{"id":"846e92be-0dcf-4d18-b0b7-f776ca723747","arxiv_id":"2505.09291","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Using the proton's quark pressure profile from a GPD fit, the authors update upper bounds on the EiBI gravity parameter kappa to about 0.1 to 0.3 in the quoted units.","lead":"This paper inserts a recent quark pressure profile of the proton, obtained from generalized parton distributions, into existing EiBI gravity formulas and obtains new upper bounds on the theory's parameter kappa. The bounds, around 0.1 to 0.3 in the quoted units, show that hadron physics can provide a competitive but model-dependent test of modified gravity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Applying quark-only D_Q(t) from Eq. (19) to Avelino's inequalities (24)/(33) assumes the quark pressure is the full EMT pressure that sources EiBI gravity; the paper itself states gluon contributions are absent, so the quoted |kappa| bounds are not yet bounds on physical pressure.","rationale":"The reader's weakest_assumption identifies exactly this mismatch, and I agree that it is load-bearing. The paper's own note after Eq. (19) admits that only the quark GFF is used; nothing in the subsequent derivation supplies the missing gluon pressure. Because EiBI's tau, apparent pressure, and inequalities depend on the total EMT, the central numbers are not merely numerically uncertain but conceptually mis-targeted. I do not see a way to repair this within the paper's framework without new input for D_G(t) and a total-pressure reanalysis. The cutoff dependence of the divergent p(r) is a second independent problem, but the quark/gluon substitution is the primary reason the central claim fails. The verdict should remain as the reader stated; no adjustment is needed.","tokens_in":11058,"tokens_out":7718,"duration_ms":80719,"concrete_test":"Compute the total quark+gluon pressure by taking D_total(t) = D_Q(t) + D_G(t), with D_Q(t) from Eq. (19) and a gluon GFF from lattice QCD or a global fit (e.g., Shanahan-Detmold 2019); recompute p_total(r) and evaluate |kappa| <= |<p_total>|/<p_total^2> over the same radial range. If the resulting bound moves outside the quoted 0.10-0.3 m^5 kg^-1 s^-2 range, or if integral r^2 p_Q(r) dr is not zero while integral r^2 p_total(r) dr is, the paper's substitution is the controlling error. Repeat the peak-pressure bounds with a fixed cutoff at r_c ~ 0.1 fm to test sensitivity to the divergent r -> 0 behavior.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that Avelino's bounds |kappa| <= 1/|p| (Eq. 24) and |kappa| <= |<p>|/<p^2> (Eq. 33) can be evaluated using the MMGPDs proton pressure. These inequalities follow from the EiBI field equations and the apparent EMT, whose rho and p in Eqs. (8)-(14) and (31) are the total energy-momentum tensor of the matter. The pressure used in the paper, however, is computed from D_Q(t) in Eq. (19), and the text after Eq. (19) states explicitly that this D(t) is the quark contribution only and does not include the gluon. In QCD the EMT is the sum of quark and gluon parts; only the total is conserved, and the von Laue condition Eq. (18) applies to the total pressure, not to p_Q(r) separately. Using p_Q in Eqs. (24) and (33) therefore produces bounds on an object that is not the pressure sourcing the modified gravity. The numerical values in Eqs. (25)-(36) are consequently not established as constraints on EiBI kappa. The problem is compounded by the divergence of p(r) at r -> 0 noted near Fig. 2, so the peak-pressure bounds depend on an unstated cutoff; but the quark/gluon mismatch is the more fundamental defect.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript derives upper bounds on the Eddington-inspired Born-Infeld (EiBI) parameter κ by combining Avelino's inequalities for EiBI gravity, Eqs. (24) and (33), with the proton pressure profile extracted by the MMGPDs Collaboration from a QCD analysis of skewness-dependent GPDs. The authors evaluate the bounds using peak pressure, average peak pressure, and first/second moments of the quark pressure distribution, obtaining limits in the range |κ| ≤ 0.10–2.69 m^5 kg^{-1} s^{-2} depending on the model parameter M^2 and the chosen estimator. They conclude that proton mechanical properties provide competitive constraints on EiBI gravity and motivate improved GPD reconstructions.","tokens_in":11369,"tokens_out":4164,"duration_ms":42802,"significance":"If the derived bounds were established, the paper would demonstrate that subatomic pressure distributions can test modified gravity, complementing astrophysical constraints from neutron stars. The manuscript is clearly written and the arithmetic from the quoted pressure profiles to the stated κ values is straightforward and reproducible. However, the central claim depends on two load-bearing identifications: that the quark-only pressure from Eq. (19) can be used as the total physical pressure in the EiBI inequalities, and that Eq. (24) is the correct finiteness condition for τ. Both identifications are problematic, and the first is explicitly contradicted by the paper's own statement that the gluon contribution is absent. Consequently, the numerical constraints in Eqs. (25)–(36) are not established as bounds on the physical pressure that sources EiBI gravity.","major_comments":[{"comment":"The pressure p(r) used in the bounds is computed from D_Q(t) in Eq. (19), and the text immediately after Eq. (19) states that this is only the quark contribution and does not include the gluon. The EiBI inequalities in Eqs. (24) and (33) involve the physical energy density and pressure of the matter that sources gravity; the von Laue condition in Eq. (18) and the averaged condition in Eq. (22) apply to the total EMT pressure. Without an explicit argument that the gluon pressure is negligible for the peak value and for the first and second moments, the numerical results in Eqs. (25)–(30) and (35)–(36) are bounds on a quark-only pressure, not on the total proton pressure appearing in the EiBI field equations.","section":"Section 'Constraints on EiBI from proton interior pressure profile', Eqs. (24)–(36)"},{"comment":"Equation (24) states that |κ| ≤ |p|^{-1} follows from the dominant energy condition and finiteness of τ. But τ in Eq. (12) is [(1+κρ)(1−κp)^3]^{-1/2}, so the reality conditions are 1+κρ > 0 and 1−κp > 0. With the dominant energy condition ρ ≥ |p|, the common bound is |κ| ≤ 1/ρ, not |κ| ≤ 1/|p|. The peak-pressure limits in Eqs. (25)–(30) are therefore not consequences of Eq. (24). In addition, p(r) diverges as r→0 as noted near Fig. 2, so the 'peak pressure' evaluations depend on an unstated radial cutoff and are not well defined as stated.","section":"Eq. (24) and Eqs. (25)–(30)"},{"comment":"The derivation of Eq. (33) from Eq. (32) is not shown. Pointwise, Eq. (32) gives |pG| ≥ |κ| p^2, and averaging yields ⟨|pG|⟩ ≥ |κ| ⟨p^2⟩. Since |⟨pG⟩| ≤ ⟨|pG⟩|, the inequality in Eq. (33), |κ| ≤ |⟨p⟩|/⟨p^2⟩, requires an additional assumption that the pressure anisotropy parameter ξ, Eq. (34), controls the ratio |⟨p⟩|/⟨|pG|⟩. The authors should provide the full derivation or cite the specific step in Ref. [54] that justifies replacing the averaged absolute value by the absolute value of the average.","section":"Eq. (33) and Eqs. (35)–(36)"}],"minor_comments":[{"comment":"The abstract and conclusions state that the bounds are 'competitive with existing bounds from neutron stars', but the quoted comparison in the Conclusions says they are 'several orders of magnitude weaker than those obtained from collider experiments'; please clarify which comparison is intended.","section":"Abstract and Conclusions"},{"comment":"The definition ξ ≡ ⟨p⟩p/⟨p^2⟩ appears to have a typo: as written ξ is dimensionful, despite the text calling it dimensionless. The intended definition should be stated cleanly.","section":"Around Eq. (34)"},{"comment":"There are several typographical issues, e.g., 'bonds' for 'bounds', 'anlyzing' for 'analyzing', and inconsistent use of 'GFF D(t)' versus 'D-form factor'. These do not affect the physics but should be corrected.","section":"Throughout"},{"comment":"The statement that the pressure 'diverges toward r = 0' is important because the central bounds depend on the behavior near r=0; the manuscript should state the limiting behavior of p(r) from Eq. (19) and specify the radial cutoff used to evaluate the peak values in Eqs. (25)–(30).","section":"Figure 2 and related text"}],"recommendation":"reject","confidential_remarks":"The manuscript's central claim is not supported because the pressure from the MMGPDs analysis is explicitly quark-only, while the EiBI inequalities require the total EMT pressure. This is a conceptual mismatch rather than a mere numerical refinement, and it is compounded by an error in the derivation of Eq. (24) and an unjustified averaging step in Eq. (33). These issues cannot be repaired by local edits within the scope of the present analysis; the authors would need a gluon-inclusive pressure extraction or a substantially revised theoretical framing. The paper is readable and the numerical evaluation is transparent, so a future version with a proper total-pressure input could be of interest."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a straightforward substitution of the MMGPDs quark pressure profile into Avelino's EiBI inequalities. The only genuinely new output is the set of numbers in Eqs (25)-(36); the machinery, including the pressure input, comes from prior papers by overlapping authors. That is a legitimate extension, not a new mechanism, and the paper says so more or less.\n\nWhat the paper does well: it gives a compact, accurate review of EiBI gravity and the pressure-radius formalism, and the arithmetic from D(t) to kappa limits is easy to follow and reproduce. The authors are candid about the model dependence (two M^2 values, different peak definitions) and about the fact that pure experimental moments are not yet available.\n\nThe soft spots are load-bearing. The pressure used, from D_Q(t) in Eq (19), is explicitly the quark contribution; the text says the gluon is not included. But the von Laue condition in Eq (18) and the EiBI field equations require the total EMT pressure. Avelino's inequalities were derived for the physical total pressure. Unless the quark pressure equals the total, Eqs (25)-(36) are bounds on a partial pressure, not on kappa. The paper flags the gluon omission but never justifies ignoring it. That is a genuine gap, not a minor technicality.\n\nThere are secondary issues. Eq (24) as stated drops the 1+kappa rho factor in tau; the condition for finite tau is more than |kappa| <= 1/|p|. The peak-pressure numbers depend on an unspecified small-radius cutoff, since p(r) diverges at r=0; the \"peak is often evaluated in a small but finite region\" is not a definition. And no uncertainties from the D(t) fit are propagated, which matters when you quote limits to two digits.\n\nNet: the paper is clear and the idea is worth exploring, but the central constraints are not yet established. The fix is not hard--use a total pressure (e.g., quark+gluon from the same framework or a lattice-based estimate), define the averaging radius, and carry errors. As it stands I would not cite the numbers, but I would send it to a serious referee, because the question is legitimate and the errors are correctable in revision.","headline":"A clear but seriously incomplete application of Avelino's EiBI bounds: the quark-only pressure does not yield constraints on kappa until the total EMT pressure is used.","tokens_in":11915,"tokens_out":3632,"would_cite":false,"duration_ms":36883,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Using the proton's internal pressure profile from generalized parton distributions, this paper derives new bounds on the EiBI gravity parameter, $|\\kappa|\\le 0.10$–$0.3\\,\\mathrm{m^5\\,kg^{-1}\\,s^{-2}}$.","keywords":["Eddington-inspired Born-Infeld gravity","proton pressure distribution","gravitational form factor","generalized parton distributions","deeply virtual Compton scattering","EiBI parameter constraints","von Laue condition"],"falsifier":"A lattice QCD calculation of the full quark-plus-gluon gravitational form factor $D(t)$ for the proton would settle the matter: if the total pressure profile differs substantially from the quark-only profile used here, the $|\\kappa|$ bounds would shift by the same factor, and if the second pressure moment disagrees with the GPD-based value, the moment-based bounds would be shown to be model-dependent.","tokens_in":10843,"feed_emoji":"⚛️","tokens_out":11134,"duration_ms":100313,"temperature":0.7,"pith_summary":"This paper uses the proton's internal pressure profile, extracted from the gravitational form factor $D(t)$ through a QCD analysis of generalized parton distributions, to constrain the extra parameter $\\kappa$ of Eddington-inspired Born-Infeld (EiBI) gravity. It reports updated bounds $|\\kappa| \\leq 0.10\\text{--}0.3\\,\\mathrm{m^5\\,kg^{-1}\\,s^{-2}}$, with the tighter end coming from the pressure profile fitted with $M^2=2\\,\\mathrm{GeV^2}$ and the looser end from average-pressure inequalities. It also finds that constraints from the first and second pressure moments are not significantly stronger than peak-pressure constraints, contrary to an earlier expectation. The result matters because it puts subatomic structure on the table as a testing ground for modified gravity, with limits competitive with neutron-star bounds.","feed_headline":"Proton's internal pressure bounds modified gravity at 0.1–0.3","feed_subtitle":"Quark pressure from GPD data yields kappa limits on par with neutron stars, opening a subatomic probe of gravity.","key_machinery":"The load-bearing machinery is a chain of three pieces: the $D(t)$ gravitational form factor, which gives the pressure $p(r)$ through a Fourier transform and radial derivatives (Eq. 15); the von Laue condition, the stability statement that the volume integral of $p(r)$ vanishes, which lets the average physical pressure be equated with the average effective gravitational pressure $p_G$ from EiBI; and the inequalities $|\\kappa| \\le |p|^{-1}$ (Eq. 24) and $|\\kappa| \\le |\\langle p\\rangle|/\\langle p^2\\rangle$ (Eq. 33), which turn peak or moment pressures into upper bounds on $\\kappa$. The new input is the $D_Q(t)$ parameterization of Eq. (19), whose $M^2$ value changes the bounds by roughly a factor of three to four.","core_discovery":"The paper claims that the quark pressure profile of the proton, obtained from the gravitational form factor $D_Q(t)$ in Eq. (19) for two values of the fit parameter $M^2$, can be inserted directly into the EiBI inequalities (24) and (33) to update the bound on $\\kappa$. The resulting constraints are $|\\kappa| \\le 0.44$ and $0.10\\,\\mathrm{m^5\\,kg^{-1}\\,s^{-2}}$ from peak pressure, and $|\\kappa| \\le 1.32$ and $0.30\\,\\mathrm{m^5\\,kg^{-1}\\,s^{-2}}$ from pressure moments, for $M^2=1$ and $2\\,\\mathrm{GeV^2}$, respectively. The stronger profile yields a bound competitive with neutron-star limits, though still weaker than collider-based limits. The paper concludes that precise experimental and theoretical determinations of the proton's mechanical properties are a viable route to testing EiBI gravity and related modifications.","pith_inferences":["The cleanest check of the bounds is a lattice QCD evaluation of the total (quark plus gluon) $D(t)$: the paper states that its $D_Q(t)$ carries only quark contributions, while the inequalities and the von Laue condition refer to the full energy-momentum tensor.","The same inequality chain could be applied to other hadrons with measured mechanical properties, giving independent subatomic bounds on EiBI gravity outside the proton.","Because the inequalities depend only on pressure moments, any future $D(t)$ extraction can be passed through them without new gravity input, making this a reusable route for testing modified gravity."],"forward_implications":["If the analysis is correct, the EiBI parameter is bounded by $|\\kappa| \\le 0.10$ to $0.3\\,\\mathrm{m^5\\,kg^{-1}\\,s^{-2}}$, on the same scale as limits from neutron-star observations.","The bound depends strongly on the pressure model: the $M^2=2\\,\\mathrm{GeV^2}$ profile gives limits three to four times tighter than $M^2=1\\,\\mathrm{GeV^2}$, so data that pin down the $t$-dependence of $D(t)$ directly sharpen the gravity constraint.","Moment-based constraints do not improve on peak-pressure constraints, so future experimental work should target direct measurements of the first and second pressure moments rather than relying on peak values.","Improvements in DVCS data, GPD reconstructions, and lattice QCD will, through the same inequalities, translate into stronger bounds on EiBI gravity and analogous modified theories."],"supporting_citations":[{"why":"Supplies the $D_Q(t)$ form factor and the two proton pressure profiles (for $M^2=1,2\\,\\mathrm{GeV^2}$) that all the new bounds are computed from.","marker":"[62]"},{"why":"Derives the inequalities in Eqs. (24) and (33) that convert peak or moment pressures into bounds on $|\\kappa|$, and gives the earlier DVCS-based bound this paper updates.","marker":"[54]"},{"why":"Provides the previous pressure profile based on DVCS data that the new GPD-based profile is compared against.","marker":"[55]"},{"why":"Establishes the standard formulas connecting $D(t)$ to pressure and shear distributions and the von Laue stability condition.","marker":"[60]"},{"why":"Defines EiBI gravity and the parameter $\\kappa$ that is being constrained.","marker":"[35]"},{"why":"Provides the neutron-star limits that the paper uses to argue the proton-pressure bounds are competitive.","marker":"[36]"},{"why":"Supplies the von Laue condition analysis for compact objects used to equate average physical pressure with average effective gravitational pressure.","marker":"[80]"}],"fun_headline_variants":["Proton pressure probes modified gravity with tight kappa limits","Quark pressure inside proton tightens bounds on EiBI gravity","Proton's internal squeeze constrains Born-Infeld gravity","Subatomic force fields test alternate gravity theory","Proton pressure yields competitive gravity bounds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The bounds assume that the quark contribution to the proton pressure, from $D_Q(t)$, is the full pressure that enters the EiBI inequalities; if the omitted gluon pressure is comparable, the derived $|\\kappa|$ limits do not constrain the physical pressure that sources gravity.","fun_headline_variants_meta":{"raw":{"variants":["Proton pressure probes modified gravity with tight kappa limits","Quark pressure inside proton tightens bounds on EiBI gravity","Proton's internal squeeze constrains Born-Infeld gravity","Subatomic force fields test alternate gravity theory","Proton pressure yields competitive gravity bounds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000713,"raw_usage":{"total_tokens":3247,"prompt_tokens":1025,"completion_tokens":2222,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":641,"completion_tokens_details":{"reasoning_tokens":2146}},"tokens_in":641,"tokens_out":2222,"duration_ms":16192,"temperature":1.0,"reasoning_tokens":2146,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:37:07.229726+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A lattice QCD calculation of the full quark-plus-gluon gravitational form factor $D(t)$ for the proton would settle the matter: if the total pressure profile differs substantially from the quark-only profile used here, the $|\\kappa|$ bounds would shift by the same factor, and if the second pressure moment disagrees with the GPD-based value, the moment-based bounds would be shown to be model-dependent.","supporting_citations":[],"review_version":1}