four ensemble specifications (E1–E4) are complete. Three observable groups: topology (\(K_{\rm fam}\)), Higgs floor, V−A spectral function (\(\kappa_V\)). Estimated ~\(10^5\) GPU-hours. Results would sharpen the Higgs mass uncertainty and constrain the \(\kappa_V\) resolution pathway.
DEG posits that spacetime is a statistical aggregate of \(N\) discrete Planck-scale atoms, each characterised by a size parameter \(a_n\) and an internal Hilbert space of dimension \(g = 442\). The dynamics is governed by a single Hamiltonian constraint — no background metric, no continuous fields at the fundamental level.
From this foundation, the programme derives: the Standard Model gauge group from \(\mathrm{SU}(21)\) group theory alone; dark energy \(w=-1\) exactly; black hole unitarity and the Page curve from the finite-dimensional Hilbert space; the discrete area quantum; and the Higgs boson mass at \(0.19\sigma\) from two disclosed EWSB inputs. The cosmological constant's magnitude is a calibrated input.
What is not claimed. DEG is not a complete theory of quantum gravity. Three calibrated inputs are used — \(\alpha_{\rm exp}^{\rm cosm}\) for the cosmological sector, and \(\varepsilon_\alpha, \varepsilon_\beta\) for the Higgs sector. The generation count from five family-triplet copies to the observed three is an open reduction problem. The atom spacing \(a\) has no derivation. The programme is offered as a coherent, falsifiable research direction with its open problems plainly stated.
Active research directions
This page is updated as the programme develops.
Like loop quantum gravity and causal set theory, DEG takes discreteness as fundamental. It differs in using a statistical mechanics approach: gravity and time emerge thermodynamically, not through geometric quantisation.
The dark energy equation of state \(w=-1\) follows as an exact geometric corollary of the constraint structure, independent of any input. The cosmological constant's magnitude is a calibrated input.
The Higgs mass prediction \(m_H = 124.8\pm2.4\ \text{GeV}\) agrees with the PDG value at \(0.19\sigma_{\rm theory}\). It is derived from CP-violating observables through a single internal phase \(\varphi_{\rm DEG}\), though two EWSB parameters feeding the calculation are disclosed inputs rather than independent derivations.
The programme is falsifiable at multiple near-term experiments. The most decisive single test is \(w = -1\): any \(5\sigma\) detection of \(w\neq-1\) by DESI or Euclid rules out the entire dark energy sector. DESI DR2 (2025) shows a \(3.1\sigma\) preference for dynamical dark energy in combined analyses — suggestive but below the falsification threshold.
Domain of validity. DEG describes the post-condensation universe — from spacetime atom formation through today. The observed CMB tilt \(n_s \approx 0.963\) is not a DEG prediction; it originates in a pre-geometric phase \(\tilde{G} \supset \mathrm{SU}(21)\times\mathrm{U}(1)\) preceding atom condensation, in the same sense QCD does not derive the electroweak gauge group.
Matteo Pinna is a theoretical physicist working independently on quantum gravity and emergent spacetime. His interest in emergent gravity began during his thesis work in 2018, shaped by a conviction that the foundations of physics should admit a simple, parameter-free description — and a specific dissatisfaction with the treatment of time in general relativity.
The starting point was a refusal to accept time as a curved fourth dimension behaving differently from the other three. If space is emergent, time should be too — and the arrow of time, rather than being imposed by initial conditions, should follow from the statistics of whatever is fundamental. DEG is the formalisation of that programme, developed over several years alongside a career in technology.
He is based in Madrid.
The consolidated manuscript is the primary reference for the programme. Not peer-reviewed.
Poster material will be made available here via Zenodo once uploaded.
If you work in quantum gravity, emergent spacetime, or related areas and find this programme of interest, I would welcome correspondence — critical feedback especially.
matteo@deg-gravity.com
I am an independent researcher based in Madrid. Collaboration enquiries and comments from researchers with relevant expertise are very welcome.
The papers above contain full derivations, explicit uncertainty budgets, and complete lists of open problems. Nothing is behind a paywall or submission requirement.
The complete research programme — all derivations, results, open problems, and falsification targets — is consolidated in the manifest on Zenodo: doi.org/10.5281/zenodo.21724820
If you are a physicist encountering DEG for the first time and would like to discuss the approach, its foundations, or its limitations, please feel free to write. I am also happy to share derivation notes on specific points not fully developed in the papers.