{"id":"84a5af67-54d0-4d1e-86c1-fe8092dbbd4a","arxiv_id":"2508.17492","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":9,"one_line_summary":"Rooting the wormhole matter density in the Hamaus cosmic void profile produces exact f(R,L_m,T) wormhole solutions whose energy-condition violations are reduced for δc=-0.9, with repulsive lensing claimed.","lead":"This paper builds exact wormhole solutions in a modified gravity theory by assuming the wormhole's matter density follows the measured density profile of cosmic voids. It claims that void-like density reduces the need for exotic matter near the throat and that light is bent away rather than captured.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The derived shape function is not asymptotically flat for the paper's chosen δc=-0.9: since the Hamaus profile tends to ρ_a>0 at infinity, X'≈κρ_a r² and X/r diverges as r², violating Eq. (3) and invalidating the lensing integral.","rationale":"The stress-test pass confirms the reader's REJECT verdict. The algebraic construction is internally coherent: with constant redshift and L_m=-ρ, Eqs. (16)-(21) follow from the linear model, and the shape function in Eq. (23) can be derived by quadrature. The decisive flaw is at the boundary: the Hamaus density profile is a cosmological profile for a finite void embedded in a mean-density background; it does not decay to zero at infinity. Since ρ(r)→ρ_a>0, the integrated shape function grows as r³, making X/r diverge and violating the traversability condition Eq. (3) that the paper itself imposes. This is not a matter of tuning δc: for the profile extended to r=∞ with ρ_a≠0, the same positive asymptotic density survives for every δc. It also invalidates the deflection-angle calculation, whose integration to infinity cannot converge. The scale mismatch between km-scale throats and Mpc-calibrated void radii is related, but the non-asymptotic flatness is sufficient by itself to sink the central claim. Fixing it requires a different construction, such as truncation plus exterior matching, which would alter the claimed exact solution. Granting the paper's independent support—the analytic integration producing Eq. (23) and the internal consistency of the energy-condition algebra—does not rescue the headline claim because the quoted boundary behavior is false. Hence the verdict should remain REJECT.","tokens_in":26013,"tokens_out":8627,"duration_ms":90297,"concrete_test":"Evaluate Eq. (23), or numerically integrate Eq. (19) with the Fig. 1 parameters, out to r=10^6 km and compute X/r. If X/r grows as (κρ_a/3)r² instead of tending to 0, asymptotic flatness fails exactly as argued. Analytically, isolate the term generated by the constant '1' in the Hamaus bracket: its contribution to Eq. (23) is Λρ_a r³/3, with all hypergeometric terms subleading for β>α, so lim_{r→∞}X/r=+∞. A repair would truncate ρ at r<r_sv and match to a Schwarzschild exterior; then re-check Eq. (3) and the convergence of Eq. (34).","verdict_should_be":"REJECT","load_bearing_attack":"With Φ=const and f=R+ηL_m+χT, the field equations reduce to X'=κr²ρ (Eq. 19). Substituting the Hamaus profile (Eq. 22) with β=6.5>α=3.75, the density-contrast term vanishes at infinity and ρ(r)→ρ_a>0. Hence X'(r)∼κρ_a r², so X(r)∼(κρ_a/3)r³ and X/r∼(κρ_a/3)r² diverges. This directly contradicts the paper's own asymptotic-flatness condition lim_{r→∞}X/r=0 in Eq. (3), for δc=-0.9 and for every δc if the profile is extended to infinity with ρ_a≠0. The apparent decay of X/r in Fig. 1 is an artifact of plotting only r≲2.5 km. The same failure makes the lensing integral in Eq. (34), which runs to r=∞, divergent; the extreme values in Fig. 7, including its integer-overflow pattern, are consistent with a numerically diverging deflection angle. A truncated void profile matched to a vacuum exterior would evade this, but that is not the solution claimed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs exact static, spherically symmetric traversable wormhole solutions in the linear f(R,L_m,T)=R+ηL_m+χT gravity theory by identifying the wormhole matter energy density with the Hamaus universal cosmic void density profile. With a constant redshift function Φ, the field equations reduce to a simple system in which the shape function satisfies X'=κr²ρ; integrating Eq. (22) with the throat condition X(r0)=r0 yields the closed-form shape function in Eq. (23) involving hypergeometric functions. The paper claims that this shape function satisfies the Morris-Thorne throat, flare-out, and asymptotic flatness conditions, that for δc=-0.9 the energy density is positive and the energy-condition violations are mitigated, that the TOV equilibrium holds, and that gravitational lensing yields a negative (repulsive) deflection angle. The work also examines the exoticity parameter, anisotropy, and embedding diagrams.","tokens_in":26205,"tokens_out":5024,"duration_ms":53537,"significance":"If the central claims were correct, the paper would provide a new exact wormhole family in which a cosmologically calibrated matter profile, rather than ad hoc exotic matter, shapes the geometry and weakens energy-condition violations. The reduction of the f(R,L_m,T) field equations to the compact system (19)-(21) is clean, and the closed-form integration of the shape function is a nontrivial technical step worth acknowledging. However, the advertised asymptotic flatness and repulsive-lensing results fail for the stated solution, and the physical transplantation of a Mpc-scale void profile to a kilometer-scale wormhole is not justified. The manuscript's main positive contributions are therefore not realized in the solution as presented.","major_comments":[{"comment":"The solution is not asymptotically flat for the parameter set used. Since the Hamaus profile (1) tends to ρ_a>0 as r→∞ when β>α, Eq. (19) gives X'∼κρ_a r² and hence X∼(κρ_a/3)r³, so X/r∼(κρ_a/3)r² diverges. This violates the paper's own asymptotic flatness condition lim_{r→∞}X/r=0 stated in Eq. (3). The text after Fig. 1 claims that X/r approaches zero as r→∞, but the plotted range is only r≲2.5 km; the asymptotic region is not shown and behaves in the opposite manner. This is not a cosmetic issue: all subsequent claims about the spacetime being asymptotically flat, and any integral over r to infinity, depend on this condition.","section":"§IV, Eq. (23) and Eq. (3)"},{"comment":"The lensing deflection angle α(rtp) is evaluated through Eq. (34) with upper limit r=∞, but the integrand contains √(1-X/r), and since X/r diverges as r², the integral is not convergent for large r. The numerical content of Fig. 7 is consistent with this failure: the plotted values include -9223372036854775808, the standard 64-bit signed integer overflow sentinel, and the color-bar entries are of order -10^153. These are not finite, negative deflection angles; they are artifacts of a numerically diverging integral. The claim that the wormhole repels light is therefore not supported by the model.","section":"§V, Eq. (34) and Fig. 7"},{"comment":"The Hamaus universal density profile is an empirical fit to cosmic voids with radii of tens of megaparsecs, characterized by r_sc and r_sv in Mpc. Here the same functional form is imposed as the wormhole energy density for r∈[0.75,∞) with r in kilometers and r_sc=75, r_sv=95. The paper provides no physical or mathematical argument that this profile applies at centimeter-to-kilometer scales or that ρ_a remains a positive constant at infinity in a compact-object context. If the profile is intended to describe only the interior of a finite void, the solution must be truncated at the void boundary and matched to an exterior vacuum or cosmological spacetime; no such matching is given. This undermines the physical interpretation of the solution as a wormhole sourced by cosmic-void matter.","section":"§II, Eq. (1) and §IV after Eq. (22)"}],"minor_comments":[{"comment":"The statement that 'both conditions X'<1 and X/r<1 hold for all r greater than r0' is not supported by the asymptotic behavior derived from Eq. (19); the claim should be restricted to the numerically explored range r≲2.5 km.","section":"§IV, energy conditions text"},{"comment":"The choice L_m=-ρ is introduced without discussion; since the field equations depend on this identification, it should be stated explicitly and justified in the text.","section":"§III, around Eq. (15)"},{"comment":"The density and pressure quantities are labeled in units of km^{-2}, which is unconventional; with G=c=1 the dimension is length^{-2}, but the relationship between the plotted values and the input parameters (in particular ρ_a=0.00001) should be clarified.","section":"Figures 3-8"},{"comment":"The figure caption and color bar contain formatting errors, including spaces in numbers, '6.8×10. 153', and the axis label 'rTurning Point'; these should be corrected.","section":"Fig. 7"},{"comment":"The expression for the exoticity parameter Ω_Exoticity appears to have a mismatched bracket at the end, making the formula ambiguous; it should be rewritten with balanced parentheses.","section":"Eq. (42)"}],"recommendation":"reject","confidential_remarks":"The asymptotic non-flatness is a decisive, internally consistent error: the paper's own Eq. (3) is violated everywhere in parameter space because ρ_a>0 persists to infinity. This is not a matter of interpretation or of an alternative convention; the solution simply does not satisfy the stated definition of a traversable wormhole, and the lensing integral is divergent. A truncated profile matched to a vacuum exterior could potentially repair the model, but that would require a different solution and would invalidate the present figures and claims. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nThe reader's stress test is right, and it lands on the heart of the paper. The wormhole family here is built on a clean exact integration of the Hamaus void profile, but the central asymptotic-flatness claim is false for the stated parameters, and the lensing plot is numerically broken. In its current form the paper should not be published.\n\nWhat is actually new is the shape function in Eq. (23): an explicit wormhole solution in linear f(R,L_m,T) gravity with the Hamaus universal void density profile used as the prescribed matter density. That specific combination is not in the prior literature, as far as I can tell. The rest of the algebra is the same constant-redshift system already solved by Moraes et al. and by the authors themselves; the paper says so explicitly, which is honest.\n\nWhat the paper does well: the integration to closed hypergeometric expressions for X, Pr, Pt is careful, and the energy-condition, TOV, and anisotropy analysis is standard and internally consistent given the field equations. The observation that rho+Pr+2Pt=0 for generic couplings is a useful structural result.\n\nThe soft spots are not minor. First, with delta_c=-0.9, the Hamaus profile tends to rho_a > 0 at infinity because alpha < beta, so Eq. (19) gives X' ~ kappa rho_a r^2 and X/r diverges as r^2. This directly violates the paper's own Eq. (3). The claim in Fig. 1 that X/r goes to zero is an artifact of plotting only r <~ 2.5 km; the divergence is slow because rho_a = 10^-5 (in km^-2), but it is there. Second, the scale mismatch is real: r_sc=75 and r_sv=95 are Mpc-scale void parameters, while the throat sits at 0.75 km and all plots are in km. No unit conversion or exterior matching is supplied. On a kilometer scale the void profile is essentially constant, so the advertised 'void-shaped' geometry is not actually being probed. Third, Fig. 7 shows integer overflow values and deflection angles of order 10^153, which is numerical nonsense; the lensing integral to infinity does not converge for the same reason the geometry is not asymptotically flat.\n\nThese flaws are repairable in principle: truncate the profile at the void edge and match to a vacuum exterior, then recompute the lensing. That would give a legitimate asymptotically flat wormhole, but the results on energy conditions and repulsive lensing would change significantly. As is, the central physical claims are unsupported.\n\nRecommendation: I would not desk-reject; I would send it to peer review with a request for major revision, because the exact-solution core is worth checking carefully. But I would not cite it in this form.","headline":"A coherent exact wormhole construction in f(R,L_m,T) using the Hamaus void profile, undermined by a false asymptotic-flatness claim and a scale mismatch that invalidates the advertised void-shaped geometry.","tokens_in":26845,"tokens_out":6370,"would_cite":false,"duration_ms":64084,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83D05","83C15"],"pacs":["04.50.Kd","04.20.Jb"],"model":"deepseek-v4-flash","headline":"This paper claims that the measured density profile of cosmic voids can be transplanted into a generalized gravity theory to produce exact, traversable wormholes that repel light rather than capturing it.","keywords":["cosmic voids","wormholes","f(R,L_m,T) gravity","traversable wormholes","energy conditions","gravitational lensing","void density profile","shape function"],"falsifier":"Integrate the shape-function equation with the same universal void profile but stop at r = r_sv and match the interior to a vacuum exterior; if the resulting deflection angle at the throat turns positive or the flare-out condition fails, the paper's central claim would not survive. A simpler independent check is to recompute the deflection integral in Eq. (34) using the proper-coordinate transformation l(r) and verify that the throat is indeed the only photon sphere for the stated parameter set.","tokens_in":25693,"feed_emoji":"🕳️","tokens_out":5094,"duration_ms":48693,"temperature":0.7,"pith_summary":"This paper tries to establish that the measured density profile of cosmic voids, vast underdense regions of the universe, can serve as the matter source for a new exact family of static, traversable wormholes in the linear f(R,L_m,T) gravity R+eta L_m + chi T. On a sympathetic reading, once the void profile is inserted into the shape-function equation X' = kappa $r^{2}$ rho, the resulting hypergeometric shape function satisfies the throat, flare-out, and asymptotic-flatness conditions for a chosen parameter set. If the construction holds, wormholes built from void-like matter would need less exotic matter than their general-relativistic counterparts, and they would deflect light outward rather than inward. The paper also claims the configuration is stable in the TOV sense and that the void contrast parameter delta_c controls where energy conditions are violated.","feed_headline":"Cosmic void profiles can build wormholes that repel light","feed_subtitle":"Universal void density profiles in f(R,L_m,T) gravity soften exotic matter and reverse gravitational lensing.","key_machinery":"The load-bearing object is the shape function X(r) obtained by integrating X' = kappa $r^{2}$ rho with rho equal to the universal void density profile of Eq. (1). The integration yields a closed form built from Gauss hypergeometric functions 2F1, with the throat condition fixing the integration constant. This shape function, through the simplified field equations X' = kappa $r^{2}$ rho, -X = kappa $r^{3}$ P_r, and X - X'r = 2 kappa $r^{3}$ P_t, determines the pressures and therefore every energy condition, the lensing integral in Eq. (34), the TOV force balance, and the exoticity and anisotropy parameters.","core_discovery":"The central claim is that a universal cosmic void density profile can be inserted into the field equations of the linear f(R,L_m,T) model to yield an exact wormhole shape function, written as Eq. (23). The shape function is claimed to meet all three standard traversability criteria: throat condition X(r0)=r0, flare-out X'(r0)<1, and asymptotic flatness X/r -> 0. With the representative parameter set delta_c=-0.9, r0=0.75, $\\alpha$=3.75, $\\beta$=6.5, rho_a=$10^{-5}$, r_sc=75, r_sv=95, the paper reports positive energy density, radial null energy condition satisfied for delta_c in (-0.925,0], tangential null energy condition satisfied at and beyond the throat, and a negative deflection angle, i.e., repulsive gravitational lensing. A further consequence claimed is that the exoticity parameter is negative, indicating a transition from exotic to ordinary matter away from the throat.","pith_inferences":["The paper integrates the void profile from r0 out to infinity, but a physical cosmic void ends near r_sv; a natural extension is to truncate the profile at the void edge and match the interior to an exterior vacuum solution, which could alter the asymptotics and the sign of the deflection angle.","The profile parameters r_sc=75 and r_sv=95 are calibrated for voids tens of megaparsecs across, while the throat sits at r0=0.75 km with rho_a in km^-2; a units-and-scales consistency check on whether void matter could support such a structure would sharpen the claim.","The predicted repulsive lensing is testable in principle: one could compute magnification and image positions for a source behind such a wormhole and search existing microlensing surveys for the unusual 'missing arc' or asymmetry signatures described in the paper."],"forward_implications":["The void contrast parameter delta_c becomes a dial for energy-condition behaviour: radial NEC holds for delta_c in (-0.925, 0] and fails closer to -1, so voids with moderate contrast require less exotic matter.","If the solution is correct, a traversable wormhole sourced by void-like density would lens background sources with a negative deflection angle, producing image patterns opposite to black hole lensing.","The TOV analysis implies the wormhole can be held open by a balance of hydrostatic and anisotropic forces alone, since the gravitational force vanishes at constant redshift.","The negative exoticity parameter suggests the matter transitions from whatever supports the throat to ordinary matter as the radius increases, softening the usual objection that traversable wormholes require exotic matter everywhere."],"supporting_citations":[{"why":"Supplies the universal void density profile of Eq. (1) that is used as the wormhole matter source.","marker":"[83]"},{"why":"Provides the Morris-Thorne traversability conditions, the shape function framework, and the embedding construction used throughout.","marker":"[60]"},{"why":"Establishes the f(R,L_m,T) gravitational action and its field equations, the starting point of the derivation.","marker":"[128]"},{"why":"The authors compare their final reduced field equations against this reference to confirm agreement with earlier f(R,L_m,T) wormhole work.","marker":"[91]"},{"why":"Supports the premise that a steeply rising inner density can soften or mask the exotic matter required to keep a wormhole throat open.","marker":"[84]"},{"why":"Provides the wormhole energy-condition background that motivates using void-like density to reduce NEC violations.","marker":"[85]"}],"fun_headline_variants":["Void density profiles shape wormholes that repel light","Cosmic voids give rise to wormholes with repulsive lensing","f(R,L_m,T) gravity: voids soften wormhole energy conditions","Wormhole geometry from universal void profiles","Void-based wormholes: less exotic matter, light deflection reversed"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result stands on the assumption that a density profile measured for cosmic voids tens of megaparsecs across, with its fitted parameters, can be applied quantitatively to the matter content of a wormhole throat at the kilometre scale and integrated unchanged all the way to infinity.","fun_headline_variants_meta":{"raw":{"variants":["Void density profiles shape wormholes that repel light","Cosmic voids give rise to wormholes with repulsive lensing","f(R,L_m,T) gravity: voids soften wormhole energy conditions","Wormhole geometry from universal void profiles","Void-based wormholes: less exotic matter, light deflection reversed"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000129,"raw_usage":{"total_tokens":1148,"prompt_tokens":1001,"completion_tokens":147,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":617,"completion_tokens_details":{"reasoning_tokens":63}},"tokens_in":617,"tokens_out":147,"duration_ms":2287,"temperature":1.0,"reasoning_tokens":63,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:05:49.040987+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Integrate the shape-function equation with the same universal void profile but stop at r = r_sv and match the interior to a vacuum exterior; if the resulting deflection angle at the throat turns positive or the flare-out condition fails, the paper's central claim would not survive. A simpler independent check is to recompute the deflection integral in Eq. (34) using the proper-coordinate transformation l(r) and verify that the throat is indeed the only photon sphere for the stated parameter set.","supporting_citations":[{"cited_title":"Banerjee, S","cited_arxiv_id":null,"evidence_quote":"Supplies the universal void density profile of Eq. (1) that is used as the wormhole matter source."},{"cited_title":"Kuhfittig, Fundamental J","cited_arxiv_id":null,"evidence_quote":"Establishes the f(R,L_m,T) gravitational action and its field equations, the starting point of the derivation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The authors compare their final reduced field equations against this reference to confirm agreement with earlier f(R,L_m,T) wormhole work."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the premise that a steeply rising inner density can soften or mask the exotic matter required to keep a wormhole throat open."},{"cited_title":"Hamaus, P","cited_arxiv_id":null,"evidence_quote":"Provides the wormhole energy-condition background that motivates using void-like density to reduce NEC violations."}],"review_version":2}