{"id":"0500d10a-6c79-46bb-9bfa-f88f89ed4f8b","arxiv_id":"2610.07498","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A near-horizon large-U(1) Ward identity gives a soft-photon relation for static spherical horizons in D>3 that agrees with the flat-space leading soft theorem in D=4 and differs in D>4.","lead":"Soft-light rules near black hole horizons are derived for any spacetime dimension above three, starting from charges on the horizon rather than at infinity. The result matches the known flat-space soft-photon rule in four dimensions and shows extra frequency and angular factors in higher dimensions.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"The horizon soft theorem rests on an unproven S-matrix Ward identity in (4.28): asymptotic large-U(1) charge conservation from H- to H+ is asserted following [4,28], not proven, and the charge is sensitive to gauge- and vacuum-dependent modes; the load-bearing failure mode is that the central…","rationale":"The reader identified the same weakest assumption: exact symmetry preservation by the horizon S-matrix and bifurcation regularity. The paper's own text acknowledges the S-matrix assumption in the paragraph after Eq. (4.27) and the bifurcation-regularity requirement in Section 3.2. I see no internal inconsistency in the mode expansion, symplectic form, or harmonic counting; those steps are internally consistent as far as the algebra goes. The soft relation (4.34) is derived from (4.28) only after injecting a strong unproven input. The paper does not claim to prove the Ward identity; it states it as an assumption. Thus the correct publication posture is CONDITIONAL: the formal result is plausible, but its range of validity is exactly the unproven assumption. The comparison with flat space (Appendix A) is sound as a rewriting of the known theorem and does not remedy the horizon input. Hence the load-bearing attack is the missing proof of the diagonal large-U(1) S-matrix preservation, and the concrete test is an independent check on a concrete background. No claim of fraud or dishonesty; the issue is mathematical support, not misconduct.","tokens_in":23600,"tokens_out":1883,"duration_ms":11083,"concrete_test":"As the challenge is conceptual, the concrete test is an independent re-derivation: starting from the covariant phase space of the full theory with no gauge-fixed 'horizon modes', and applying the charge (2.40) to a finite-ω scattering process computed explicitly on a Schwarzschild–Tangherlini background in D=4, verify whether the matrix element <out|[QS,out S - S QS,in]|in> vanishes as ω→0 without additional assumptions. If it does not vanish for generic in/out states (e.g., a two-point amplitude with a soft photon), the Ward identity (4.28) has no general validity and Eq. (4.34) is not a universal soft theorem. Alternatively, compute the same charge flux through the bifurcation sphere using the time-reflected modes of §4.2 and check whether the diagonal charge is conserved off-shell; a nonzero flux invalidates the relation.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central derivation is the conversion of the diagonal large-U(1) Ward identity, Eq. (4.28), into the soft-photon relation (4.34). The paper states the key input as: '... assume that scattering from H- to H+ preserves this symmetry, with no charge flux through other boundary components' (paragraph between Eq. (4.22) and (4.23), and again before (4.28)). This is an input assumption, not a derived statement. In particular, the large-U(1) charge (2.40)-(2.44) is gauge-variant: it is constructed on Av=0 radial gauge with ε=ε(x), and the soft charge (4.23) is defined from the horizon modes (4.8)-(4.9), which are themselves gauge- and vacuum-dependent (positive-Killing-frequency vacuum (4.18), scalar sector only). The identity (4.28) requires the S-matrix to preserve the diagonal soft and hard charges separately on the in/out states; if the horizon S-matrix does not map the diagonal charge algebra onto itself, the identity fails and (4.34) does not follow. The paper cites [4,28] for this step, but those works do not establish the horizon version; the same input is a standing limitation spelled out in the text itself ('Assuming that the diagonal large-U(1) symmetry is preserved by the S-matrix, as in [4,28], the corresponding Ward identity is...'). The bifurcation-regularity issue flagged by the reader (Section 3.2, 'Extension to B additionally requires regularity in V=e^{κv} as V→0') compounds this: the positive-Killing-frequency modes e^{-iωv} used in (4.8)-(4.9) and the vacuum (4.18) are not shown to satisfy the regularity requirement, which is needed for the matching of the diagonal charge across B.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"The paper studies source-free Maxwell theory, coupled to a charged complex scalar for the hard sector, near a nonextremal bifurcate Killing horizon in a static, spherically symmetric spacetime of dimension D>3. Working in a regular Eddington–Finkelstein chart with radial gauge, it imposes near-horizon falloffs that retain both radiative angular data and a Coulombic charge aspect, and solves the Maxwell equations as a characteristic hierarchy in ρ=r−r_H (Section 2). It then constructs the covariant horizon phase space, the radiative brackets, and the large-U(1) charge split into soft and hard parts. Expanding in Killing frequency and spherical harmonics and quantizing via the horizon symplectic form, it derives a soft-photon relation from the diagonal large-U(1) Ward identity: Eq. (4.34) and its position-space form (4.36). The flat-space leading soft-photon theorem is re-expressed in the same spherical-mode basis (Appendix A) and compared: in D=4 both relations carry the same soft-frequency weight and the same angular hard-charge dependence, while for D>4 the flat-space relation contains an additional ω^{(6−D)/2} weight and a Γ(ℓ+1)/Γ(ℓ+D−3) angular factor.","tokens_in":24098,"tokens_out":8443,"duration_ms":49983,"significance":"If the central relation (4.34) holds, every nonextremal static spherical horizon in D>3 carries the soft-photon relation, and the D=4 matching with the flat-space theorem is a genuine, falsifiable check of the frequency and angular structure. The construction is explicit and internally consistent: the characteristic hierarchy (2.20)–(2.29), the recursive radial expansion (3.46)–(3.48) establishing integer-power horizon radiation in every D>3, the extended phase-space brackets (2.45)–(2.47), and the mode normalization (4.15)–(4.20) are all spelt out, with no free parameters or fitted constants. The Appendix A conversion, including the commutator normalization (A.20) that matches (4.17), is a useful standalone contribution, and the paper's repeated statement that the comparison does not identify the horizon and null-infinity scattering problems is appropriately hedged. The paper is honest about what is assumed; the remaining question is how much of that assumption is load-bearing.","major_comments":[{"comment":"The central derivation of the soft relation (4.34)–(4.36) rests entirely on the assumption that scattering from H− to H+ preserves the diagonal large-U(1) charge with no flux through other boundary components. The paper acknowledges this in its wording ('Assuming that the diagonal large-U(1) symmetry is preserved by the S-matrix, as in [4,28]'), so the conditional status is not hidden; however, the point is load-bearing, because without (4.28) the soft theorem does not follow. The cited works [4] and [28] establish the flat-space QED and Schwarzschild-soft-hair versions, not the generic static spherical horizon in D>3 treated here, and the charge (4.23) in play is constructed in a specific radial-gauge, positive-Killing-frequency vacuum. In particular, 'no flux through other boundaries' is nontrivial for asymptotically flat or AdS black holes, whose diagonal large-U(1) charge generically flows to null infinity. I recommend that the authors either supply an argument for the preservation (for instance from classical conservation of Qε together with an explicit vanishing of flux through B and the future endpoint) or, failing that, state prominently that (4.34) is conditional on this symmetry-preservation input and discuss what changes if the other-boundary flux is nonzero.","section":"Section 4.2, Eq. (4.28)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The treatment of the bifurcation sphere is incomplete. The paper states that extension to B additionally requires regularity in V=e^{κv} as V→0 (sentence b119, end of Section 3.2), but the modes (4.8)–(4.9) and the vacuum (4.18) are built from positive-Killing-frequency exponentials e^{−iωv}, and no argument is given that these satisfy the stated V-regularity. This is not a cosmetic point: the matching condition (2.35), the charge at B (2.41), and the soft-charge definition (4.23) all run through B, so the Ward identity (4.28) is only well posed if the diagonal charge can be transported across B. Positive-Killing-frequency modes of this type are not smooth in Kruskal-type coordinates at B for generic real ω, so the derivation's treatment of B appears to be formal as it stands. The authors should either demonstrate the required regularity of the modes they use, or explicitly state that the matching across B is an input assumption rather than a derived property.","section":"Sections 3.2 and 4.1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The crossed form of the soft insertion, ω( bA^{S,out}_{ωℓm} S + S bA^{S,in†}_{ωℓm} ), involves a phase and antipodal-matching convention for the incoming branch that is asserted rather than derived ('we choose the incoming modes with the same horizon normalization as on H+'; the incoming radial profiles are stated to be complex conjugates of the outgoing ones). For the flat-space case the analogous crossing is discussed in Appendix A (A.22), but for the horizon case the convention is stated without the corresponding derivation. Since the sign and phase of the second term in (4.31) determine the right-hand side of (4.34), this convention should be spelled out more explicitly, or a short justification analogous to Appendix A should be added.","section":"Equations (4.31)–(4.34)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The two panels show the two horizon orientations, but the '+/-' labels on the H± branches are redundant with the captions and the way they are typeset is easy to misread; please clarify which branch is past and which is future in each panel.","section":"Figure 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The position-space form (4.36) would read more cleanly if the sentence immediately following it stated explicitly that the ℓ=0 sector is handled by total charge conservation (4.30) and that no soft insertion is generated for constant ε; this fact is present in the text but is worth highlighting next to (4.36).","section":"Section 4.2, after Eq. (4.36)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The symbol c^I_ℓ is defined at (4.16) for the horizon modes and reused at (A.20) for the flat-space spherical modes without a forward cross-reference; adding a pointer at (A.20) to (4.16) would help the reader verify that the two normalizations agree by construction.","section":"Notation (4.16) and (A.20)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Reference [47] is listed only by arXiv id 2609.39288 with no indication of journal status or publication date; please state the status, as the paper relies on it for the local Ward-identity context.","section":"Reference list","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The paper is technically sound in its construction and unusually honest: it states both key assumptions (the S-matrix symmetry preservation before (4.28) and the B-regularity requirement in Section 3.2) rather than hiding them. The question for the editor is whether the field's standard practice of assuming large-gauge symmetry preservation by the S-matrix suffices here. I lean toward requiring the authors to do a bit more: the generic-D statement is the paper's main selling point, and its two unproven inputs are precisely what the soft-hair literature often leaves implicit. If the authors add an explicit conditional framing and address the B-regularity of their modes, the paper would be close to acceptable. The self-citations (the author's own [44,45,46]) are used substantively and appropriately, and I see no novelty-disclosure problem."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"Two things to know. First, the genuinely new result is Eq. (4.34): a generic-D>3 horizon Maxwell soft-photon relation derived from the diagonal large-U(1) Ward identity, with the flat-space leading soft theorem rewritten in the same spherical basis, so the D=4 agreement and the D>4 differences are comparisons of like with like. The D>4 discrepancy is honest — the omega^{(6-D)/2} and Gamma(l+1)/Gamma(l+D-3) factors are worked out in Appendix A from the Funk–Hecke integral, and the paper explains the frequency weight as a boundary-coefficient conversion, not a change in the 1/omega pole. Second, the caveat to carry with you when you cite it: the result rests on an input assumption, and the paper says so in the text ('Assuming that the diagonal large-U(1) symmetry is preserved by the S-matrix, as in [4,28]...' before (4.28)). At a horizon this is not a theorem the way it is at null infinity, and no independent justification is supplied.\n\nWhat the paper does well: the characteristic hierarchy in Sec. 2 is explicit and internally consistent — news, electric charge aspect, horizon Gauss law, and a phase space with the correct endpoint zero-mode term for the soft charge (2.47). The near-horizon integer-power expansion in every D>3, contrasted with the half-integer branches at odd-D null infinity, is a clean observation. The D=4 matching is a real sanity check, and the author repeatedly declines to overclaim: he states three times that the comparison does not identify the horizon and null-infinity scattering problems.\n\nSoft spots, in proportion. The S-matrix Ward identity is the hinge, and it is asserted, not proved. The charge (2.40)-(2.44) is gauge- and vacuum-dependent, so 'the S-matrix preserves the diagonal charge' is a dynamical condition, not a kinematical identity. Second, Sec. 3.2 states that extension to the bifurcation sphere B requires regularity in V=e^{kappa v} as V->0 (the sentence after (3.48)), but the positive-Killing-frequency modes e^{-i omega v} in (4.8)-(4.9) and the vacuum (4.18) are not checked against that requirement. If it fails, the diagonal-charge matching across B slides and (4.34) loses its standing. These are the standard soft-hair caveats rather than fresh defects, but here they carry the whole derivation, so they deserve referee pressure. Minor: [47] (Zhuge–Cheng, near-horizon soft theorems from local Ward identities) is cited but not discussed; it is nearly simultaneous with this posting, so the omission is defensible, but the author should be asked to comment in revision.\n\nWho it is for: the soft-theorem and IR-structure community, and the soft-hair program specifically. Clean, self-contained, no free parameters, no circularity — the flat-space theorem is an external benchmark and the derivation is not fitted to it. It deserves a serious referee: worth engaging, provided the B-regularity and the S-matrix assumption are pressed.","headline":"A careful, honest derivation of a generic-D horizon Maxwell soft-photon relation with a genuine spherical-basis comparison to flat space; the D=4 check passes, and the acknowledged S-matrix Ward-identity assumption plus an unverified B-regularity condition are the load-bearing caveats a referee must probe.","tokens_in":24624,"tokens_out":4177,"would_cite":true,"duration_ms":26595,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek/deepseek-v4-flash","headline":"This paper derives a soft-photon relation at any nonextremal static spherical horizon in D>3 dimensions and shows it matches the flat-space theorem only in D=4.","keywords":["soft photon theorem","large gauge symmetry","Ward identity","black hole horizon","higher dimensions","Maxwell theory","Eddington-Finkelstein coordinates","infrared structure"],"falsifier":"One concrete check is whether the positive-frequency modes (4.8)–(4.9) and the vacuum (4.18) actually satisfy the bifurcation-sphere regularity condition in $V=e^{\\kappa v}$ as $V\\to 0$, which the paper states but does not verify; if they fail, the vacuum is not an admissible state and the Ward identity lacks standing. A second check is to compute a concrete horizon scattering amplitude, for instance charged massless scalars scattering on a Schwarzschild–Tangherlini horizon, and read off the $\\omega\\to 0$ residue of the soft insertion to see whether its coefficient matches $ig_D^2\\pi^{-1}r_H^{-(D-4)/2}$ and whether the large-$U(1)$ charge is in fact conserved across the two horizon branches.","tokens_in":27070,"feed_emoji":"⚡","tokens_out":4369,"duration_ms":57222,"temperature":0.7,"pith_summary":"This paper sets out to show that Maxwell theory near any nonextremal static spherical horizon — a Schwarzschild–Tangherlini or Reissner–Nordström black hole, their asymptotically AdS counterparts, or a de Sitter cosmological horizon — in dimension $D>3$ obeys a soft-photon theorem of the same large-gauge-symmetry type as flat space, and to compare the two relations in a common basis. It first establishes that regular near-horizon boundary conditions in Eddington–Finkelstein coordinates keep both radiative and Coulombic data, so a smooth horizon supports Maxwell radiation with an ordinary integer-power radial expansion in every dimension, in contrast to null infinity where odd $D$ forces half-integer powers. It then quantizes the horizon modes with normalization fixed by the horizon symplectic form and derives the soft relation from the diagonal large-$U(1)$ Ward identity. The result is that in $D=4$ the horizon and flat-space soft relations have the same soft-frequency dependence and the same angular dependence of the hard-charge terms, while for $D>4$ the flat-space relation carries an extra frequency weight and an $\\ell$-dependent angular factor that the horizon relation lacks.","feed_headline":"Horizon soft-photon law holds in every dimension D>3","feed_subtitle":"A Ward-identity derivation: horizons and flat space agree in D=4 but split apart for D>4.","key_machinery":"The load-bearing object is the diagonal large-$U(1)$ charge built from the near-horizon covariant phase space: the horizon symplectic form fixes the commutators of Killing-frequency spherical-harmonic modes, and the charge separates into a soft part (an integrated gradient of the Maxwell news) and a hard part (charged matter on the horizon). The soft-photon relation is exactly the Ward identity of this charge, obtained by assuming the horizon $S$-matrix preserves the diagonal charge with no flux through other boundaries. A second piece of machinery is the regular Eddington–Finkelstein near-horizon expansion in integer powers of $\\rho = r-r_H$, which turns the Maxwell equations into a characteristic hierarchy and shows that a smooth horizon supports radiative data, with nonzero news and finite flux density, in every dimension $D>3$ with no even–odd distinction.","core_discovery":"The central claim is Eqs. (4.34)–(4.36): for each scalar harmonic $\\ell\\ge 1$, $\\lim_{\\omega\\to 0^+}\\omega\\,\\langle\\mathrm{out}|\\,bA^{S,\\mathrm{out}}_{\\omega\\ell m}S + S\\,bA^{S,\\mathrm{in}\\,\\dagger}_{\\omega\\ell m}\\,|\\mathrm{in}\\rangle = \\frac{i g_D^2}{\\pi r_H^{(D-4)/2}}\\left[\\sum_{j\\in\\mathrm{out}}q_j Y_{\\ell m}(x_j) - \\sum_{k\\in\\mathrm{in}}q_k Y_{\\ell m}(x_k)\\right]\\mathcal{M}$, whose position-space form localizes the soft insertion on the horizon sphere at the angular positions of the hard charged particles. If correct, every nonextremal static spherical horizon in $D>3$ carries a soft-photon relation derived purely from the diagonal large-$U(1)$ Ward identity. The paper's central comparison then shows that in $D=4$ this horizon relation has the same soft-frequency dependence and the same angular dependence of the hard-charge terms as the flat-space leading soft-photon theorem written in the same spherical-harmonic basis and commutator normalization, while for $D>4$ the flat-space relation carries an extra frequency weight $\\omega^{(6-D)/2}$ and an angular factor $\\Gamma(\\ell+1)/\\Gamma(\\ell+D-3)$ that are absent from the horizon relation.","pith_inferences":["A testable extension of the paper's logic: the explicit $D>4$ discrepancy between the horizon and flat-space soft relations could serve as a diagnostic for whether a soft photon in a higher-dimensional spacetime was emitted from a horizon or from a bulk scattering process, since the two carry different soft-frequency weights.","If the gravitational analogue, which the paper flags as natural next work, reproduces the same dimensional dichotomy, the $D=4$ versus $D>4$ split would become a robust organizing fact about soft behaviour at horizons rather than a peculiarity of Maxwell theory.","The bifurcation-sphere regularity gap in the argument suggests the honest way to complete it is a concrete construction of the horizon vacuum that is manifestly regular in $V=e^{\\kappa v}$, which would also settle whether the positive-Killing-frequency sector is the physically correct one.","The paper's D=4 agreement, read together with its own disclaimer that the two scattering problems are not identified, hints that the leading soft structure itself, not the dynamics, is what is shared between horizon and flat-space cases in four dimensions."],"forward_implications":["If the central claim holds, any nonextremal static spherical horizon in $D>3$ — black hole, AdS, or de Sitter — emits soft photons according to one and the same relation, depending on the horizon radius $r_H$ and on the angular positions and charges of the hard particles alone.","In $D=4$, the horizon soft relation and the flat-space leading soft-photon theorem coincide in their soft-frequency and angular content, so the leading soft behaviour of the two scattering problems agrees in that dimension.","For $D>4$ the two differ explicitly, by the frequency weight $\\omega^{(6-D)/2}$ and the angular factor $\\Gamma(\\ell+1)/\\Gamma(\\ell+D-3)$, and these differences cannot be absorbed into an overall normalization, making the dimensional split observable in principle.","The integer-power radial expansion of radiative data at a smooth horizon in every dimension, versus half-integer powers at odd-$D$ null infinity, shows the half-integer structure at null infinity is an asymptotic artifact rather than a generic requirement for radiation."],"supporting_citations":[{"why":"Supplies the diagonal large-U(1) Ward identity method and the assumption that the S-matrix preserves the charge.","marker":"[4]"},{"why":"Supplies the soft-hair horizon implementation of large gauge symmetry that the paper extends to generic static spherical horizons.","marker":"[28]"},{"why":"Supplies the covariant phase space construction and the soft-charge normalization and endpoint-mode conventions used on the horizon.","marker":"[13]"},{"why":"Supplies the flat-space higher-dimensional soft-photon theorem including the finite-frequency weight whose crossing produces the omega^{(6-D)/2} factor.","marker":"[51]"},{"why":"The D=4 curved-spacetime soft-photon precedent that this work generalizes to generic dimensions.","marker":"[42]"},{"why":"The de Sitter horizon soft-photon precedent extended here to generic static spherical horizons.","marker":"[44]"},{"why":"The original flat-space soft-photon theorem whose spherical-mode form is derived in Appendix A for the comparison.","marker":"[1]"}],"fun_headline_variants":["Horizon soft-photon law extends to all dimensions D>3","Static horizon soft theorems hold for D>3, match flat space only in D=4","Large-U(1) Ward identity yields horizon soft-photon law in D>3","Soft photons at spherical horizons: D=4 matches flat space, D>4 splits"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The derivation rests on two unproven premises: that the positive-Killing-frequency vacuum and modes used in the quantization are regular at the bifurcation sphere, and that the horizon S-matrix preserves the diagonal large-U(1) charge with no charge flux through other boundaries.","fun_headline_variants_meta":{"raw":{"variants":["Horizon soft-photon law extends to all dimensions D>3","Static horizon soft theorems hold for D>3, match flat space only in D=4","Large-U(1) Ward identity yields horizon soft-photon law in D>3","Soft photons at spherical horizons: D=4 matches flat space, D>4 splits"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000165,"raw_usage":{"cost":0.000164668,"is_byok":false,"cost_details":{"upstream_inference_cost":0.000164668,"upstream_inference_prompt_cost":0.000118748,"upstream_inference_completions_cost":4.592e-05},"total_tokens":1217,"prompt_tokens":1053,"completion_tokens":164,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":256,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":73}},"tokens_in":1053,"tokens_out":164,"cost_source":"openrouter_usage","duration_ms":2147,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":73,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-07T02:27:14.238706+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"One concrete check is whether the positive-frequency modes (4.8)–(4.9) and the vacuum (4.18) actually satisfy the bifurcation-sphere regularity condition in $V=e^{\\kappa v}$ as $V\\to 0$, which the paper states but does not verify; if they fail, the vacuum is not an admissible state and the Ward identity lacks standing. A second check is to compute a concrete horizon scattering amplitude, for instance charged massless scalars scattering on a Schwarzschild–Tangherlini horizon, and read off the $\\omega\\to 0$ residue of the soft insertion to see whether its coefficient matches $ig_D^2\\pi^{-1}r_H^{-(D-4)/2}$ and whether the large-$U(1)$ charge is in fact conserved across the two horizon branches.","supporting_citations":[{"cited_title":"New symmetries of massless QED","cited_arxiv_id":"1407.3789","evidence_quote":"Supplies the diagonal large-U(1) Ward identity method and the assumption that the S-matrix preserves the charge."},{"cited_title":"Soft Hair on Black Holes","cited_arxiv_id":"1601.00921","evidence_quote":"Supplies the soft-hair horizon implementation of large gauge symmetry that the paper extends to generic static spherical horizons."},{"cited_title":"Lectures on the Infrared Structure of Gravity and Gauge Theory","cited_arxiv_id":"1703.05448","evidence_quote":"Supplies the covariant phase space construction and the soft-charge normalization and endpoint-mode conventions used on the horizon."},{"cited_title":"Asymptotic Symmetries and Weinberg's Soft Photon Theorem in Mink$_{d+2}$","cited_arxiv_id":"1903.02608","evidence_quote":"Supplies the flat-space higher-dimensional soft-photon theorem including the finite-frequency weight whose crossing produces the omega^{(6-D)/2} factor."},{"cited_title":"Soft theorems in curved spacetime","cited_arxiv_id":"2206.11564","evidence_quote":"The D=4 curved-spacetime soft-photon precedent that this work generalizes to generic dimensions."},{"cited_title":"Soft theorems in de Sitter spacetime","cited_arxiv_id":"2308.08861","evidence_quote":"The de Sitter horizon soft-photon precedent extended here to generic static spherical horizons."},{"cited_title":"Weinberg,Infrared photons and gravitons,Phys","cited_arxiv_id":null,"evidence_quote":"The original flat-space soft-photon theorem whose spherical-mode form is derived in Appendix A for the comparison."}],"review_version":1}