{"id":"91c461a0-9ad8-4ad4-acf5-5657519984b8","arxiv_id":"2610.40263","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A velocity-projected spinor-helicity formalism for heavy particles yields three-point and Compton amplitudes with explicit 1/m power counting, and minimal gravitational coupling matches Kerr spin multipoles at finite spin.","lead":"A new calculation method for very heavy spinning particles projects the particle's spin variables onto a fixed reference direction, making the heavy-mass expansion simpler. The paper uses this method to construct gravitational scattering amplitudes and shows they match the known spin structure of a Kerr black hole.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"Classical Compton claim hinges on whether the undetermined terms are truly local: the w-term in Eq. (5.27) carries the spurious pole ⌈3˜2⌋^{-1}, so a direct comparison with Ref. [31] is needed to confirm the difference is contact-like rather than nonlocal.","rationale":"The reader's weakest assumption identifies the correct locus: the classical Kerr Compton statement is conditional on contact terms that factorization does not fix. My concern sharpens this: the unclassified terms may not be contact-like at all, because the w-term in Eqs. (5.16) and (5.27) already contains the spurious pole 1/⌈3˜2⌋. For finite spin, the paper consistently removes such poles only to sub-leading order in 1/m, and the classical resummation promotes w into an exponent where the pole structure is not controlled for generic kinematics. Thus the open question is not merely 'do contact terms contribute at the same order' but 'is the difference with the known Kerr amplitude local.' That is exactly what comparing Eq. (5.27) with Ref. [31] would settle. I did not elevate the imported foundations from Refs. [63] and [69] to primary status: the computed three- and four-point amplitudes use the free-field equation of motion Eq. (3.12) rather than the general integrate-out function F of Eq. (3.27), and the Young-tableau basis in Appendix C supports the operator dictionary but is not the engine of the Compton bootstrap. I also found no internal contradiction in the bottom-up/top-down match, the scalar limits, or the multipole matching C_S^n = 1; the conditional verdict already captures the residual risk. Because the reader's verdict is conditional and my concern only specifies a sharper test within that conditionality, I recommend no change in verdict.","tokens_in":51301,"tokens_out":10633,"duration_ms":91778,"concrete_test":"Evaluate Eq. (5.27) and the published Kerr Compton amplitude of Ref. [31] (and, if needed, the root-Kerr amplitude of Ref. [32]) at a complex kinematic point with finite v·k_s, v·k_u, and t, with ⌈3˜2⌋→0 (equivalently ⟨3|−p1|2]→0 in the k1=0 frame), for a nonzero classical spin vector a not in the polar-scattering configuration. Form D ≡ A_paper − A_[31] and multiply by (v·k_s)(v·k_u)t. If D has a pole or branch cut as ⌈3˜2⌋→0, the missing terms are not purely contact and the classical claim needs revision. If D becomes a polynomial in momenta and spin, the 'up to contact terms' caveat is confirmed and the conditional verdict stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The classical application of the central claim requires that the coherent-state resummed minimal-coupling amplitude be the complete Kerr Compton amplitude. The paper explicitly acknowledges that factorization leaves contact terms undetermined ([b401], [b265]), so the mere existence of such terms is not a new criticism. The load-bearing question is whether the missing terms are actually local contact terms. In Eq. (5.16), the vector w is defined with a denominator ⌈3˜2⌋, the same spurious locus that Section 4.3 removes order-by-order in the quantum HPET expansion. After the coherent-state resummation, w enters the exponent of Eq. (5.27), so for generic spin directions and non-polar kinematics the classical amplitude can develop singularities as ⌈3˜2⌋→0. The paper only states that in the polar-scattering special case the pole in w is canceled, and defers classification of contact terms. Consequently the statement that the classical amplitude agrees with the literature 'up to contact terms' is not yet established: if the difference between Eq. (5.27) and the Kerr amplitude of Ref. [31] contains a nonlocal or spurious-pole term at the same classical order, the claim fails; if the difference is polynomial after factoring physical poles, the conditional reading is correct. Without an explicit comparison, the completeness assumption behind the classical Kerr claim remains unverified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"The paper develops a velocity-projected spinor-helicity formalism (\"v/-spinors\") for heavy particles of arbitrary spin S, in which both large and small components of the projected massive spinors are retained. The authors show how to pass from relativistic AHH amplitudes to HPET amplitudes by projection followed by 1/m expansion, and they construct the same three-point amplitudes bottom-up from SU(2) little-group covariance, kinematics, and reparameterization invariance (RPI-I). They then bootstrap four-point photon and gravitational Compton amplitudes from the three-point minimal couplings and argue that, to the displayed sub-leading order in 1/m, the resulting amplitudes are free of the soft-bracket spurious pole ⌈3˜2⌋^{-1}; the bottom-up and top-down expansions are shown to agree term by term. In the gravitational application, the projected minimal coupling is matched to the worldline multipole Lagrangian, giving C_S^n=1 for n≤2S, and the coherent-state classical limit yields the 1PM elastic amplitude and a gravitational Compton amplitude. The latter is claimed to agree with the literature up to contact terms. The internal consistency of the three-point and Compton calculations appears sound, but the classical Compton comparison is not fully established because of the nonlocal w term in Eq. (5.27).","tokens_in":51681,"tokens_out":12198,"duration_ms":108983,"significance":"The formalism is a useful contribution: it makes the Euclidean little-group symmetry manifest, simplifies reparameterization invariance, and gives a concrete on-shell-to-HPET operator correspondence. The paper contains nontrivial internal checks: the three-point bottom-up construction is verified against the AHH form, the photon and graviton Compton amplitudes are obtained by two independent routes and match each other term by term, scalar and heavy-mass limits reproduce known results, and the finite-spin Kerr matching is performed in a general frame. The classical elastic amplitude in Eq. (5.22) matches the known exponentiated soft factor. However, the main new physical application in the classical section is conditional: agreement with Refs. [31,32] is asserted only up to contact terms, and the vector w defined in Eq. (5.16) carries a spurious-pole denominator whose role in generic kinematics is not resolved. This weakens the abstract's classical claim until either a direct comparison is supplied or the claim is restricted.","major_comments":[{"comment":"The statement that the classical gravitational Compton amplitude agrees with the literature \"up to contact terms\" is not yet established. The vector w is defined with an explicit denominator ⌈3˜2⌋ and enters the exponent of the coherent-state-resummed amplitude, so for generic spin directions and non-polar kinematics it can produce a nonlocal singularity rather than a local contact term. The paper treats only the special polar-scattering case, where the pole in w is canceled by the numerator, and it acknowledges that contact terms are undetermined, but it does not address the locality of the difference. Please compare Eq. (5.27) directly with the classical Kerr Compton amplitudes of Refs. [31,32]; a concrete check is whether, after multiplying by the physical denominators (2p1·q2)(2p1·q3)t, the difference is polynomial in momenta. If the difference is non-polynomial, the agreement claim should be withdrawn or restricted to the polar-scattering and other explicitly verified parts of the amplitude.","section":"Section 5.2.2, Eqs. (5.16) and (5.27)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The four-point amplitude is presented as \"the\" Compton amplitude free of spurious poles up to sub-leading order, but factorization determines only residues at the physical poles and does not exclude local contact terms at the same order. The paper itself notes this at the end of Section 4.1 and again in Section 5.2.2, so the algebraic derivation is not at fault. The unresolved point is that the abstract and the closing statements of Sections 4.3 and 6 read as though the factorization bootstrap uniquely fixes the amplitude. Please state explicitly in the abstract and conclusions that Eqs. (4.7) and (4.9) are the minimal-coupling factorization-bootstrap amplitudes, and that the four-point HPET amplitude is defined only up to contact terms that are not classified here.","section":"Section 4.3 and Section 4.1, Eqs. (4.24), (4.7), (4.9)","authors_acknowledge":"Second, since Eq. (5.27) is derived purely from the factorization, the potential additional contact terms are undetermined for the Kerr black hole, in contrast to Ref. [31], and fixing them requires further physical input beyond the scope of this work.","authors_acknowledge_p":0.72}],"minor_comments":[{"comment":"Refs. [63] and [69] are self-citations listed only by arXiv identifiers, and the general integrate-out form in Eq. (3.27) and the Young-tableau operator basis of Appendix C are imported from them. Please clarify whether these works are published or under review, and specify which particular statements are being assumed.","section":"References [63] and [69]","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence \"at the spurious pole exists at order k^3/m^3 and higher in the HPET expansion\" is grammatically unclear and should be rewritten, for example as \"the spurious-pole contribution first appears at order k^3/m^3.\"","section":"Section 4.2, after Eq. (4.15)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The vector w is defined inside a displayed equation without an equation label; please number the definition so that the later discussion of its pole structure can refer to it precisely.","section":"Section 5.2.1, Eq. (5.16)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"There are several small wording issues, including \"an intermediate velocity-projected amplitudes\" and \"which is free of spurious poles\"; these should be corrected, and the abstract should carry the uniqueness caveat described in the second major comment.","section":"Abstract and Introduction","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The internal calculations appear consistent and the formalism is likely publishable, but the classical Compton claim in Section 5.2.2 is the load-bearing point for the abstract. If the authors either perform the requested comparison with Refs. [31,32] or restrict the claim to the polar-scattering case, I would support acceptance. The reliance on two self-cited preprints is worth a request for clarification rather than a concern about the algebra itself."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"Dear colleague,\n\nThe thing to know: the velocity-projected spinor formalism is real and worth engaging with. The central construction—keep both large and small components, impose RPI before integrating out—does what it claims, and the internal cross-checks are genuinely independent. I am much more skeptical of the classical gravitational Compton claim, and the stress-test note lands: the w-term in Eq. (5.27) carries 1/⌈2̃⌉, and the paper does not show that this is a local contact term.\n\nWhat is actually new: the v/-spinor with both components, the linear RPI-I transformation, and the explicit three-point arbitrary-spin amplitudes. The bottom-up construction is not circular: it starts from little-group covariance, imposes RPI, and matches the projected AHH amplitude. The four-point Compton amplitudes in Eqs. (4.7) and (4.9) are bootstrapped and then reproduced top-down term by term; scalar and heavy-mass limits check out. That is a substantial, internally consistent piece of work. The spurious-pole cancellation up to subleading order is the strongest concrete result.\n\nSoft spots, in order:\n\n1. Section 5.2.2: Eq. (5.16) defines w with an explicit 1/⌈2̃⌉, and after coherent-state resummation w sits in the exponent of Eq. (5.27). The authors are candid about this: they state the pole is canceled only in polar scattering and that contact terms are not fixed [b265,b401]. But that candor does not convert the issue into a minor caveat. A term with a spurious pole is not a local contact term, so the abstract's \"agreed with the literature up to contact terms\" is not established. A direct comparison with Ref. [31] is needed. If the difference is polynomial after physical poles are factored, fine; if it contains the spurious pole, the classical Compton claim fails. This does not damage the quantum HPET results, but it is load-bearing for the Kerr application.\n\n2. Moderate: two structural ingredients, the general integrate-out form and the Young-tableau operator basis, are imported from same-group arXiv preprints that I have not seen verified elsewhere. Not suspicious by itself; just unverified input.\n\n3. Minor: the gravitational coupling is left undetermined in the bottom-up bootstrap and fixed later by matching; fine, but worth noting.\n\nI would bring this to a reading group, and I would cite it for the formalism. Send it to a serious referee. The referee should be asked to test Section 5.2.2 against Ref. [31]; if that comparison cannot be made, the classical section should be weakened to a statement about the quantum amplitudes and the three-point matching.","headline":"Formal core is solid and genuinely new; the classical Kerr Compton claim is weaker than the abstract suggests because the w-term in Eq. (5.27) is not shown to be a local contact term.","tokens_in":52211,"tokens_out":4612,"would_cite":true,"duration_ms":40012,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek/deepseek-v4-flash","headline":"Velocity-projected spinors retaining both components let reparameterization invariance be imposed before the $1/m$ expansion, giving spurious-pole-free Compton amplitudes and Kerr multipoles with $C_S^n = 1$.","keywords":["heavy-particle effective theory","spinor-helicity formalism","velocity-projected spinors","reparameterization invariance","gravitational Compton amplitudes","Kerr black hole","higher-spin amplitudes","spurious poles"],"falsifier":"Expand the graviton Compton amplitude one order higher in $1/m$: the paper's own velocity-projected building block already shows a spurious pole at order $k^5/m^5$, and at $k^3/m^3$ for the photon, so computing the next-to-next-to-leading-order term of the bootstrapped amplitude and checking whether a $1/\\lceil 3\\,\\tilde 2\\rfloor$ singularity reappears is a direct test of whether the pole-free property survives beyond sub-leading order. A first-principles determination of the Kerr contact terms at the same classical order, for instance by matching to the worldline effective theory, would likewise settle whether the minimal-coupling amplitude alone is the complete Kerr Compton amplitude.","tokens_in":52771,"feed_emoji":"🕳️","tokens_out":16871,"duration_ms":118168,"temperature":0.7,"pith_summary":"This paper develops an on-shell version of heavy-particle effective theory (HPET) in which spinor-helicity variables are projected onto the $SU(2)$ little group of a timelike reference velocity $v^\\mu$, so that amplitudes carry only rotation-group indices and explicit $1/m$ power counting. Its central move is to keep both the large and the small components of the projected spinors, forming an intermediate velocity-projected amplitude in which reparameterization invariance, the remnant of Lorentz symmetry, takes a simple linear form and can be imposed before any expansion in the inverse heavy-particle mass. From these building blocks the paper constructs the three-point amplitudes for two equal-mass particles of arbitrary spin $S$ coupled to a soft massless boson of helicity $h$, and bootstraps four-point photon and graviton Compton amplitudes that are free of spurious poles\\,---\\,unphysical singularities that plague high-spin amplitudes\\,---\\,up to sub-leading order. Applied to gravity, the projected minimal coupling reproduces the Kerr black hole's spin-induced multipoles with all Wilson coefficients $C_S^n=1$ up to order $2S$ for finite spin, and the classical limits of elastic scattering and gravitational Compton scattering agree with the literature up to contact terms that factorization does not fix. If correct, this gives a parameter-light bridge from on-shell amplitudes to HPET operators and to Kerr black-hole observables that works in any reference frame.","feed_headline":"Kerr multipoles emerge from velocity-projected spinors","feed_subtitle":"Retaining both spinor components restores Lorentz symmetry before the inverse-mass expansion, fixing Kerr couplings to one.","key_machinery":"The central object is the velocity-projected spinor $|k^\\pm\\rfloor^{IL}=\\tfrac12(\\langle p^I v^L\\rangle\\pm[v^L p^I])$, in which the two-component Lorentz indices of the massive and massless spinors are contracted with reference-velocity spinors, leaving only the $SU(2)$ little-group indices of the timelike velocity $v^\\mu$; the large component scales as $\\sqrt{m}$ and the small one as $k/\\sqrt{m}$. Its work is carried by keeping both components in an intermediate velocity-projected amplitude: reparameterization invariance acts linearly ($|k^+\\rfloor\\to|k^+\\rfloor-\\delta v|k^-\\rfloor$ and vice versa) before any $1/m$ expansion, and the subsequent elimination $|k^-\\rfloor=(2m+v\\cdot k)^{-1}k_\\perp|k^+\\rfloor$ organizes the HPET amplitudes by power counting, with each term corresponding to a local operator through an $SU(2)$ Young-tableau dictionary. For the Kerr application, the spin operator $q\\cdot S=-\\tfrac12 q_\\perp$ acting on symmetrized products of $2S$ spinors turns each multipole insertion into one power of $q\\cdot S/m$, so that integrating out the small component and organizing the spin-induced multipoles are one and the same operation.","core_discovery":"The paper's central claim is that a velocity-projected spinor carrying both a large and a small component is the right on-shell variable for heavy-particle effective theory. Contracting all Lorentz spinor indices with the reference-velocity spinors leaves only $SU(2)$ little-group indices, and the reparameterization invariance that restores the Lorentz symmetry broken by choosing $v^\\mu$ takes the simple linear form $|k^+\\rfloor\\to|k^+\\rfloor-\\delta v\\,|k^-\\rfloor$, $|k^-\\rfloor\\to|k^-\\rfloor-\\delta v\\,|k^+\\rfloor$ while both components are kept. The small component is then eliminated through its equation of motion $|k^-\\rfloor=(2m+v\\cdot k)^{-1}k_\\perp|k^+\\rfloor$, producing HPET amplitudes with manifest $1/m$ power counting and a one-to-one map to local operators. On this basis the paper determines the most general three-point amplitudes for two equal-mass spin-$S$ particles and a soft helicity-$h$ boson, and bootstraps the four-point photon and graviton Compton amplitudes, claiming they are free of spurious poles for any finite $S$ up to sub-leading order, with the bottom-up factorization route and the top-down projection of the relativistic amplitudes agreeing order by order. Applied to gravity, the projected minimal coupling matches the Kerr multipole Lagrangian with $C_S^n=1$ exactly to order $2S$ for finite spin, and the coherent-state resummed classical amplitudes agree with the literature up to contact terms that factorization does not determine.","pith_inferences":["Because the paper only proves spurious-pole freedom through sub-leading order, and its own velocity-projected building block already develops a pole at order $k^3/m^3$ (photon) and $k^5/m^5$ (graviton), the next order is the natural stress test: if the pole reappears there, the pole-free property is a sub-leading-order phenomenon rather than a general feature of the formalism.","The same ordering trick\\,---\\,imposing reparameterization invariance on an intermediate amplitude that keeps the small component, and only then expanding\\,---\\,could simplify higher-point heavy-particle processes such as gravitational bremsstrahlung, where small-component corrections and boost invariance currently multiply badly.","Since one spin-operator insertion is simultaneously one power of $1/m$ and one multipole order, the formalism suggests a purely on-shell route to non-relativistic operator bases such as those of NRQCD-type theories with spin, a direction the paper's conclusion also points toward.","The contact-term freedom means the factorized amplitude is the minimal set; a matching to the worldline effective theory at the same classical order could reveal whether the coherent-state minimal coupling is the complete Kerr amplitude or misses spin effects at that order, which the paper explicitly leaves open."],"forward_implications":["Three-point amplitudes for two equal-mass spin-$S$ particles and one soft helicity-$h$ boson are fixed by $SU(2)$ little-group covariance and reparameterization invariance alone, and coincide with the general relativistic three-point amplitudes of the massive spinor-helicity formalism.","The photon and graviton Compton amplitudes of Eqs. (4.7) and (4.9) are free of spurious poles for any finite spin up to sub-leading order in $1/m$, and the bottom-up factorization bootstrap agrees term by term with the top-down projection of the relativistic amplitudes.","The projected gravitational minimal coupling matches the Kerr multipole Lagrangian with all Wilson coefficients $C_S^n=1$ exactly up to order $2S$ for finite spin, in a general frame and without an added Lorentz boost or holomorphic-classical-limit kinematics.","In the heavy-mass limit the spin interactions decouple for all finite $S$, an analog of heavy-quark spin symmetry, and the scalar limits reduce to the known spinless Schwarzschild amplitudes.","The classical first-post-Minkowskian (1PM) elastic scattering amplitude and the classical gravitational Compton amplitude agree with the published results up to contact terms that factorization leaves undetermined."],"supporting_citations":[{"why":"Supplies the massive spinor-helicity formalism and the most general relativistic three-point amplitudes that the top-down projection route starts from.","marker":"[39]"},{"why":"Defines the earlier on-shell heavy-particle variables (large component only) that the velocity-projected spinors extend and are cross-checked against.","marker":"[28]"},{"why":"The constructive heavy-particle effective theory providing the reparameterization and coset framework used in the bottom-up construction.","marker":"[63]"},{"why":"Gives the worldline effective theory multipole Lagrangian that the three-point gravitational minimal coupling is matched to.","marker":"[25]"},{"why":"Supplies the spin-operator action on symmetrized spinor products and the minimal-coupling-to-Kerr matching that yields $C_S^n=1$.","marker":"[40]"},{"why":"Establishes the spin-exponentiated minimal-coupling amplitudes whose classical limit the elastic 1PM result is compared with.","marker":"[43]"},{"why":"The higher-spin QFT Compton amplitude for a rotating black hole that the classical exponentiated Compton amplitude is compared with; contact terms there are fixed, whereas here factorization leaves them undetermined.","marker":"[31]"},{"why":"Quantum gravitational Compton amplitudes that the $k_1=0$ velocity-projected amplitude reproduces after expanding the small component.","marker":"[50]"},{"why":"The heavy-mass effective field theory scalar graviton Compton amplitude compatible with the $S=0$ limit of Eq. (4.9).","marker":"[19]"}],"fun_headline_variants":["Velocity-projected spinors build heavy-particle effective theory","Gravitational Compton from projected minimal coupling","Kerr multipoles reproduced by HPET projection","On-shell HPET with reparameterization invariance","Spinor projection yields classical gravitational amplitudes"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The load-bearing premise is that the coherent-state sum of minimal-coupling amplitudes is the complete Kerr amplitude; the paper itself acknowledges that factorization alone leaves local contact terms undetermined, so if those terms contribute at the same classical order, the agreement with the literature holds only up to them.","fun_headline_variants_meta":{"raw":{"variants":["Velocity-projected spinors build heavy-particle effective theory","Gravitational Compton from projected minimal coupling","Kerr multipoles reproduced by HPET projection","On-shell HPET with reparameterization invariance","Spinor projection yields classical gravitational amplitudes"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.00021,"raw_usage":{"cost":0.000209937,"is_byok":false,"cost_details":{"upstream_inference_cost":0.000209937,"upstream_inference_prompt_cost":3.0849e-05,"upstream_inference_completions_cost":0.000179088},"total_tokens":2159,"prompt_tokens":1175,"completion_tokens":984,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":1045,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":928}},"tokens_in":1175,"tokens_out":984,"cost_source":"openrouter_usage","duration_ms":9935,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":928,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-30T06:34:29.294833+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"Expand the graviton Compton amplitude one order higher in $1/m$: the paper's own velocity-projected building block already shows a spurious pole at order $k^5/m^5$, and at $k^3/m^3$ for the photon, so computing the next-to-next-to-leading-order term of the bootstrapped amplitude and checking whether a $1/\\lceil 3\\,\\tilde 2\\rfloor$ singularity reappears is a direct test of whether the pole-free property survives beyond sub-leading order. A first-principles determination of the Kerr contact terms at the same classical order, for instance by matching to the worldline effective theory, would likewise settle whether the minimal-coupling amplitude alone is the complete Kerr Compton amplitude.","supporting_citations":[{"cited_title":"Scattering Amplitudes For All Masses and Spins","cited_arxiv_id":"1709.04891","evidence_quote":"Supplies the massive spinor-helicity formalism and the most general relativistic three-point amplitudes that the top-down projection route starts from."},{"cited_title":"On-shell heavy particle effective theories","cited_arxiv_id":"2001.09164","evidence_quote":"Defines the earlier on-shell heavy-particle variables (large component only) that the velocity-projected spinors extend and are cross-checked against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The constructive heavy-particle effective theory providing the reparameterization and coset framework used in the bottom-up construction."},{"cited_title":"Spinning gravitating objects in the effective field theory in the post-Newtonian scheme","cited_arxiv_id":"1501.04956","evidence_quote":"Gives the worldline effective theory multipole Lagrangian that the three-point gravitational minimal coupling is matched to."},{"cited_title":"The simplest massive S-matrix: from minimal coupling to Black Holes","cited_arxiv_id":"1812.08752","evidence_quote":"Supplies the spin-operator action on symmetrized spinor products and the minimal-coupling-to-Kerr matching that yields $C_S^n=1$."},{"cited_title":"Black-hole scattering with general spin directions from minimal-coupling amplitudes","cited_arxiv_id":"1906.10071","evidence_quote":"Establishes the spin-exponentiated minimal-coupling amplitudes whose classical limit the elastic 1PM result is compared with."},{"cited_title":"Compton Amplitude for Rotating Black Hole from QFT","cited_arxiv_id":"2312.14913","evidence_quote":"The higher-spin QFT Compton amplitude for a rotating black hole that the classical exponentiated Compton amplitude is compared with; contact terms there are fixed, whereas here factorization leaves them undetermined."},{"cited_title":"Scattering in Black Hole Backgrounds and Higher-Spin Amplitudes: Part II","cited_arxiv_id":"2212.07965","evidence_quote":"Quantum gravitational Compton amplitudes that the $k_1=0$ velocity-projected amplitude reproduces after expanding the small component."},{"cited_title":"One-loop Gravitational Bremsstrahlung and Waveforms from a Heavy-Mass Effective Field Theory","cited_arxiv_id":"2303.06111","evidence_quote":"The heavy-mass effective field theory scalar graviton Compton amplitude compatible with the $S=0$ limit of Eq. (4.9)."}],"review_version":1}