The problem
Imagine you could weigh all the visible matter in a galaxy — stars, gas, dust — and calculate how much gravity it should produce. Then you measure how stars actually orbit at various distances from the centre. What you find is baffling.
Near the centre, where matter is densely packed, stars orbit fast. So far, so good. But as you move outward, where visible matter thins out, stars should orbit progressively slower — just as the outer planets in our solar system orbit more slowly than the inner ones. They don't. Stars at the outer edges of galaxies orbit at roughly the same speed as those near the centre. Rotation curves are flat.
This is one of the great open problems in physics. It has been known since the 1970s and still lacks a consensus explanation.
The standard solution posits invisible matter — dark matter — forming a vast halo around each galaxy, whose additional gravity accounts for the observed velocities. It works mathematically, but no dark matter particle has been directly detected despite decades of searching. Another approach, called MOND, modifies the law of gravity at very low accelerations. It also works reasonably well, but introduces a universal constant (a₀) without deriving it from any deeper principle.
This research programme starts from a different question.
The question
What if the gravitational response of a galaxy depends not only on where its matter is now, but also on how it got there?
Galaxies don't appear from nothing. They form over billions of years through gravitational collapse, mergers with other galaxies, gas accretion, stellar compaction, material ejection. Each galaxy has a unique history. The question is whether that history leaves a trace in its present gravitational dynamics.
A system is Markovian when its present state contains all the information needed to determine its future response. A thermostat is Markovian: it doesn't matter how the room reached 22°C, only the current temperature matters. But many physical systems are not like that. A magnet remembers whether it was magnetised up or down — its response depends on its history. This is called hysteresis, and it is a form of memory.
The hypothesis of this programme is that galaxies might work more like magnets than thermostats. Not memory in a metaphorical sense, but an operationally measurable property: if two galaxies with the same present state show different gravitational responses, and that difference is associated with their evolutionary trajectory, then the system retains memory.
The coherence state ψ
To test this hypothesis, it must be quantified. In the model developed in this series, each galaxy is characterised by a coherence state ψ, a number between 0 and 1 that captures how dynamically "organised" the system has become.
Think of ψ as an indicator of dynamical maturity. A young, gas-rich galaxy with a loosely organised disc tends to have ψ near 1. A massive, evolved galaxy with a compact, well-defined stellar disc tends toward ψ near 0. But — and this is the key point — ψ cannot be fully reconstructed from the galaxy's present properties. Two galaxies with the same mass, the same size, and the same amount of gas can have different values of ψ. That difference is what we call the memory component.
If ψ were simply another way of measuring mass or size, it would not be interesting. What makes it interesting is that the part of ψ that does not come from present properties still predicts gravity. That is what should not happen in a memoryless system.
The results
This series of seven papers develops the hypothesis from initial formulation to empirical tests. The central results come from Paper VII, which applies five formal tests of non-Markovianity to 143 galaxies from the SPARC catalogue. Here are the most important.
Twin galaxies with different gravity. NGC 3198 and UGC 09037 are two galaxies with nearly identical present properties: same flat velocity (150 km/s), similar gas fractions (0.11 vs 0.15), comparable disc scales. Yet their effective gravity differs by a factor of 2.2. In any model where gravity depends only on the present state, these two galaxies should behave almost identically. They do not. In total, 81 galaxy pairs are identified with this property: similar present states, radically different gravitational responses.
RAR scatter is structure, not noise. The Radial Acceleration Relation (RAR) connects the observed gravitational acceleration to the acceleration predicted by visible matter. It is one of the most important empirical relations in galactic astrophysics, and its tightness has been one of the strongest arguments in favour of MOND. But it has some scatter, which has always been treated as observational noise — measurement errors, distance uncertainties, etc. When galaxies are separated by their ψ value, that scatter splits in two: high-ψ galaxies form a branch above the mean, low-ψ galaxies form one below. The statistical separation between both branches is overwhelming (p = 6 × 10⁻⁹⁵). What looked like noise is real dynamical structure, organised by the coherence state.
Historical information predicts gravity. This is perhaps the result most difficult to explain without memory. Nine baryonic variables are taken for each galaxy — mass, size, gas, concentration, surface brightness, morphology, bulge presence, etc. — and the best possible prediction of ψ is built from them. The leftover (the residual, which we call ψ_mem) should be noise if ψ contains no additional information. But ψ_mem still predicts effective gravity with a correlation of +0.441 (p = 3.4 × 10⁻⁸). Even more striking: the mutual information between ψ_mem and gravity exceeds that of any individual baryonic variable by a factor of 50. It is as if, after squeezing out all the information that present properties can give, there remains a residual that knows something about gravity that present properties do not know.
Hysteresis. In the plane formed by gas fraction and coherence, early-type galaxies (ellipticals, lenticulars) and late-type galaxies (spirals, irregulars) occupy opposite branches. At the same gas fraction, an early-type galaxy has a different ψ from a late-type one. This is precisely the definition of hysteresis: the macroscopic response depends not only on the present state, but on the path by which the system arrived at that state.
The signal survives every control. We tried to break the effect in every way we could think of. We created 500 synthetic universes by shuffling ψ across galaxies: the effect appears in none of them (p < 0.002). We regularised the fitting to prevent saturation at the extremes (ψ ≈ 0 or ψ ≈ 1) from generating artefacts: the signal does not weaken, it strengthens (ρ = +0.707). We applied bootstrap to the topology of the state space: attractors, branches, hysteresis — all stable, all 95% confidence intervals exclude zero. If this is an artefact, it is an extraordinarily resilient one.
What it means
The claim is not that dark matter has been refuted. The claim is more precise: galactic dynamics contains irreducible historical information that purely instantaneous models do not capture.
This forces any framework — ΛCDM, MOND, or any alternative — to explain why galaxies with identical present states respond gravitationally in different ways. This is not a problem only for dark matter. It is a problem for any description of galactic gravity that treats the present state as sufficient.
In this framework, the effective gravity of a galaxy behaves as a collective state that retains partial information about the system's formation history. Not as an extra force, but as an emergent response with memory. The idea is closer to non-equilibrium statistical physics — order parameters, phase transitions, hysteresis — than to classical modifications of Newton's law.
If correct, the deepest consequence would not be "there is no dark matter" but something more subtle: observable galactic gravity may not be an instantaneous function of matter, but a collective historical state.
The paper series
The programme is developed across seven open-access papers:
I. Gravitational Memory and the Origin of Flat Rotation Curves — phenomenological formulation and validation on 25 SPARC galaxies. Introduces the gravitational memory hypothesis and the correction v_obs² = v_bar²/(1−ε). 23/25 galaxies with χ²/dof < 1.
doi:10.5281/zenodo.19970906
II. Non-Local Memory Operator and Galactic Rotation Curves — theoretical derivation of the fractional operator D = Δ + (−Δ)^α + m² and the cascade exponent β = 53/15 from three-dimensional Kolmogorov turbulence.
doi:10.5281/zenodo.19999489
III. Parameter-Free Canonical Profiles and Radial Regime Transition — three-phase taxonomy (dwarf, transition, mature disc), parameter-free canonical profiles derived from the operator's spectral attractors. R² = 0.955 over 171 galaxies.
doi:10.5281/zenodo.20054201
IV. Spectral Attractors and Geometric Screening in Galactic Dynamics — analysis of the spectral flow β(ε), ghost-free condition, geometric screening mechanism recovering Newtonian gravity in the inner disc.
doi:10.5281/zenodo.20075609
V. Irreducible Dynamical Information in the Galactic Coherence State — five statistical irreducibility tests for ψ: permutation (0/10,000), ΔAIC < −20, matched pairs (77% success), spectral efficiency (86%), window α ∈ [0.55, 0.65].
doi:10.5281/zenodo.20104807
VI. Spectral Dimensional Closure of the Galactic Memory Operator — derivation of α_K = 3/5 from topological necessity (d = 3 → α = d/(d+2)), with zero adjustable parameters. The universal formula has zero free universal parameters.
doi:10.5281/zenodo.20111475
VII. Operational Evidence for Gravitational Memory in Disc Galaxies — five formal non-Markovianity tests, bimodal RAR (KS 6×10⁻⁹⁵), 81 twin pairs, information bypass ×50, hysteresis, robustness controls (saturation, null universes, bootstrap).
doi:10.5281/zenodo.20112695
All papers are collected in the programme's Zenodo community:
zenodo.org/communities/gravitational-memory
What remains open
A great deal.
Replication on independent catalogues is the necessary next step. SPARC is an excellent catalogue with 175 galaxies with detailed rotation curves, but the community will need to see the same results in larger samples: BIG-SPARC (~4,000 galaxies), MaNGA (2D kinematics), SAMI, GAMA. That will determine whether the signal is robust or catalogue-dependent.
The theoretical formulation of the memory operator may be an effective approximation to something deeper. The fact that the formula works does not mean the physical interpretation is final. There may be alternative formulations that capture the same phenomenon.
If ψ is truly a collective state parameter, we need to understand how it forms, how it evolves, what role environment plays (do cluster galaxies have different ψ?), and whether it can be derived from cosmological simulations.
And if gravitational memory is a real property of self-gravitating systems, its implications extend well beyond rotation curves: gravitational lensing, structure formation, scatter in scaling relations, transitions between dynamical regimes.
This is an open programme, not a closed conclusion.
About the author
I am an independent researcher with no institutional affiliation. This work has been developed entirely outside the conventional academic circuit, published in open access, using public data (SPARC, THINGS, LITTLE THINGS) and reproducible code. The entire series is freely available.
I do not come from academia. I hold no chair and lead no research group. This means the results must stand exclusively on their content, not on the institutional authority of whoever presents them. All code, data, and papers are public so that anyone can verify, reproduce, or refute them.
If you work in galactic dynamics, modified gravity, dark matter, or non-equilibrium statistical physics and find these results relevant, I welcome your critical evaluation.
Contact: meizoso@legalpin.com
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The history of matter may shape the present response of gravity.
