Adversarial audit · 5 simulations · 29 agents

Does gravity kill distinguishability faster than recordability?

“Gravity is an information-selection machine: it destroys distinguishability faster than it destroys recordability.”

Partly. Gravity really does shrink what a distant observer can learn about a source to a few numbers. But most of that shrinking is shared by every long-range field, and the sharper claims fail as stated. What is genuinely gravitational is which numbers survive, why they can never be hidden, and the black-hole endpoint where everything else is exported.

Claims tested 7Refuted 2Damaged 3Survive with repair 2Theorem extracted 1

H · coreDamagedHolds only as a relative, finite-resource statement.

C1 · far fieldDamagedFine detail fades as claimed; redundancy depends on the noise model.

C2 · ratioRefutedS_g is ill-posed and rises with r.

C3 · black holesRepairableTrue after a horizon forms, but it is no-hair plus Price’s law.

C4 · uniquenessRefutedA charged sphere does the same thing.

C5 · DarwinismDamagedSelection is kinematic, and has prior art.

C6 · accessibilityRepairableRight framing, if resource bounds are explicit.

01 · The hypothesis, made testable

Two quantities and six claims

Let X be the full microscopic state or history of a source, and Z = f(X) a low-dimensional coarse variable: mass, centre of energy, angular momentum, low multipoles. G_r,t is the channel from source to the gravitational field an observer can access at separation r or time t, with finite noise, aperture and duration.

Fine distinguishability

D_fine(r,t) = sup over f(x)=f(x′) of ½ ‖G_r,t(ρ_x) − G_r,t(ρ_x′)‖₁

Coarse redundancy

R_Z(ε; r,t) = max N such that N disjoint field fragments each decode Z with error ≤ ε

Selection ratio

S_g(r,t) = D_fine / R_Z (hypothesis: S_g falls as r or t grows)

HWith increasing separation or relaxation time, distinguishability within a fixed coarse class contracts while the number of fragments recording the coarse variables is preserved or grows.

C1Far field: sources agreeing on multipoles ℓ ≤ L differ by ~r^−(L+2). Resolvable fine detail falls with r while the patches that each recover M stay numerous or grow.

C2The ratio S_g decreases monotonically in r and t.

C3Collapse and ringdown drive formation-history distinguishability to zero while (M, J) stay widely recorded.

C4The same interaction compresses and broadcasts, and this is special to gravity beyond generic multipole falloff.

C5Gravity generates the coarse-graining that decides which variables can be redundantly recorded: a gravitational Quantum Darwinism.

C6The claim concerns local accessibility. Global information is conserved.

02 · Verdicts

Scorecard after the attack

Eight specialist attackers each hit the hypothesis from one angle: universality, radiation and memory, holography, information theory, black-hole relaxation, instability and chaos, Quantum Darwinism, and an honest steelman. A referee weighed the reports, re-ran the load-bearing numbers, and ruled.

Claim	Verdict	Why	Decisive attack
H	Damaged	Survives only as a relative, resource-explicit statement about the static field in r. Fails in t without horizons, fails in the wave zone.	Redundancy falls as r^−2k at fixed precision; a 3-body pair goes from D = 0 to 0.99; radiative ratios freeze with r.
C1	Damaged	The fading half is right but is textbook upward continuation shared by any Laplace field. The redundancy half fails for noisy field sensors; for readout-limited probes it holds inside a window (see section 05).	Electrostatics gives identical exponents. R_M = 1249 → 312 → 78 → 19 → 4 → 1 → 0 at r = 2…90a.
C2	Refuted	S_g divides a bounded distance by an integer count. It rises as r^L+k−1, is infinite once R_Z = 0, and falls when detectors improve.	Four independent computations; referee check reproduced R_Z = 0 with D_fine = 0.92.
C3	Repair	True for memoryless observers after a sub-extremal horizon forms, with Z redefined as remnant charges plus BMS frame data. Not new.	Superkicks (≈4,000–5,000 km/s) turn fine spin orientation into permanent coarse charge; ~50% of flux crosses the horizon.
C4	Refuted	Compression plus broadcast is a property of the Laplace Green’s function and Gauss-law constraints.	A charged conducting sphere reproduces every weak-field number.
C5	Damaged	The selected pointers are Gauss-law charges, fixed by constraints, not dynamics. Where gravitational dynamics does select, it often amplifies.	Korbicz–Tuziemski 2017; Brandão–Piani–Horodecki 2015; horizon decoherence leaves zero exterior redundancy.
C6	Repair	Consistent framing, but in quantum gravity fine information is in principle readable at infinity, so the bound must be on resources.	Holography of information (Laddha–Prabhu–Raju–Shrivastava 2021).

03 · Deep dive

What the simulations show

Five numerical experiments, run before and alongside the swarm. Units: G = M = 1, source radius a = 1, times in units of M. Each chart has a data table underneath.

The far field has an exact blind spot

Singular values of the map from 1,018 interior mass voxels to the radial field on a sphere of radius r, counted above three precision floors. Every count is a perfect square (9, 16, 36, 64, 81, 144, 289…): the field sees whole multipole orders ℓ ≤ L(r) and nothing else. At r = 10a and one-part-per-million precision, 96% of the source’s degrees of freedom are invisible. Most of that is an exact null space (the non-harmonic part of the density), which no instrument can see. The rest is geometric fading as (a/r)^ℓ.

Resolvable fine structure collapses

Number of resolvable source parameters beyond the mass, for random clumpy positive sources and fixed-noise field sensors. Fisher information in order ℓ falls as r^−2ℓ−2 (measured slopes −2, −4, −6, −8, −10 for ℓ = 0…4), so the fine share falls as (a/r)^2ℓ.

Redundancy depends on the noise model

Independent copies of M (fragments that each recover M to 0.1%), indexed to 1 at r = 1.5a, with equal-area fragments for both detector types. Both start by gaining copies as the sphere grows. Field sensors stop at r* ≈ 60a, where one patch can no longer read M alone, then lose copies as r⁻² because Gauss’s law spreads a fixed flux over a growing area. Orbit clocks in the most favourable readout model (endpoint timing with fixed clock jitter) keep gaining, because each orbiter’s error on M stays flat with distance, until orbits stop closing within the observing time (r ≈ 2,900a). This difference comes from the noise model, not from gravity. Add random forces on the probe and orbit clocks fall back to the r⁻² law; give a drop gravimeter readout-limited noise and it matches the orbit clock.

Two collapse histories, one black hole

Regge–Wheeler evolution of two very different initial pulses (histories A and B) on the same Schwarzschild black hole, observed at r* = 30M. Left: signal envelope. Both ring at the same frequency, fitted at Mω = 0.372 − 0.0879i (exact 0.3737 − 0.0890i), so M stays readable. Right: how distinguishable the waveforms remain after fitting out an overall amplitude and phase. It drops from 22% to about 0.1% within 80M, bumps up while the ringing hands over to the tail (240–300M), then settles near 10⁻⁴. The history compresses into a few amplitudes, though not monotonically. Measured tail exponents: −3.11, −5.12, −7.15 for ℓ = 0, 1, 2 (Price: −3, −5, −7).

Positivity is the first gravity-specific ingredient

Particles N	Gravity \|dipole\|/M	Gravity \|Q_zz\|/M	EM neutral \|dipole\|	EM dipole shift when one particle moves

N point sources in a unit ball, 40 trials each. In gravity every source has the same sign, so the leading record M is exactly unchanged by any rearrangement, and for random clouds finer moments shrink as N^−1/2 relative to it. Neutral matter in electromagnetism has zero monopole, so its leading far-field record is the dipole, a fluctuation that moves by up to 78% when a single particle crosses the ball. The robust gravitational statement is the positivity bound |Q_ℓ| ≤ M·a^ℓ, which holds for every source. The N^−1/2 shrinkage holds only for random, isotropic clouds: real bodies have coherent structure (Earth’s J₂ ≈ 1.1×10⁻³), as the red team pointed out.

04 · The strongest attacks

What broke, and how

Information theory

Recordability dies too

At fixed detector noise, Gauss’s law keeps the total flux constant while noise accumulates over an area growing as r². Copies of M fall as r⁻² for gravimeters and r⁻⁴ for the tidal sensors a freely falling observer is limited to, reaching zero at a finite radius.

Hits H, C1, C2

Universality

A charged sphere does the same

Swap G·M for k·Q and every weak-field exponent and prefactor is unchanged. The heat equation reproduces them with r replaced by √t. Far-field compression is a property of the Laplacian, not of gravity.

Hits C4, C1

Instability and chaos

Gravity also amplifies

Two Pythagorean three-body states with identical M, P, J and centre of mass, and an identical field at t = 0, become fully distinguishable from their exterior quadrupole by t ≈ 50 (one e-fold per 0.83 crossing times). Jeans growth and superradiance do the same at larger scales.

Hits the time clause of H

Radiation and memory

No selection along the light cone

In the wave zone every multipole falls as 1/r, so fine-to-coarse ratios freeze at emission. GW190412’s (3,3) mode, seen from 740 Mpc, carries fine structure at a ratio set by the source, not the distance.

Confines H to the static sector

Black-hole relaxation

Fine data can become coarse

Rotating the in-plane spins of an equal-mass binary keeps M, J and P fixed but steers the remnant’s recoil up to ~4,000 km/s. A fine variable becomes a permanent, maximally redundant coarse charge.

Forces C3’s Z to be defined after the fact

Holography

In principle, gravity reveals more

Because gravity’s Hamiltonian is a boundary term, an ideal observer at infinity can distinguish bulk states that a non-gravitational theory hides completely. The hypothesis survives only with explicit resource bounds, where this leakage is ~10⁻⁹⁴.

Hits C6, C4

Quantum Darwinism

Already known, and generic

Selection of one shared observable is generic for any channel with many outputs (Brandão–Piani–Horodecki 2015). Gravitational objectivity of centre-of-mass position was derived by Korbicz and Tuziemski in 2017. Horizon decoherence leaves zero exterior copies.

Hits C5

Steelman

The ratio points the wrong way

With 20,000 detectors, fine distinguishability stays saturated at 1.0 out to 50a while copies of M fall 800 → 51 → 3 → 0 between 5a and 30a. S_g mixes a bounded quantity with an integer count, so its exponent is an artefact.

Retires S_g

05 · Where I disagree with the referee

The redundancy verdict turns on the noise model

The referee ruled the redundancy half of C1 refuted for every detector model. That seemed too strong, because astronomers measure masses with orbits, not gravimeters, and every planet and spacecraft orbit constrains the Sun’s GM. So I simulated orbit clocks: test bodies timed against a reference direction with fixed jitter over a fixed duration.

Each orbiter appeared to read M to the same or better precision at every distance (relative error 1.5×10⁻⁶ at 2a down to 3×10⁻⁸ at 128a), until orbits stopped closing within the observing time. Its sensitivity to the quadrupole J₂ fell as r⁻². Taken at face value, both halves of C1 hold.

I sent this dissent to three skeptics of its own. Here is what survived.

Survives

The referee’s ruling was too broad

The r⁻² loss of copies does not follow from Gauss’s law alone. It follows from assuming each sensor has white acceleration noise. Probes limited only by readout (timing jitter, position readout) can keep a flat per-probe error, so copies of M grow with sphere area inside a window. That window closes at whichever comes first: orbits no longer close within the observing time, or random forces on the probe start to dominate.

Refuted

It isn’t frequency, and it isn’t gravity

A drop gravimeter with fixed drop height and readout-limited noise does exactly as well, and it measures amplitude. A local free-fall pair oscillates at the same Kepler frequency. Electron gyration does the same job for magnetic fields. Give the orbiter the gravimeter’s force noise and its Fisher information matches the gravimeter to 0.5%. My claimed S_g exponent mixed two noise models and is withdrawn.

Corrected

My own simulation flattered the clocks

The improvement with distance in my run came entirely from the ranging term 3δr/r, a light-travel-time measurement, not from gravity. Kepler’s law gives GM/r³, so M needs an outside ruler, and the best timing fit actually degrades as r^3/4. For circular equatorial orbits J₂ is degenerate with M, and leaving it out biased my fit by up to 250σ. The real-world check still points the right way: the Sun’s GM is known to 7.5×10⁻¹¹ and its J₂ only to 1% (MESSENGER), but both come from joint fits dominated by radar ranging, not from many independent copies.

Votes: two skeptics ruled the dissent true but narrower, one ruled it refuted on gravity-specificity. All three agreed on one thing: under every consistent readout model, coarse M is recorded far more robustly than fine J₂, and the gap widens with distance. General relativity widens it further, since periapsis precession masks the J₂ signal by a factor that grows with r.

Net effect on the verdict

C1 stays damaged, for a sharper reason. The redundancy clause is neither true nor false for gravity as such; it is a statement about the noise model. In the readout-limited regime it holds inside a finite window. In the force-noise regime it fails as r⁻². Neither regime is specific to gravity. A gravity-specific remnant does remain: by the equivalence principle, one orbiter of unknown composition decodes GM, while an electromagnetic orbit gives only (q/m)·Q. That changes no scaling exponent.

06 · What survives

A narrower principle and one real theorem

Repaired principle. For a positive-energy source observed through its stationary field with finite resources, information about fine structure dies faster than information about the conserved charges. That is a relative statement, not an absolute one: coarse recordability also dies for local field sensors. In time, the only general contraction happens after a horizon forms, where memoryless observers see the exterior converge to the remnant’s charges with ℓ-ordered tails. There is no selection with distance in the wave zone, and with unbounded resources quantum gravity reverses the direction.

Coarse-dominance selection theorem · Newtonian, proved

Let ρ ≥ 0 be supported in a ball of radius a with mass M, and write x = a/r for r > a.

Pointwise dominance (sharp). Each multipole’s field obeys |∇Φ_ℓ| ≤ (ℓ+1) x^ℓ GM/r², with equality for a point mass on the boundary.
Moment bound. Σ_m |Q_ℓm|² ≤ (2ℓ+1) M² a^(2ℓ) / 4π, so for any sensor array the signal share of order ℓ is at most (ℓ+1)²/(2ℓ+1) · x^(2ℓ), independent of layout and noise.
Uniform fine bound. Sources agreeing on all ℓ ≤ L give D_fine ≤ erf(√N · 2GM/r² · x^(L+1)[(L+2)−(L+1)x]/(1−x)² / 2√2σ) = O(r^−(L+3)).
Equivalence-principle shift. The mass dipole equals M·X_cm, so internal rearrangements first show up at ℓ = 2: one extra power of a/r compared with generic charges.
Explicit non-claim. Absolute redundancy obeys R_Z ≤ ε² F_tot ∝ r^(−2(L_Z+k)) for field sensors of derivative order k, and vanishes beyond a finite radius.

Proof: addition theorem plus the Legendre inequality P_ℓ² + (1−x²)P_ℓ′²/ℓ(ℓ+1) ≤ 1, integrated against ρ ≥ 0; Cramér–Rao plus additivity for (5). Verified numerically for ℓ = 1…12 and 200 random sources. Open: the general-relativistic version for Geroch–Hansen moments under the dominant energy condition (Kerr saturates it).

07 · How

The mechanism has four stages

Eight accounts of the mechanism were built and then attacked by a red team. What survived is one mechanism with three jobs, each with a different origin. A conserved charge floor is enforced by the constraints. Everything else is attenuated, elliptically in distance and dissipatively into horizons in time. A finite-resolution observer sets the threshold. In the strip below, the label at the foot of each stage says which part is gravity's own.

1 · project

An exact blind spot

The static exterior depends on the density only through its harmonic moments. The rest of the density is an infinite-dimensional null space that no instrument can see: about 1 − 6/P of all degree-P densities. A random density with correlation length ξ shows only about 3.8 ξ/a of its variance. In general relativity, Birkhoff’s theorem puts all spherical dynamics there: a collapsing star looks exactly like Schwarzschild.

Generic Laplace physics

2 · contract

Geometric fading

Moving outward is a semigroup in ln r with rate ℓ+1, so order ℓ loses ℓ e-folds of signal relative to M per e-fold of distance. Singular values are σ_ℓ ∝ (a/r)^ℓ+1/((2ℓ+1)√(2ℓ+3)). By data processing, no information measure can grow with r.

Generic · positivity picks M

3 · export

Leak into sinks

Once a horizon forms, perturbations leak through the light ring (damping 0.089–0.096/M) and into the horizon, where infalling signals redshift as e^−t/4M. Curvature backscatter leaves one number per (ℓ, m) in a t^−(2ℓ+3) tail. Information is moved out of reach, not destroyed.

Needs a horizon (gravity)

4 · protect

A floor that can’t be removed

The constraints make the 10 Poincaré charges (energy, momentum, angular momentum, centre of mass) into surface integrals. Spin-2 radiation needs ℓ ≥ 2, so at linear order they cannot be radiated away. Positivity means M can never cancel or be screened.

Content is gravity-specific

The split explains C4. The broadcast comes from the constraint equations, and the compression from the Green’s function and from the evolution equations with horizons. These are two different parts of Einstein’s equations, so “the same interaction does both” is true only in a weak sense. A key nuance survived the red team: protected does not mean most widely recorded. Earth’s angular momentum J is a protected charge, yet its gravitomagnetic signal is 10⁷–10⁸ times weaker than that of the unprotected oblateness J₂.

Infrared

Soft gravitons sort by coarseness

The leading soft factor and the memory depend only on momenta. The subleading factor adds angular momenta, and internal structure first appears at sub-subleading order. The structure-blindness is forced by Weinberg’s theorem. The hierarchy runs in frequency, not in distance.

Quantum

A universal but slow pointer basis

Gravity einselects the moments of the energy density, and the equivalence principle cancels the dipole channel, so the first einselected moment is the quadrupole. For a 10 µm grain this is about 10⁶² weaker than photon scattering: a universal floor, not how everyday objects become classical.

Matter

Phase mixing hides, chaos reveals

Collisionless orbits wind information into ever finer filaments while the fine-grained distribution is conserved, which is pure accessibility loss. The same unscreened attraction drives Jeans growth and N-body chaos, which push fine differences back up into coarse multipoles.

08 · Why

Where the selection comes from

Each kind of explanation was built in its strongest form and then red-teamed. They answer different questions, so they are ranked rather than merged. The short answer has three tiers. Which variables survive is close to a theorem. Why the rest fades needs nothing special. Why it fades in time down to exactly the charges is dynamical and contingent.

It could hardly be otherwise: gravity gauges spacetime translations

Derivable

Start from Lorentz invariance, quantum mechanics, a massless spin-2 particle and positive energy. Weinberg’s 1964 soft theorem then forces every system to couple identically to energy-momentum, which is the equivalence principle. Noether’s second theorem makes the charges of a gauged symmetry surface integrals; for translations and rotations those charges are energy, momentum and angular momentum. Universality makes the mass dipole equal M·X_cm, so the ℓ ≤ 1 sector cannot radiate. The positive energy theorem makes the monopole impossible to remove. This fixes the identity of the coarse floor. It does not make anything else fade. Electromagnetism has the same surface-charge structure, but its charge is optional, two-signed and screened in bulk matter. Earth’s net charge is about 10⁻⁹ of its gravitational-equivalent charge.

Most of it needs no special why

Derivable

Fading with distance is the Laplace Green’s function acting as a low-pass filter, the zero-frequency limit of evanescent waves, read through a noise floor. The exponents are identical for electrostatics and geomagnetism. This explanation also predicts no selection with distance in the wave zone, which is confirmed. What it cannot explain is the residue: an unscreened, universal, single-sign long-range field exists at all (generic field theory expects screening, Higgsing or confinement); horizons keep only gauged charges; and the broadcast charges are spacetime-symmetry charges.

Attraction makes horizons, and horizons keep only charges

Well supported

Because the charge is positive and unscreened, collapse is generic above the Chandrasekhar and TOV limits. With Penrose’s theorem and cosmic censorship, horizons form; they absorb, null infinity radiates, and 4D uniqueness leaves only (M, J, Q). The same positivity that guarantees the coarse record also drives Jeans growth and chaos, so before any horizon forms gravity amplifies fine structure. This holds only for black holes, only in four dimensions, and only for matter without stable long-range hair.

The direction of time is borrowed

Plausible

Selection in distance is time-symmetric. Selection in time (ringdown, tails, no-hair) needs retarded, no-incoming-radiation boundary conditions; run backwards, it is a white hole emitting hair. Those boundary conditions trace back to a low-Weyl-curvature past, Penrose’s past hypothesis. The arrow comes from cosmology’s initial condition, not from gravitational dynamics.

Why 3+1 dimensions is the sweet spot

Plausible

In 2+1 dimensions gravity has no local degrees of freedom. The outside of any source is flat except for a conical deficit of 8πGM, so compression is perfect and there is nothing local to record. In 4+1 dimensions, black rings and Myers–Perry holes share the same M and J (for j² ≥ 27/32), so relaxation no longer erases history, and stable circular orbits around Tangherlini holes are absent. Only 3+1 combines local fields with unique rotating black holes. Observers need stable orbits and atoms, so anthropic selection may explain d = 4, with black-hole uniqueness riding along at the same integer. The red team rejected a proposed common cause linking the two.

Gravity as an equation of state

Mostly redescription

Jacobson’s thermodynamic derivation, the entanglement first law and canonical energy all fit the picture, but each claimed discriminator failed. Emergent gravity compresses the state to the local stress tensor, an infinite-dimensional field, not to multipoles. “Temperature-locked” ringdown (ω_I/πT_H = 0.71–0.98) is dimensional analysis for Schwarzschild. Within classical GR this view predicts nothing the bootstrap view doesn’t.

Observers need objective records

Doesn’t explain it

Objectivity of some observable is generic for any channel with many outputs. Everyday records are made by light, not gravity: photon scattering writes about 10⁸ records per microsecond, while detecting a micron-sized grain by its gravity takes about 5×10¹³ seconds with a good accelerometer. Observers don’t need gravitational selection, so it is at most a by-product.

Was it designed this way?

Mapped neutrally rather than answered. “Designed” can mean four different things: an agent choosing laws for a goal, a selection process over many possible universes, apparent design that is really necessity, or emergence from a deeper level. The selection splits into a necessary layer (which charges are broadcast, given the premises), a generic layer (fading, shared with every field) and a contingent layer (four dimensions, energy conditions, matter without long-range hair, a low-entropy past). Only the premises and the contingent layer are possible targets for a design or selection explanation. The mechanisms themselves are not.

Each option predicts something different. Strict necessity predicts no consistent alternatives, which is false classically but open for quantum gravity. Observer selection predicts features sitting in life-permitting windows; d = 4 fits, gravitational selection itself does not. Design with no stated goal predicts nothing and can’t be tested. Design with a stated goal becomes a testable selection principle. “Maximise objective recordability” would predict that gravity carries everyday records, and it doesn’t. The hypothesis shows no fine-tuning of its own. It is what any universal, positive, gauged charge does in four dimensions once horizons exist.

09 · Next

Tests that would settle it

First, retire S_g. Replace it with matched, resource-explicit ratios: the Fisher share F_ℓ/F₀ ∝ (a/r)^2ℓ, the information ratio I(X;Y|Z)/I(Z;Y), or fine-to-coarse redundancy at equal resources. Every statement should name the sensor type, the number of sensors, the noise, the duration, the aperture and whether the observer keeps records. Define “coarse” without reference to the gravitational channel, as the asymptotic-symmetry charges, so the claim isn’t circular.

Test	If the principle is right	If it is wrong	Effort
GR coarse-dominance bound. Prove \|M_ℓ\| ≤ C_ℓ·M·R^ℓ for Geroch–Hansen moments of matter obeying the dominant energy condition; test on Kerr (which saturates it) and neutron-star multipole tables.	The one gravity-specific piece extends to strong fields: a modestly new theorem.	Coarse dominance is a Newtonian artefact.	Moderate; the highest-value open problem.
Redundancy across noise models. Map R_M(r) for each sensor class (field, tidal, drop, orbit) under readout-limited versus force-noise-limited operation, with shared versus self-contained reference frames, using measured noise budgets (GRACE, LISA Pathfinder, atom gravimeters).	A realistic class keeps redundancy growing over astrophysical ranges, and the clause survives conditionally.	Force noise dominates every realistic class, and redundancy falls as r⁻² everywhere.	Easy to moderate.
Electromagnetic control. Rerun every channel computation with a charged body and spin-1 fields.	Exponent differences beyond the ℓ ≥ 2 shift and the positivity prefactor would show new gravity-specific selection.	Identical exponents (as found so far for tails and Laplace falloff) keep C4 refuted.	Easy; partly done.
Horizon test in full numerical relativity. Snapshot history distinguishability for binary families that share remnant (M, J, P), including nonlinear tails and Kerr mode coupling.	ℓ-ordered forgetting survives nonlinearity, and repaired C3 is clean.	Nonlinear tails reverse the ordering.	Moderate; existing tail studies can be reused.
Finite-resource holography bound. Derive how bulk-state distinguishability through boundary energy measurements scales with observing time and precision.	Leakage falls as (GΔ/εc⁴r)² or faster, and the finite-resource clause is consistent.	Leakage is not negligible at astrophysical resolution.	Hard; open research.
Self-gravitating information flow. A self-consistent Vlasov–Poisson or N-body study of when gravity contracts fine distinguishability (phase mixing) versus amplifies it (Jeans, chaos).	A sharp criterion separating the two regimes.	No clean criterion: the time clause stays restricted to horizons.	Moderate.

Observations test only the inputs. MICROSCOPE’s equivalence-principle bound (η ≲ 10⁻¹⁵), the absence of dipole radiation in binary pulsars, Kerr-consistent ringdowns and an eventual memory detection all check the premises. The repaired principle predicts nothing beyond general relativity plus information theory.

10 · Sources

Prior art and references

The novelty assessment is low: the fading law is satellite-geodesy upward continuation, C3 is no-hair plus Price (1972) and Gundlach–Price–Pullin (1994), and gravitational Darwinism has direct precedents. What may be new is the coarse-dominance packaging, the demonstration that ratios like S_g are ill-posed, the finding that the redundancy verdict turns on the noise model, and the open GR moment bound. References below were checked by the agents that cited them.

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