{"id":"b48f1b1e-98f5-468e-8d18-30c82fc113e8","arxiv_id":"2607.07406","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":9,"one_line_summary":"A non-zero topological angle in a confining dark sector induces CP-violating pion-baryon couplings that naturally generate velocity-dependent dark matter self-interactions and dark electric dipole moments for direct detection.","lead":"This paper shows that a CP-violating 'theta angle' in a QCD-like dark sector naturally creates long-range dark matter self-interactions and enhances direct-detection signals via a dark electric dipole moment. A generalist might read it because it ties dark matter halo dynamics and laboratory experiments to a single parameter, offering a concrete, testable composite dark matter model.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"Perturbativity assumption is correctly identified, but the concern is slightly mischaracterized: the scattering is solved non-perturbatively via the Schrödinger equation; the real issue is whether the leading-order chiral Lagrangian derivation of the pion-nucleon couplings is reliable, and the paper","rationale":"The reader correctly identifies the perturbativity assumption as the most load-bearing concern — it is the assumption the paper itself flags, and it underlies both the self-interaction and direct detection predictions. However, the reader's framing ('perturbative assumption... in computing self-scattering cross-sections') is imprecise: the scattering is solved non-perturbatively via the Schrödinger equation (Eq. 3.5–3.6), so perturbation theory is not used for the scattering itself. The perturbativity condition instead governs whether the leading-order chiral Lagrangian correctly captures the pion-nucleon couplings. The deeper, unaddressed issue is that the benchmark requires g_A ≈ 0.015 (from the Goldberger-Treiman relation with g_πNN = 0.11 and f_π ~ √(N_c) m_n/(4π)), which is far below the SM value and not discussed as to its plausibility. The chiral expansion parameter m_π/Λ ~ 0.006 is very small, so the chiral EFT framework is internally consistent; the question is whether the specific LEC values (especially g_A) are realizable in a concrete confining theory. The paper's qualitative mechanism — θ induces CP-violating pion-baryon couplings that generate both a Yukawa potential and an EDM — is robust and well-motivated by analogy with QCD. The NREFT matching for direct detection (Table 2) is standard and correct. The EDM formula (Eq. 4.4) agrees with the known SM result. The cosmological history is plausible. The annual modulation discussion is honest about practical limitations. No code or data is shipped, but the numerical calculations (phase shifts, recoil spectra) use standard methods and tools (WimPyDD). The verdict should remain CONDITIONAL: the framework is sound and the mechanism is genuine, but the quantitative predictions rest on an unverified assumption about the size of the pion-nucleon couplings (and specifically g_A) that the paper acknowledges but does not resolve. The paper does not overclaim — it presents the benchmark as illustrative and explicitly defers systematic exploration — so the CONDITIONAL verdict with MODERATE confidence is appropriate.","tokens_in":27929,"tokens_out":10832,"duration_ms":326950,"concrete_test":"Verify the Goldberger-Treiman consistency at NLO: compute the NLO chiral correction to g_πNN = g_A m_n/f_π (1 + O(m_π²/Λ², g_A²)) for the benchmark parameters (g_A ≈ 0.015, m_π/m_n ≈ 0.006), and check whether the correction to ḡ_πNN from Eq. 2.4 remains below ~10%. If the NLO correction to the Goldberger-Treiman relation exceeds 10% for g_A ≈ 0.015, the leading-order derivation of the CP-violating coupling is unreliable, and both the self-interaction cross section in Fig. 1 and the EDM in Eq. 4.4 would need revision. This can be done analytically using standard NLO chiral perturbation theory results (e.g., Pich 1995, Ref. [30]).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader correctly identifies the perturbativity of g_πNN and ḡ_πNN as the weakest link, but the concern is slightly mischaracterized. The paper does not use perturbation theory for the self-scattering calculation — it solves the Schrödinger equation non-perturbatively via the variable-phase method (Eq. 3.5–3.6). The perturbativity assumption (stated in Sec. 2.2 and App. A) instead concerns the validity of the leading-order chiral Lagrangian derivation of the pion-nucleon couplings themselves: Eq. 2.4 (ḡ_πNN ∝ θ) and the Goldberger-Treiman relation g_πNN = g_A m_n / f_π. The benchmark has g_πNN = 0.11, which with f_π ~ √(N_c) m_n/(4π) implies g_A ≈ 0.015 — two orders of magnitude below the SM value of 1.27. The paper does not discuss whether such a small axial coupling is natural or achievable in a concrete SU(3) gauge theory with N_f = 2. While the chiral expansion itself is well-controlled (m_π/Λ ~ 0.006), the reliability of the leading-order Goldberger-Treiman relation when g_A is this small has not been verified. If NLO chiral corrections to the Goldberger-Treiman relation are large for small g_A, the derived value of ḡ_πNN (and hence both the self-interaction cross section and the EDM) could be shifted. The paper is appropriately cautious — it labels the benchmark as 'illustrative' and acknowledges that 'definitive conclusions beyond this regime are difficult to draw' — but the quantitative predictions for both SIDM and direct detection hinge on this unverified assumption.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"This paper studies the phenomenology of composite dark matter in a QCD-like confining dark sector with a non-vanishing topological angle $θ$. The central observation is that $θ$ induces CP-violating scalar pion–baryon couplings ($̄g_{πNN} ∝ θ$), which generate an attractive Yukawa potential between dark neutrons mediated by light dark pions. This simultaneously yields velocity-dependent self-interactions relevant for small-scale structure and, via a dark photon portal, induces a dark neutron electric dipole moment that enhances direct detection rates. The self-scattering cross section is computed non-perturbatively via the variable-phase method (Schrödinger equation), and the direct detection signal is matched onto the NREFT framework, with limits derived from LZ (2025) data. A benchmark point (Table 1) illustrates the simultaneous realization of SIDM phenomenology and observable direct detection. The chiral Lagrangian derivation of the CP-violating couplings is presented in Appendix A for $N_f = 2$ and generalized to arbitrary $N_f$ in Appendix B.","tokens_in":28951,"tokens_out":1463,"duration_ms":352140,"significance":"The paper presents a well-motivated and internally coherent framework in which a single parameter ($θ$) controls both dark matter self-interactions and direct detection rates, providing a concrete realization of the SIDM paradigm within a composite dark sector. The non-perturbative treatment of self-scattering via the variable-phase method (Eqs. 3.5–3.6) is a strength, as is the systematic NREFT matching for direct detection (Table 2) and the honest assessment of annual modulation prospects (Sec. 4.4). The EDM loop calculation (Eq. 4.4) correctly reproduces the SM neutron analogue. The generalization to arbitrary $N_f$ in Appendix B adds value. The framework is falsifiable through both astrophysical and laboratory observables. The main limitation is the reliance on leading-order chiral Lagrangian relations for the pion–nucleon couplings in a regime where the axial coupling $g_A$ is very small, which has not been independently verified.","major_comments":[{"comment":"Appendix A, Eq. (A.3): The Goldberger-Treiman relation gives $g_{πNN} = g_A m_n / f_π$. With the benchmark values $g_{πNN} = 0.11$, $m_n = 96.14$ GeV, and $f_π ∼ √{N_c} m_n/(4π)$ for $N_c = 3$, one infers $g_A ≈ 0.015$, which is two orders of magnitude below the SM value of 1.27. The paper does not discuss whether such a small axial coupling is natural or achievable in a concrete $SU(3)$ gauge theory with $N_f = 2$. While the chiral expansion parameter $m_π/Λ$ is well-controlled, the reliability of the leading-order Goldberger-Treiman relation when $g_A$ is this small has not been verified. If NLO chiral corrections to this relation are large for small $g_A$, the derived value of $̄g_{πNN}$ — and hence both the self-interaction cross section and the EDM — could be shifted. The authors should add a discussion of this point, including whether NLO corrections to the Goldberger-Treiman ratio","section":null},{"comment":"Sec. 2.2 and Appendix A: The perturbativity condition $g_{πNN}, ̄g_{πNN} ≲ √{4π}$ is stated, and the benchmark satisfies it ($g_{πNN} = 0.11$, $̄g_{πNN} = 0.35$). However, the paper acknowledges that the SM does not satisfy this condition ($g_{πNN} ≫ 1$). The concern is not about the self-scattering calculation (which is solved non-perturbatively via the Schrödinger equation), but about the validity of the leading-order chiral Lagrangian derivation of the couplings themselves. The paper should clarify more explicitly that the perturbativity assumption concerns the chiral Lagrangian derivation of Eqs. (2.4) and (A.3), not the scattering calculation, and discuss whether the benchmark point lies in a regime where this leading-order derivation is trustworthy.","section":null}],"minor_comments":[{"comment":"Table 1: The parameter $c$ (appearing in Eq. 2.4) is not listed. Given that $c = 0.7$ in the SM (footnote 1), it would be useful to state the value used for the benchmark explicitly.","section":null},{"comment":"Sec. 2.4, Eq. (2.8): The pion lifetime formula depends on $N_c$ and $e_d$. For the benchmark, $e_d = 1.0$ is used but not stated in Table 1; adding it would help reproducibility.","section":null},{"comment":"Sec. 3.1, Eq. (3.1): The tree-level cross section is expanded to $O(v^4)$, but the non-perturbative result in Eq. (3.6) is used for all subsequent results. A brief statement of the range of validity of Eq. (3.1) versus the full Schrödinger treatment would be useful.","section":null},{"comment":"Figure 1: The color scheme distinguishing the SIDM-favored regions (light blue, dark blue) and the cluster-excluded region could be clarified; the legend is small and difficult to read.","section":null},{"comment":"Sec. 4.4, Fig. 7: The y-axis labels show very small numerical values with limited significant figures (e.g., '6.2 × 10⁻³'). Consider using scientific notation more consistently or adjusting the axis scale.","section":null},{"comment":"Sec. 5: The statement that the benchmark is 'located close to the peak in Fig. 1, where the overlap between the two requirements is favorable' could be quantified — how sensitive are the conclusions to the exact choice of benchmark point within the overlap region?","section":null},{"comment":"Reference [88] (LZ 2025): The citation appears to be to a 2025 result; please confirm this is publicly available or appropriately cited at the production stage.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The reader's report and stress-test note correctly identify the small-$g_A$ issue as the main theoretical uncertainty. The paper is appropriately cautious — it labels the benchmark as 'illustrative' and acknowledges that 'definitive conclusions beyond this regime are difficult to draw.' The central qualitative claim (that $θ$ can simultaneously control self-interactions and direct detection) does not depend on the exact benchmark values. I recommend minor revision: the authors should add a short discussion of the small-$g_A$ issue and clarify the scope of the perturbativity assumption. The paper is well-suited for JHEP."},"author_rebuttal":{"model":"glm-5.2","summary":"We thank the referee for a careful reading and for identifying two important points regarding the reliability of the leading-order chiral Lagrangian relations. We address each comment below.","responses":[{"response":"We thank the referee for raising this important point, which we had not adequately addressed in the original manuscript. The referee's numerical inference is correct: the benchmark point implies g_A ≈ 0.015, which is indeed much smaller than the SM value of 1.27. We have thought carefully about whether this is problematic and conclude that it is a genuine caveat that must be stated explicitly, though it does not invalidate our framework. We address the two sub-questions separately. (1) Is a small g_A natural or achievable? The axial coupling g_A is a low-energy constant of the chiral Lagrangian that is not fixed by any symmetry of the SU(N_c) gauge theory with N_f = 2 vector-like fermions. In the SM, g_A ≈ 1.27 is an O(1) number, but there is no known symmetry argument or theorem requiring g_A to be O(1) in a generic confining gauge theory. Its value depends on non-perturbative strong dynamics and would need to be determined, e.g., by lattice calculations in the specific dark gauge theory. We are not aware of any mechanism that would make g_A parametrically small (in the way that, say, small quark masses make m_π parametrically small), so we cannot claim that g_A ≈ 0.015 is 'natural' in the technical sense. It is, however, not forbidden by any consistency condition. (2) Are NLO corrections to the Goldberger-Treiman relation enhanced for small g_A? This is the more substantive concern. At NLO in chiral perturbation theory, the Goldberger-Treiman discrepancy is Δ_GT = 1 − g_{πNN} f_π/(g_A m_N) = −2 m_π^2 d_18 / g_A, where d_18 is an NLO low-energy constant. The key observation is that Δ_GT is inversely proportional to g_A, so for g_A ≈ 0.015, even a modest value of d_18 could produce an O(1) correction to the LO Goldberger-Treiman relation. This would in turn shift the CP","revision_made":"partial","referee_comment":"Appendix A, Eq. (A.3): The Goldberger-Treiman relation gives g_{πNN} = g_A m_n / f_π. With the benchmark values g_{πNN} = 0.11, m_n = 96.14 GeV, and f_π ~ √{N_c} m_n/(4π) for N_c = 3, one infers g_A ≈ 0.015, which is two orders of magnitude below the SM value of 1.27. The paper does not discuss whether such a small axial coupling is natural or achievable in a concrete SU(3) gauge theory with N_f = 2. While the chiral expansion parameter m_π/Λ is well-controlled, the reliability of the leading-order Goldberger-Treiman relation when g_A is this small has not been verified. If NLO chiral corrections to this relation are large for small g_A, the derived value of ḡ_{πNN} — and hence both the self-interaction cross section and the EDM — could be shifted. The authors should add a discussion of this point, including whether NLO corrections to the Goldberger-Treiman ratio..."},{"response":"We agree that this distinction should be made more explicit in the manuscript. The perturbativity condition g_{πNN}, ḡ_{πNN} ≲ √(4π) ensures that the tree-level extraction of the pion–baryon couplings from the leading-order chiral Lagrangian (Eqs. (2.4) and (A.3)) is reliable — i.e., that higher-order terms in the chiral expansion of the Lagrangian do not generate comparable or larger corrections to these couplings. It is a separate condition from the non-perturbative treatment of the scattering problem, which is solved exactly via the Schrödinger equation using the variable-phase method. We will revise Sec. 2.2 and Appendix A to state this distinction clearly. Regarding the benchmark: with g_{πNN} = 0.11 and ḡ_{πNN} = 0.35, both couplings are well below √(4π) ≈ 3.5, so the LO chiral derivation of the couplings is internally consistent at the level of the perturbative expansion in the couplings. The chiral expansion parameter m_π^2/Λ^2 ~ (m_π/(4π f_π))^2 ~ 10^{-4} for the benchmark is also well-controlled. However, as discussed in our response to the first comment, the small implied value of g_A introduces a separate concern about NLO corrections to the Goldberger-Treiman relation that is not captured by the perturbativity condition on the couplings alone. We will add a sentence cross-referencing this caveat when the perturbativity condition is introduced.","revision_made":"yes","referee_comment":"Sec. 2.2 and Appendix A: The perturbativity condition g_{πNN}, ḡ_{πNN} ≲ √{4π} is stated, and the benchmark satisfies it (g_{πNN} = 0.11, ḡ_{πNN} = 0.35). However, the paper acknowledges that the SM does not satisfy this condition (g_{πNN} ≫ 1). The concern is not about the self-scattering calculation (which is solved non-perturbatively via the Schrödinger equation), but about the validity of the leading-order chiral Lagrangian derivation of the couplings themselves. The paper should clarify more explicitly that the perturbativity assumption concerns the chiral Lagrangian derivation of Eqs. (2.4) and (A.3), not the scattering calculation, and discuss whether the benchmark point lies in a regime where this leading-order derivation is trustworthy."}],"tokens_in":27889,"tokens_out":2666,"duration_ms":143388,"standing_objections":["The naturalness of the small axial coupling g_A ≈ 0.015 implied by the benchmark point cannot be definitively assessed without non-perturbative input (e.g., lattice calculations) in the specific dark gauge theory. While no symmetry forbids a small g_A, we are not aware of a mechanism that would make it parametrically small, and the NLO Goldberger-Treiman discrepancy Δ_GT ∝ 1/g_A could be enhanced. This is an inherent limitation of the leading-order chiral analysis that we cannot fully resolve at present."]},"desk_editor":{"model":"glm-5.2","letter":"The main thing to know: this paper shows that a topological θ angle in a confining dark sector induces CP-violating pion-baryon couplings that simultaneously produce velocity-dependent self-interactions (SIDM) and a dark neutron EDM detectable via dark-photon portal. Both phenomena trace to the same θ. The qualitative mechanism is genuinely new and well-motivated — the light mediator arises naturally as a pseudo-Goldstone boson rather than being inserted by hand, and the CP-violating coupling is derived from chiral Lagrangian, not fitted to phenomenology. The self-scattering calculation is done properly: they solve the Schrödinger equation non-perturbatively via the variable-phase method rather than relying on Born approximation. The EDM loop result (Eq. 4.4) matches the known SM neutron analogue, and the NREFT matching for direct detection is standard and correctly executed. The annual modulation discussion, while ultimately pessimistic about experimental reach, is a thoughtful addition. The generalization to arbitrary N_f in Appendix B is nontrivial and extends the framework beyond the QCD-inspired benchmark. The soft spot is the perturbativity assumption on the pion-nucleon couplings, and the stress-test note correctly refines what the reader flagged. The concern is not about the scattering calculation (which is non-perturbative) but about whether the leading-order chiral Lagrangian derivation of the couplings themselves is reliable. The benchmark has g_πNN = 0.11, which via the Goldberger-Treiman relation and f_π ~ √(N_c) m_n/(4π) implies g_A ≈ 0.015 — two orders of magnitude below the SM value. The paper does not discuss whether such a small axial coupling is natural in a concrete SU(3) gauge theory, nor whether NLO chiral corrections to Goldberger-Treiman become large when g_A is this small. If they do, both the self-interaction cross section and the EDM could shift. The paper is appropriately cautious — it labels the benchmark illustrative and flags the limitation explicitly — but the quantitative predictions do rest on this unverified assumption. The form factors b_n and μ_n are also estimated dimensionally rather than computed, which is standard for this kind of work but adds a second layer of uncertainty to the direct detection rates. These are real but proportionate concerns. The qualitative story — θ induces CP-violating couplings that naturally realize SIDM and enhance direct detection — does not depend on the precise numbers. This paper is for theorists working on composite dark matter, SIDM, or dark-sector CP violation. It deserves a serious referee who can assess the chiral Lagrangian derivation and the NREFT matching. I'd recommend peer review.","headline":"Clean idea linking dark-sector θ to both SIDM and direct detection; quantitative claims hinge on an untested chiral regime","tokens_in":28905,"tokens_out":637,"would_cite":true,"duration_ms":90738,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"One dark angle controls both halo collisions and detector signals","keywords":["self-interacting dark matter","composite dark matter","CP violation","dark photon","direct detection","dark pion","topological angle","electric dipole moment"],"falsifier":"If lattice QCD calculations for the CP-violating pion-baryon coupling in the relevant parameter regime show that the perturbative Yukawa potential analysis substantially overestimates or mischaracterizes the self-scattering cross section, or if the dark neutron electric dipole moment induced by θ differs significantly from the one-loop estimate, the quantitative link between halo self-interactions and direct detection rates would break down. Additionally, if future direct detection experiments exclude the benchmark parameter space (dark neutron mass ~100 GeV, kinetic mixing ε ~ 10⁻⁵) without a","tokens_in":28202,"feed_emoji":"🔧","tokens_out":1348,"duration_ms":235976,"temperature":0.7,"pith_summary":"This paper argues that a single parameter — the topological angle θ in a confining dark sector — can simultaneously generate the velocity-dependent self-interactions needed to address small-scale structure problems and the electric dipole moments that enhance direct detection rates. In a QCD-like dark sector with dark neutrons as dark matter, a nonzero θ induces CP-violating couplings between dark pions and dark baryons. These couplings produce an attractive Yukawa potential mediated by the naturally light dark pions, yielding self-scattering cross sections in the range relevant for self-interacting dark matter (0.1–100 cm²/g at dwarf-galaxy velocities, dropping below cluster bounds). The same θ also generates a calculable dark neutron electric dipole moment that, through a dark photon portal, dominates direct detection recoil rates and can be distinguished from CP-conserving magnetic dipole interactions by its distinct annual modulation pattern. The paper presents a benchmark point (dark neutron mass ~96 GeV, dark pion mass ~558 MeV, dark photon mass ~150 MeV) where both phenomena are simultaneously realized and consistent with cosmological, astrophysical, and laboratory constraints.","feed_headline":"One dark angle controls both halo collisions and detector signals","feed_subtitle":"A single CP-violating parameter in a QCD-like dark sector generates both the self-interactions that shape galactic halos and the electric d","key_machinery":"The topological angle θ; the CP-violating scalar pion-baryon coupling ḡ_πNN ∝ θ; the Yukawa potential V(r) ∝ -ḡ²_πNN e^{-m_π r}/(4πr); the dark neutron electric dipole moment d_n ≃ (e_d/2m_n)(g_πNN ḡ_πNN/2π²) log(m_n/m_π±); the dark photon portal with kinetic mixing ε connecting dark and visible sectors","core_discovery":"The central mechanism is that the topological angle θ in a confining dark sector induces a scalar pion-baryon coupling ḡ_πNN proportional to θ (Eq. 2.4), which is qualitatively different from the ordinary pseudoscalar coupling g_πNN. The scalar coupling generates an attractive long-range Yukawa potential V(r) = -ḡ²_πNN/(4π) · e^{-m_π r}/r (Eq. 3.2) that is not velocity-suppressed, unlike the CP-conserving interaction which gives cross sections suppressed by v⁴. This same θ simultaneously induces a dark neutron electric dipole moment d_n ∝ θ (Eq. 4.4) through loop diagrams involving the CP-violating pion coupling. The paper shows that both the self-interaction cross sections relevant for halo","pith_inferences":["If lattice calculations of the CP-violating pion-baryon coupling in the non-perturbative regime (where g_πNN ≳ 1, as in Standard Model QCD) confirm that the Yukawa potential structure persists with enhanced strength, the viable parameter space for simultaneously achieving SIDM phenomenology and detectable direct detection signals could be significantly broader than the perturbative benchmark sugge","The correlation between self-interaction cross sections and direct detection rates through the single parameter θ implies that null results from direct detection experiments can be translated into upper bounds on dark matter self-interactions in this framework, and conversely, astrophysical measurements of halo core densities can constrain the direct detection signal strength.","If future dark photon searches (beam-dump, fixed-target) probe the kinetic mixing parameter space below the current bounds used in the benchmark, the direct detection signal could be tested independently of dark matter recoil experiments, providing a complementary probe of the same dark sector parameters."],"forward_implications":["If θ is the common origin for both halo self-interactions and direct detection signals, a future detection of a dark neutron EDM-like recoil spectrum would imply a specific prediction for the dark matter self-interaction cross section in halos, and vice versa, making the two observables correlated rather than independent.","The annual modulation phase reversal between the EDM operator O_11 and the magnetic dipole operator O_5 provides a potential experimental discriminant for the CP-violating origin of a direct detection signal, though the paper notes this would require roughly 100× more events than detecting the time-averaged rate.","The framework naturally accommodates gravothermal collapse regimes (σ/m ~ 100 cm²/g at low velocities), connecting to recent observations of unusually compact dark matter halos.","The CP-violating dynamics from θ could itself play a role in generating the primordial dark matter asymmetry, potentially linking the relic abundance mechanism to the same parameter governing halo physics and direct detection."],"fun_headline_variants":["Dark sector θ angle drives both halo dynamics and direct detection signals","CP-violating θ term in a QCD-like dark sector generates long-range self-interactions and d","Composite dark matter phenomenology governed by a single CP-violating topological angle θ"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The perturbative assumption that the pion-nucleon couplings g_πNN and ḡ_πNN are sufficiently small (roughly below √(4π)) to justify computing self-scattering cross sections using perturbation theory. The benchmark uses ḡ_πNN = 0.35, but the paper acknowledges that Standard Model QCD does not satisfy this condition (g_πNN is much larger than 1), so the quantitative predictions for both self-interaction cross sections and direct detection rates could be different if the non-pet","fun_headline_variants_meta":{"raw":{"variants":["Dark sector θ angle drives both halo dynamics and direct detection signals","CP-violating θ term in a QCD-like dark sector generates long-range self-interactions and dipole-mediated detection signals","Composite dark matter phenomenology governed by a single CP-violating topological angle θ"]},"model":"glm-5.2","effort":"low","cost_usd":0.0,"raw_usage":{"total_tokens":736,"prompt_tokens":677,"completion_tokens":59,"prompt_tokens_details":null},"tokens_in":677,"tokens_out":59,"duration_ms":46958,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T11:44:34.125858+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"If lattice QCD calculations for the CP-violating pion-baryon coupling in the relevant parameter regime show that the perturbative Yukawa potential analysis substantially overestimates or mischaracterizes the self-scattering cross section, or if the dark neutron electric dipole moment induced by θ differs significantly from the one-loop estimate, the quantitative link between halo self-interactions and direct detection rates would break down. Additionally, if future direct detection experiments exclude the benchmark parameter space (dark neutron mass ~100 GeV, kinetic mixing ε ~ 10⁻⁵) without a","supporting_citations":[],"review_version":1}