Gravitational decoherence of a composite particle: the interplay between gravitons and a classical Newtonian potential

Lucas Chibebe C\'eleri; Thiago H. Moreira

REVIEW 3 major objections 5 minor 90 references

Gravitational decoherence of a composite particle: the interplay between gravitons and a classical Newtonian potential

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The graviton background, amplified by a particle's internal degrees of freedom, makes spatial superposition decoherence inevitable even for microscopic masses; a classical Newtonian potential can only slow it, and in principle trigger recoh

desk verdict A genuinely checkable extension of the 2023 composite-particle graviton decoherence model, in which the long-time inevitability claim is robust but the new Newtonian slowdown/recoherence claims rest on a leading-order sign that the paper itself flags as perturbatively unsecured. read the letter →

arxiv 2602.22517 v2 pith:OHILC7GJ submitted 2026-02-26 quant-ph gr-qc

Thiago H. Moreira , Lucas Chibebe Céleri This is my paper

classification quant-phgr-qc

keywords gravitonsdecoherencecompositeparticleNewtonianpotentialrecoherencenoisekernelinfluencefunctionalopenquantumsystems

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether the unshieldable quantum gravitational environment — the graviton bath — can destroy spatial superpositions of a composite particle that also sits in a classical Newtonian gravitational field. The central claim is yes, inevitably: although gravitons alone only decohere macroscopic superpositions, the coupling of gravitons to the particle's internal degrees of freedom acts as a second environment that drives decoherence in the long-time limit even for microscopic masses. The classical Newtonian potential slightly slows this process, and for particles with no internal dynamics it even allows the decoherence function to decrease and turn negative — a recoherence-like behaviour, at least in principle and on timescales that can be astronomically long. The results are derived through an influence-functional calculation of the reduced density matrix for four initial graviton states (vacuum, thermal, coherent, squeezed), with the notable feature that squeezed states, expected for relic gravitons, shorten the decoherence time exponentially.

What carries the argument

The central object is the decoherence functional Γ(t), which multiplies the off-diagonal density-matrix elements and is built from the graviton noise kernel N_g(t,t′) = ⟨{h,h}⟩ after the internal degrees of freedom are integrated out. The key identity is the coincidence limit N_g(t) = (Λ⁴/15π)(Λ²/3 − T_zz), where Λ ~ ℏc/L₀ is the UV cutoff set by the detector size L₀ and T_zz = 2GM_N/R_N³ is the Newtonian tidal tensor along the superposition axis; the minus sign before T_zz is what produces both the slowing (δΩ) and the recoherence. Amplification by internal structure is governed by the ratio R = ηπ k_B T_int Λ/(mc²)², which sets the scale of the graviton-plus-internal contributions that dom

What would settle it

Compute the graviton noise kernel N_g(t) keeping the O(T²_ij) terms dropped in Eq. (34b) and evaluate it at GM_N/R_N³ = (1/6)(Λ/ℏ)², where δΩ = 0: if the next-order contribution is comparable to or larger than the leading term, the predicted recoherence and the slowdown factor δΩ collapse. A complementary check would be a molecule interferometer measuring the decoherence slowdown δΩ near a dense mass and comparing with Eq. (52).

Watch

Extended reading notes

Core claim

The central discovery is that the decoherence function Γ(t) for a composite particle's spatial superposition, derived via the Feynman-Vernon influence functional with gravitons and internal degrees of freedom traced out, grows without bound at long times — Γ ∝ (4/135) δΩ (v/c)² (η k_B T_int Λ/E_P²)(Λt/ℏ)³ — even for the vacuum graviton state. The factor δΩ = 1 − 6(ℏ/Λ)² G M_N/R_N³ encodes the Newtonian tidal field, which enters with a minus sign. Without internal dynamics the pure graviton contribution saturates and cannot localize microscopic superpositions; with them, decoherence is inevitable, with decoherence time τ_dec ~ 10⁵ s for representative molecular parameters. Switching internal

Load-bearing premise

The predicted slowing and recoherence rest on the sign of the leading-order Newtonian correction to the graviton noise, a sign that is only trusted because the calculation drops O(T²_ij) noise terms and truncates the tidal expansion at second order; once the tidal frequency GM_N/R_N³ approaches (ℏ/Λ)²/6, the dropped terms are no longer small.

Editorial extensions

If this is right

A composite particle with internal modes at temperature T_int ≳ 10⁴ K will be fully decohered by the graviton vacuum in about 10⁵ s for η ~ 1, v ~ 10⁻⁶ c, L₀ ~ 10⁻⁹ m — no Planck-scale momenta required.
Pure graviton decoherence alone (no internal degrees of freedom) saturates at (16/5π) δΩ (v/c)² (m/M_P)², so gravity alone cannot localize microscopic superpositions.
Squeezed graviton states, expected for relic gravitons, shorten the long-time decoherence time by (cosh 2r)^{-1/3}, e.g. a factor ~10⁻²⁹ for r ~ 100.
For particles without internal dynamics, the Newtonian potential causes Γ(t) to decrease as −(8/5)(ℏ/Λ)²(GM_N/R_N³) ln(Λt/ℏ) at long times, opening a recoherence window at t ≳ (ℏ/Λ) exp[(1/8)(Λ/ℏ)² R_N³/(G M_N)] — practically unreachable near Earth.
The classical Newtonian potential only slows decoherence slightly when internal degrees of freedom are present: δΩ ≃ 1 for typical terrestrial parameters.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The recoherence window and the slowdown both hinge on the sign of the leading-order tidal term in the noise kernel; retaining the O(T²_ij) terms dropped at Eq. (34b) could alter or erase the crossing, so a next-order calculation of N_g(t) is the natural check.
The Ohmic, δ-correlated internal kernel (Eq. 41) is what produces the clean t³ growth; replacing it with a structured spectral density could change the exponent, so the inevitability claim is tied to that choice.
Because the same noise kernel governs graviton-mediated coupling between particles, the composite-particle amplification found here should also amplify graviton-induced entanglement between neighbouring test masses; quantifying that link could give a tabletop probe of the mechanism.
The authors' suggestion to add a non-gravitational (e.g. electromagnetic) bath that itself couples to the graviton environment is the natural next step; other classical backgrounds, such as Schwarzschild or an expanding universe, would enter through the same tidal-tensor structure.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, this is a real extension of Moreira & Céléri 2023, adding a classical Newtonian tidal potential to the graviton-bath decoherence model for a composite particle. The genuinely new pieces — the T_zz corrections to the graviton noise kernel (Eqs. B4/B10), the δΩ prefactors, and the recoherence condition (Eqs. 68–69) — all reduce cleanly to the earlier results when the tidal tensor vanishes. Second, the headline claims split: "decoherence inevitable in the long-time limit via internal DoFs" is robust, but the "slowed down by the Newtonian potential" and the "recoherence" claims rest on the leading-order sign of a term after dropping the very higher-order terms the paper concedes it is dropping.

What the paper does well: the derivation is careful and checkable. Appendix B gives the noise kernels, Appendix C the full decoherence functions, and the short-time limit reproduces the Kanno–Soda–Tokuda bound mv ≫ ~110 kg·m/s. The long-time x^3 growth follows from the stated kernels, and the asymptotic tables match the plotted behavior. The authors also explicitly flag the perturbative caveat right after Table II — they know they are working at the edge of the tidal expansion.

The soft spots, in proportion. The Newtonian slowdown and recoherence come from the −GM_N/R_N^3 term in Eqs. (58) and (68), which is the linear-in-T_zz part of N_g obtained after dropping O(T^2) from the stochastic covariance (Eq. 34b) and truncating the Fermi-normal expansion at second order (Eq. 11). In the region where Γ crosses zero, those neglected terms are no longer small, so the sign of the total correction is genuinely unsecured. The paper's own perturbative warning covers this, but the abstract's recoherence claim is more confident than the calculation supports. That is the main referee concern. Secondary: the squeezed-state estimate τ_s = (cosh2r)^(−1/3)τ_v with r ~ 10^2 uses a long-time formula whose regime Λτ/ℏ ≫ 1 is violated by several orders of magnitude at that τ_s; the exponential trend is plausible, but the numerical suppression factor should not be quoted as it stands.

The robust core — long-time decoherence inevitability for composite systems with internal DoFs, and the fact that δΩ ≃ 1 for typical Earth parameters — is not threatened. The paper deserves a serious referee. I would ask for a bound on the dropped O(T^2) and cubic-tidal terms in the Γ-crossing region, and a clear statement that the recoherence timescale is sensitive to that truncation. With that addressed, this is a solid contribution to the gravitational decoherence literature.

Referee Report

3 major / 5 minor

Summary. The paper extends the graviton-induced decoherence analysis of Ref. [64] to include a classical Newtonian potential. Working in the Feynman–Vernon influence-functional framework, the authors derive the reduced dynamics of the external degrees of freedom of a composite particle interacting with a graviton bath, internal degrees of freedom, and a Newtonian tidal field. They compute the gravitational noise kernel for vacuum, thermal, coherent, and squeezed graviton states, and provide explicit decoherence functions for two path configurations. The main claims are that (i) for short times the graviton bath alone dominates and reproduces the Planck-mass condition of Ref. [22]; (ii) in the long-time limit the graviton–internal coupling produces an x³ growth of the decoherence function, making decoherence inevitable even for microscopic masses; and (iii) the classical Newtonian potential slightly slows this process and, for systems without internal dynamical degrees of freedom, can in principle lead to recoherence. The paper includes detailed appendices with the noise kernels and asymptotic tables.

Significance. If the results are correct, the paper provides a concrete and checkable extension of graviton-induced decoherence to composite systems in a gravitational background. The derivations are explicit: noise kernels are given in Appendix B, full decoherence functions in Appendix C, and the asymptotic tables match the plotted behavior. The short-time limit reproduces the known Planck-mass condition, and the long-time x³ growth is a robust prediction of the graviton–internal interplay. The new qualitative claims — the slight slowdown of decoherence by the Newtonian potential and the in-principle recoherence in its absence — are interesting but rest on a leading-order perturbative truncation; their quantitative reliability needs to be established.

major comments (3)

[Sec. IVC, Eqs. (68)–(69)] The recoherence prediction is controlled by the sign and coefficient of the ln(Λt/ℏ) term in Eq. (68). This term is derived after dropping O(T²_ij) from the stochastic variance in Eq. (34b) and truncating the Fermi-normal-coordinate expansion at quadratic order in Eq. (11). The crossover time (69) is exponentially sensitive to this coefficient: a small fractional error changes the zero by many orders of magnitude or removes it. The paper's perturbative caveat (after Table II) is not quantitative. Please provide an explicit estimate of the leading neglected terms — e.g., the O(T²) contributions to the noise kernel N_g — and state the condition under which the sign of the logarithmic coefficient is controlled.
[Eqs. (52), (58)] The long-time 'inevitable decoherence' result in Eq. (58) is proportional to δΩ, which becomes negative for (Λ/ℏ)² < 6 GM_N/R_N³. In that regime the leading-order expression would predict recoherence even with internal degrees of freedom, contradicting the abstract's claim. The authors note that they work perturbatively, but the manuscript should explicitly state the validity condition δΩ>0 for Eq. (58) and explain why the omitted higher-order tidal terms cannot change the sign of the total correction in the stated regime. As written, the abstract overstates the inevitability without this caveat.
[Sec. IIB and Eq. (15)] The neglect of the O(φh²) graviton–Newtonian-potential term in the graviton action is justified in Appendix A by the small-angle dominance of the graviton scattering cross-section. However, a large small-angle cross-section indicates a substantial interaction, not a negligible one. Since the noise kernel (26b) is built from the graviton two-point function, an O(φh²) correction to the graviton action could in principle contribute to N_g at the same order as the retained T_zz term. The authors should give a quantitative estimate of this contribution for the parameters considered, or state clearly why it is subdominant relative to the T_zz term in the noise kernel.

minor comments (5)

[Abstract/Sec. IVC] The abstract says recoherence can occur 'at least in principle', while Sec. IVC describes the timescale as 'infinitely long' and, for typical parameters, comparable to the age of the universe. Consider unifying the wording so the practical impossibility is not lost in the abstract.
[Eq. (56)] The condition mv ≫ sqrt(90π/δΩ) M_P c assumes δΩ > 0. If δΩ becomes negative, the square root is imaginary; the manuscript should explicitly state that this short-time condition is valid only for δΩ > 0, which is the regime intended by the perturbative treatment.
[Table II] The neutron-star value of GM_N/R_N³ is included for 'informational purposes', but no corresponding detector size L0 is indicated. To avoid the impression that the comparison is within the model's validity, add a sentence or footnote clarifying that this entry lies outside the perturbative regime for the L0 values listed.
[Figures 3–6] The figures would benefit from labeled axes and, for the functions with logarithmic growth (e.g., f_v^{III}), a log-linear or log-log plot to make the asymptotic behavior visible.
[General] There are a few stylistic and typographical issues, including inconsistent use of 'slowdown'/'slow down' and 'recoherence-like' in the abstract versus 'recoherence' in the body. These do not affect the technical content.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: decoherence functions are derived outputs of the stated model; the main self-citation imports an independent prior internal-DoF model, and the perturbative-truncation caveat is a robustness limitation, not an input-output identity.

full rationale

The paper's load-bearing results—Γ(t), δΩ, the long-time decoherence growth Γ∝(Λt/ℏ)^3, and the recoherence crossover—are obtained by evaluating the influence-functional integrals with specified couplings (matter + graviton field + Newtonian potential). The parameters η, T_int, Λ, T_g, α, and r are assigned physical or phenomenological values; none is fitted to reproduce the claimed slowdown or recoherence. The internal-DoF noise kernel N_int=ηπT_intδ(t−t′) is imported from the authors' prior publication [64] with stated Ohmic, high-temperature assumptions; this is an independent earlier derivation, not a definition in terms of the present paper's target result, and the present paper's Newtonian extension is not contained in [64]. The sign of the Newtonian correction and the recoherence timescale depend on the leading-order T_zz term after dropping O(T²_ij) and higher tidal terms; the authors explicitly caution that they are working in a perturbative regime and dropping higher-order tidal terms (Sec. IV, after Table II). That is a validity/robustness caveat, not a circular step—the truncated terms are not secretly reintroduced as inputs. Overall, the claimed predictions are genuine outputs of the model rather than equivalent to its inputs by construction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central quantitative results — long-time Γ ∝ ηk_BT_intΛ(Λt/ℏ)³ and the recoherence condition — depend on the UV cutoff Λ, the internal-DoF coupling η and temperature T_int and, for the non-vacuum results, on T_g, α, r. All are stated inputs from physical or phenomenological arguments (detector size, molecular internal temperature, relic-graviton squeezing from [69]); none are fitted to the target decoherence results, though η = 1 is a hand-chosen 'strong coupling' value. The influence-functional treatment additionally rests on dropping the dissipation channel, truncating the stochastic variance at linear order in T_ij, and neglecting the O(φh²) graviton-scattering term. No new entities (particles, forces, dimensions) are postulated: the graviton bath and the Ohmic internal bath are standard elements carried from prior literature.

free parameters (6)

Graviton energy cutoff Λ = Λ ~ ℏc/L0; L0 = 10⁻⁹–10³ m in the numerical estimates
Regulates the graviton spectrum; set by the detector-size (geodesic separation) argument of Secs. II and IV, not by data. All central results scale with powers of Λ (up to Λ⁷), so the quantitative estimates are cutoff-sensitive.
External–internal coupling η (Ohmic bath strength) = η ~ 1 in the 'strong coupling' numerical example
Controls the long-time decoherence rate in Eq. (58); the paper notes explicit mass dependence could enter through η. Not measured; the 'strong coupling' value is chosen by hand.
Internal temperature T_int = 10⁴ K (complex molecules, cited from [77])
Enters linearly in the long-time decoherence rate and in the ratio R = ηπk_BT_intΛ/(m²c⁴). Plausible system parameter, not tied to a specific experiment.
Graviton temperature T_g = 1 K used in the recoherence estimate; otherwise unspecified
Characterizes the thermal graviton state; the paper itself warns it is a phenomenological noise-spectrum parameter without a precise thermodynamic definition.
Squeeze parameter r = r ~ 10² (relic gravitons, cited from [69])
State parameter of the squeezed graviton bath; drives the claimed exponential reduction of the decoherence time via (cosh2r)^(−1/3).
Coherent displacement α = unspecified (enters as α²/3)
State parameter of the coherent graviton bath; contributes K1,c = α²/3 to the decoherence function.

assumptions (6)

domain assumption Linearized perturbative quantum gravity is a valid effective description of gravitons on a weakly curved background.
Secs. IIA–IIB and Appendix A: the metric is written as g = η + h(B) + h with h(B) = −2ϕδ; gravitons are quantized TT perturbations. Non-renormalizability is noted but treated as a predictive EFT.
domain assumption Fermi normal coordinate expansion truncated at second order in ξ is valid, i.e., ξ² ≪ R_N³/M_N and ξ² ≪ ω⁻².
Eqs. (3)–(13): the metric components and the tidal tensor T_ij = (M_N/R_N³)(3δ_i3δ_j3 − δ_ij) come from this truncation; higher-order tidal terms are dropped.
domain assumption The dissipation channel (O(ξ⁴)) can be dropped from the influence functional, leaving the noise (O(ξ²)) term.
Eq. (29) and surrounding text: standard in the linear-coupling open-quantum-system treatment, but it is an approximation whose accuracy is not tracked over the long times where the recoherence prediction is made.
domain assumption Internal DoFs form an Ohmic bath at high temperature with white-noise kernel N_int = ηπT_intδ(t − t′).
Eq. (41), quoted from the authors' prior Ref. [64]. The long-time growth of Γ and the central 'inevitability' claim inherit this Markovian high-temperature form.
ad hoc to paper The O(φh²) graviton–Newtonian-potential scattering term in the graviton action can be neglected.
Sec. IIB, right after Eq. (15): dropped on the argument that the graviton scattering cross section is dominated by small angles (dσ/dΩ ~ θ⁻⁴); no quantitative estimate of the relative size of this term versus the retained O(φh) matter coupling is given.
ad hoc to paper The stochastic noise variance is truncated as ⟨NN⟩ = N_g + O(T²_ij), i.e., quadratic tidal terms are dropped.
Eq. (34b): the paper keeps only terms linear in the tidal tensor in the noise kernel. The recoherence/slowing predictions rely on the sign of the linear term, which is exactly where the dropped O(T²) terms would first contaminate the result.

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Pith. "Pith review of Gravitational decoherence of a composite particle: the interplay between gravitons and a classical Newtonian potential." pith.science (2026). https://pith.science/paper/OHILC7GJ

@misc{pith2026260222517,
  author       = {Pith},
  title        = {Pith review of: Gravitational decoherence of a composite particle: the interplay between gravitons and a classical Newtonian potential},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OHILC7GJ}},
  note         = {Machine review of arXiv:2602.22517}
}

read the original abstract

The fact that gravitational environments cannot be shielded (since gravity is universal) makes them of great theoretical interest to decoherence mechanisms and to the quantum-to-classical transition. While past results seemed to indicate that graviton-induced decoherence of spatial superpositions happens only for macroscopic systems, recently it was shown that this mechanism can be enhanced through the system's own dynamical internal structure. In this work, we extend this analysis by including the interaction with a classical Newtonian potential. We show that, although the graviton bath alone dominates the mechanism for short times compared to a timescale established by the size of the quantum spatial superposition, the interaction between the gravitons and the internal degrees of freedom of the system renders decoherence inevitable in the long-time limit, even for microscopic masses. We also show that this mechanism is slightly slowed down by the interplay with the classical Newtonian potential, which, for systems without dynamical internal degrees of freedom, can even lead to recoherence-like behaviour, at least in principle.

Figures

Figures reproduced from arXiv: 2602.22517 by the authors.

**Figure 1.** Two test masses M and m, with M ≫ m, and their geodesic deviation in Fermi normal coordinates, represented by the vector ξ. The mass m is also described by internal degrees of freedom, represented by the curly red lines. Next, let us specify our metric field to describe a small perturbation hµν, which describes the gravitational radiation on some background spacetime g˜µν, gµν = ˜gµν + hµν, |hµν| ≪ |g˜µν|. (5) The … view at source ↗

**Figure 2.** ). Note from Eq. (11) that the metric expansion in Fermi normal coordinates holds as long as ξ 2 ≪ R3 N /MN , and also ξ 2 ≪ ω −2 , with ω denoting the angular frequency of the incoming waves. This means that we need to introduce a physical energy cutoff for incident gravitational radiation, Λ ∼ L −1 0 , where L0 is some typical geodesic separation, also referred to as the "detector size". This necessity will becom… view at source ↗

**Figure 3.** Different contributions for the decoherence [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Different contributions for the decoherence [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

**Figure 5.** Figure 5: Different contributions for the decoherence [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

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Linearized Einstein equation Consider a given background metric˜gµν that is an exact known solution to Einstein’s equation. In situations where there is a small deviation from such exact solution, one can look for an approximate solution by writing gµν = ˜gµν +h µν,|h µν| ≪ |˜gµν|,(A1) linearising Einstein’s equation inhµν. The metric perturbationhµν sati...

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In that case, we consider the expansion (A8) withh(B) µν =−2ϕδ µν, withϕbeing the time-independent Newtonian potential

Newtonian limit Let us see how the linearized Einstein equation works when the background is described in the Newtonian limit. In that case, we consider the expansion (A8) withh(B) µν =−2ϕδ µν, withϕbeing the time-independent Newtonian potential. The gravitational action is then reduced to Sgrav = 1 64π Z d4x˜gµνhij∂µ∂νhij = 1 64π Z d4x hij□hij + 2ϕ hijδµ...

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Z t/2 0 dt1dt2 t1t2Ng(t1, t2) + Z t t/2 dt1dt2 (t−t 1)(t−t 2)Ng(t1, t2) +2 Z t/2 0 dt1 Z t t/2 dt2 t1(t−t 2)Ng(t1, t2) # + 16ηπTintΞ2v2

Configuration 1 Configuration 1 is the one described by Ξ(t) = Ξ =constant in time (C1a) and ∆ξ(t′) = 2vt′ for0< t ′ ≤t/2 2v(t−t ′)fort/2< t ′ < t ,(C1b) 22 for some constant velocityv, andtdenotes the time span of the superposition state. The decoherence function reads Γ1(t) = 8m2Ξ2v2 "Z t/2 0 dt1dt2 t1t2Ng(t1, t2) + Z t t/2 dt1dt2 (t−t 1)(t−t 2)Ng(t1, t...

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Configuration 2 Configuration 2 is described by Ξ(t) =V t,∆ξ(t) = ∆vt,(C10a) and V= v1 +v 2 2 ,∆v=v 1 −v 2,(C10b) for which the decoherence rate becomes Γ2(t) = 1 4 ηπT int v2 1 −v 2 2 2 t 2 + Tzz t3 3 + 4 Z t 0 dt1 t4 1Ng(t1) + m2 2 v2 1 −v 2 2 2 Z t 0 dt1dt2 (t1t2)2Ng(t1, t2).(C11) Proceeding as we did for the last configuration leads to Γ(A) 2 (t) = πη...

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