What changes
The present curvature response depends causally on past curvature through a finite retarded kernel.
Independent theoretical-physics programme · public edition I–XII · 21 August 2026
Gravity with a finite causal memory.
CMG adds a retarded curvature-memory channel to Einstein gravity. A Dynamic Planck Network is the proposed microscopic origin; its continuum matching remains conditional.
What is strongest
A precisely stated near-GR linear closure and its fixed-background DESI DR1 benchmark.
What remains open
Action-to-closure matching, full Boltzmann likelihoods, nonlinear screening and microscopic calibration.
Locked gravitational notation
One action, two distinct effective amplitudes.
The action-level coupling and the DESI-facing closure amplitude are not identified without a derivation.
Nonlocal action
Effective sector
S ⊃ −
α̃
2
∫ d⁴x √−g R(□ + βrate²)−1
ret
R
(□ + βrate²)U = −R
α̃ ∈ (−1,0), with ηact ≡ −α̃ ∈ (0,1).
Fixed-background no-slip closure
DESI-facing
μ(k,a) = 1 −
ηcla²βIR²
k² + a²βIR²
γ(k,a) = 1
βIR ≡ βrate/c is a dimensional bridge, not an amplitude-matching proof.
Interactive linear response
Where the closure departs from GR.
Large k recovers μ → 1. At long wavelengths, the no-slip closure approaches μ → 1 − ηcl.
Long-wavelength limit
μ → 0.950
Pedagogical shape explorer at a = 1. It is not a likelihood fit and does not implement the separate action-level perturbation candidate.
Observational baseline
DESI permits a near-GR sector; it does not select CMG.
0.086σ from the GR value Ag = 1, using the full 6 × 6 covariance and exact ΛCDM growth baseline.
Representative large-βratio range; at βratio = 30 the physical interval remains unconstrained.
Substantial late-time suppression would have to arise from the separate, still-uncalibrated nonlinear response sector.
Claim boundary
The DESI limits constrain ηcl in a fixed-background phenomenological closure. They are not limits on ηact from the nonlocal action.
Research status
Evidence is labelled by what it actually establishes.
The public edition separates controlled results, benchmarks, conditional constructions and the specific calculations that remain open.
Controlled
Linear scalar truncation
Tree-level window −1 < α̃ < 0, equivalently 0 < ηact < 1. This is not a proof of nonlinear or ultraviolet stability.
Benchmark
DESI DR1 linear growth
Ag = 0.9962 ± 0.0437, only 0.086σ from GR. CMG is allowed in this sector, but not preferred over ΛCDM.
Conditional
DPN → continuum bridge
The spectral relation identifies a slow graph mode with the memory rate under explicit coarse-graining assumptions; normalization and SI calibration remain open.
Open
Action-level cosmological closure
The general-gauge SymPy route and radiation cross-check pass, and the prototype provider has passed its internal gate. Direct integration replaces the rejected averaged-fluid route; the start-time criterion fails, the admissible Λ root is non-unique, and production hardening plus a separately frozen likelihood remain open.
Benchmark
Regular SU(2) control
The finite-volume V4 control is reproducible, but it is not a physical DPN port. The elastic graph gap, transfer gap, correlation mass and continuum Yang–Mills gap remain distinct: λ₂(Lel) ≠ Δtransfer ≠ mcorr ≠ ΔYM.
Galaxies
g† = 1.1735 × 10⁻¹⁰ m s⁻² is an empirical SEM–RAR fit. Its DPN interpretation is not yet a microscopic prediction.
Gauge sector
Recovered faces verify B₁B₂ = 0 and the discrete Hodge structure. cγ = 0.7380 is a static zero-momentum coefficient; the registered status is D2_CONTRACT_FAILED, while its depth ladder supports a finite-time-transient diagnosis only. A microscopic provider and two-species common cone remain open.
Matter sector
Exact charge conservation holds in the stated GKSL closure; emergent chirality remains conditional on explicit spectral assumptions.
Measurement
The motif calculation supplies the necessary positive Q = 3 sign; physical stability still requires the density threshold and consistently extracted gaps. No proton identification follows from the sign test.
Open the full programme-status infographic ↗
Decisive open calculations
The programme advances only if these gates close.
Action-level provider
Use the passed general-gauge and radiation prototype as the starting point; resolve the start-time plateau, choose a physical Λ branch, harden the production provider and obtain independent tensor-tool confirmation before opening a likelihood.
Nonlinear calibration
Embed the response in PM/N-body or dynamic DPN simulations; calibrate βμ(x) and Γeff(x) against halo observables.
Joint likelihood
Compute CMB TT/TE/EE, lensing, DESI growth and BAO with a self-consistent action-level Boltzmann implementation.
Microscopic provider and scaling
Derive a generator-native DPN provider before physical gauge sampling, then test ξphys, continuum convergence and retarded-kernel scaling on large dynamic ensembles.
Research corpus
Publications and technical records.
Gravity & observations
DPN, continuum & UV
Matter & measurement
Direct answers
Frequently asked questions.
Does CMG replace dark matter?+
Not as a completed claim. The SEM–RAR sector reproduces an empirical galactic response, but cluster dynamics, nonlinear structure formation and the full CMB likelihood remain open tests.
Has CMG solved the S₈ tension?+
No. The DESI-compatible linear closure is near GR. Any material late-time suppression would require a separately calibrated nonlinear screening sector.
Are ηact and ηcl the same parameter?+
No identification is currently justified. ηact belongs to the nonlocal action; ηcl is the amplitude of the fixed-background no-slip closure used in the DESI-facing test.
Is the reported photon speed physical?+
The value 0.7380 is a static zero-momentum coefficient on recovered faces, not cγ/cDPN. The preregistered D2 contract failed; its depth ladder supports a finite-time-transient diagnosis only. A physical answer requires raw-export dispersion, a microscopic provider, dynamic weights and two species compared with one physical clock.