{"id":"0d55fae5-de8d-46cd-abb8-689c07369c6c","arxiv_id":"gr-qc/0410001","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"A status report on Einstein-Aether theory: a generally covariant gravity theory with a dynamical preferred frame, covering its wave spectrum, post-Newtonian behavior, energy conditions, and cosmological consequences.","lead":"Einstein-Aether theory is a generally covariant gravity theory in which a dynamical unit timelike vector field picks out a preferred rest frame, breaking local Lorentz symmetry. This 2004 proceedings review collects what was then known about its wave modes, post-Newtonian limit, energy, stars, black holes, and cosmology, and lists the open problems.","discovery_kind":"review","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"Section 6.3's 'plenty of parameter space' is a linearized stability statement, half-sourced to an in-preparation reference, and the observationally sharpest PPN parameters (α1, α2, §5) are uncomputed, so observational viability is untested rather than established.","rationale":"I checked the parts of the paper that can be checked from the text alone, and they hold. The §4.1 light-cone condition (c4 = 0, c3 = −c1, c2 = c1/(1 − 2c1)) follows correctly from Table 1: with c13 = 0 and c4 = 0, the spin-0 speed c123(2 − c14)/[c14(1 − c13)(2 + c13 + 3c2)] reduces to c2(2 − c1)/[c1(2 + 3c2)] = 1, which rearranges to exactly the quoted c2. The §6.1 energy rescaling E = (r0/2G)(1 − c14/2) is consistent with GN = G/(1 − c14/2), so E = r0/2GN as claimed. The §8 chain Gcosmo < G < GN follows from the stated subluminality and positivity conditions on a sample point (c1 = 0.1, c3 = −0.1, c2 = 0.1, c4 = 0). Nothing I can compute is internally inconsistent. Where I agree with the reader: the second half of the paper leans on Refs. 20, 28, 29 and 34, all labelled in preparation or unpublished, and the energy positivity conditions of §6.2.1 are the most load-bearing of these because they feed directly into the §6.3 parameter-range conclusion. Where I differ: the reader's weakest_assumption treats nonlinear energy positivity as an extrapolation the authors make. They do not make it; §6.2 says 'We can make no definite statement about the non-linear energy at this time' and §6.3 calls it 'an important open question.' A review that names its open problems should not be marked down for failing to close them. The sharper gap is the uncomputed α1 and α2 in §5, which is what actually determines whether the surviving parameter range is observationally viable, and which the paper flags but does not weigh against its own §6.3 conclusion. I would leave the verdict at CONDITIONAL: the paper is a careful, candid survey whose checkable content is sound, and the reservation is real but should attach to the uncomputed preferred-frame PPN parameters and the in-preparation energy analysis, not to a nonlinear claim the authors explicitly decline to make.","tokens_in":14528,"tokens_out":12284,"duration_ms":98158,"concrete_test":"Extend the Ref. 18 post-Newtonian expansion to a source boosted relative to the asymptotic æther, and extract α1 and α2 as functions of (c1, c2, c3, c4). If α2 comes out O(1) for generic couplings, the 10^-7 observational bound cuts the §6.3 parameter range down to the c13 = 0 slice (where §5 guesses α2 = 0), and the 'wide viable range' claim narrows materially. If α2 vanishes or is suppressed by the same combinations §6.3 already requires to be small, the concern does not land and the viability claim stands as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The viability claim has two halves. The first — that the theory is a consistent linearized theory with positive-energy, stable modes over a wide coupling range — is assembled in §6.3 from two sources: the wave spectrum and stability conditions of Ref. 19 (Phys. Rev. D 70, 024003, published) and the mode energy densities of Ref. 20, listed as 'in preparation.' The specific inequalities quoted in §6.2.1 — (2c1 − c1² + c3²)/(1 − c13) > 0 for the vector modes and c14(2 − c14) > 0 for the trace mode — are the load-bearing inputs to the §6.3 conclusion c1 > 0, c14 > 0, c123 > 0, and a reader cannot check them from this text. That is a rule-12-legitimate gap, and it is the one the reader correctly located. The second half — that the surviving parameter range is observationally viable — is weaker than the paper's framing suggests. §5 states plainly that α1 and α2 'have not yet been computed for the Æ-theory,' then hazards a guess from Will's unconstrained vector-tensor results that α2 ≠ 0 generically. If that guess is right, the 10^-7 bound on α2 does not merely 'yield constraints of this order' (§5); it plausibly excludes generic ci, leaving only the c13 = 0 slice where the paper guesses α2 = 0. §6.3's 'plenty of parameter space' is a statement about linearized stability alone and does not survive that inference untouched. I part company with the reader on one point: nonlinear energy positivity (§6.2, §6.3) is not an unstated assumption the authors rely on. They disclaim it twice in explicit terms, so penalizing the review for not establishing it misreads what a proceedings survey claims.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"This manuscript is a review, based on a talk at the Deserfest, of Einstein-Aether theory: a generally covariant theory of a metric coupled to a dynamical unit timelike vector field u^a, defined by the action of Eq. (1) with four dimensionless couplings c1 through c4. The paper sets out the action and field equations (Eqs. 1-7), discusses the Maxwell-like special case c1+c3=c2=c4=0 and its known pathologies (caustics and negative-energy configurations), summarizes the linearized wave spectrum about flat space (Table 1: two spin-2, two spin-1, and one spin-0 mode, each with its own speed), reports the static post-Newtonian result beta = gamma = 1, treats energy positivity in the linearized and gravitational-decoupling limits, and covers stars, black holes, and Robertson-Walker cosmology, where the aether stress tensor reduces to Eq. (17) and renormalizes both G and the spatial-curvature term. The abstract's stated aim, that open questions are stressed (abstract:s2), is met: the paper repeatedly and explicitly flags what has not been computed, including the nonlinear energy and the preferred-frame PPN parameters.","tokens_in":14935,"tokens_out":7437,"duration_ms":118838,"significance":"As a status report the manuscript is useful, and in the places I could check it is internally consistent. I verified that the 'all modes propagate on the light cone of g_ab' condition stated in §4.1 (c4 = 0, c3 = -c1, c2 = c1/(1-2c1)) is exactly what Table 1 requires when the three squared speeds are set to unity, and that the inference G_cosmo < G < G_N in §8 does follow from the constraints listed in §6.3: c13 <= 0 together with c123 > 0 gives c2 > -c13, hence c13 + 3c2 > -2c13 >= 0, so the first inequality holds. The theory makes falsifiable predictions, namely distinct propagation speeds for the five modes, a modified energy-loss rate for compact binaries, and a shifted primordial helium abundance, and the paper is candid about which of these have not yet been computed. Footnote b, correcting an earlier equivalence claim and crediting the correction, is good scholarly practice and worth naming.","major_comments":[{"comment":"The positivity inequalities quoted in §6.2.1, (2c1 - c1^2 + c3^2)/(1 - c13) > 0 for the vector modes and c14(2 - c14) > 0 for the trace mode, are the load-bearing inputs to the §6.3 summary conclusion c1 > 0, c14 > 0, c123 > 0, which is one of the paper's headline results. They are attributed to Ref. 20, listed as 'in preparation'. A reader cannot check them from this text, and the reduction to c1 > 0 and c14 > 0 in the small-c_i limit is asserted rather than shown. Since this is a review, quoting a published derivation would be entirely appropriate; quoting an unpublished one for the central constraint summary is not. Either supply a short derivation (the mode energy densities follow from the quadratic action and Table 1 polarizations, so a few lines should suffice), or state explicitly in §6.3 that the summary conditions rest on unpublished work and mark them as provisional.","section":"§6.2.1 and §6.3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The paper states plainly that the preferred-frame PPN parameters alpha1 and alpha2 'have not yet been computed for the Æ-theory', then hazards a guess from Will's unconstrained vector-tensor results that alpha2 is generically non-zero. The consequence of that guess is stronger than the text allows: with the current bound alpha2 < 10^-7, a generic non-zero alpha2 would plausibly exclude generic values of c_i and leave only the c13 = 0 slice where the paper guesses alpha2 = 0. The sentence 'constraints of this order on the parameters of Æ-theory might be expected, at least for generic parameters' understates this. I would ask the authors to say directly that if the guess is correct, the observational viability of the generic parameter space is in question, and that the c13 = 0 slice is the case that survives. This is a framing issue rather than an error, but it bears on how the §6.3 'plenty of parameter space' statement should be read, and the two sections should be reconciled explicitly.","section":"§5","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The field-redefinition discussion in §2 is used to justify the c1 + c3 = 0 convention, on which the claim rests that 'with the c1 + c3 = 0 description we ensure that non-zero coefficients always represent true deviations from GR'. The transformation law relating c_i to c'_i is attributed to Ref. 11, listed as 'to be published', and only one consequence (the choice B = 1 - c'_1 - c'_3, with the stated proviso c'_1 + c'_3 < 1) is given. Because this convention organizes the entire parameter space and the interpretation of every subsequent constraint, the transformation should be written out explicitly at least for the c1 + c3 = 0 slice, or the claim should be softened to note that it depends on an unpublished result. The Barbero-Villaseñor equivalence conditions are quoted from a published source and need no defence.","section":"§2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Two further load-bearing results rest on unpublished sources. The aether contribution to the energy flux integral, Eq. (13), is attributed to Ref. 28 ('unpublished'), and it is the route by which the total energy Eq. (16) is obtained; the alternative route via the Einstein pseudotensor is Ref. 29, also unpublished. Separately, the §7 claim that regular black-hole solutions exist, obtained 'using a shooting method', rests entirely on Ref. 34 ('unpublished') with no description of the solution space, the shooting parameters, or the range of c_i covered. For a review these are legitimate things to report, but the text should say which of these results are checked in the present manuscript and which are quoted from work not yet available to the reader. At minimum, Eq. (16) can be cross-checked against the asymptotic forms Eqs. (14) and (15) in the text, and it would help to show that check explicitly.","section":"§6.1, Eq. (13), and §7","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The spin-0 squared speed is printed as c123(2 - c14)/c14(1 - c13)(2 + c13 + 3c2), whose grouping is ambiguous as typeset. Please add explicit brackets in the denominator. The caption also uses c13 and c14 without defining them; the preceding text defines c123 and says 'etc', which is marginal for a table a reader will consult in isolation.","section":"Table 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The footnote refers to 'the factor s in the polarization h_I3', but Table 1 lists squared speeds while the polarization entry uses s unsquared. Please state explicitly whether s in that entry is the speed or its square, since the phase-shift remark depends on the distinction.","section":"§4.1, footnote g","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The chain G_cosmo < G < G_N is asserted as implied by the positive-energy, stability, and subluminality constraints. The second inequality follows immediately from c14 > 0 and Eq. (10), but the first requires c13 + 3c2 > 0, which is not one of the listed conditions. It does follow, via c123 > 0 and c13 <= 0, but one line of algebra would save the reader the check.","section":"§8","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The helium-abundance constraint 15c1 + 21c2 + 7c3 + 8c4 < 2 is quoted with the note that the c4 dependence was omitted in Ref. 13 and has here been 'included'. Since the c4 extension is the authors' own addition, a sketch of how it enters, or a pointer to where it is derived, would be appropriate.","section":"§8","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence 'with U_N is proportional to 1/r' contains a stray verb. There is also a residual 'a' footnote marker in §1 whose note appears to be missing from the extracted text; please confirm it is present in the final version.","section":"§5","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The section title 'Stars and black holes?' carries a question mark that is presumably deliberate, but the section does assert that asymptotically flat black-hole solutions exist. If the question mark is meant to signal that the existence proof is numerical and unpublished, say so in the first sentence of the section rather than only in the title.","section":"§7","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that a monopole moment may generate the spin-0 trace mode, and that binary-pulsar agreement 'should yield constraints', is presented as expectation rather than result. That is fine for a review, but it should be flagged as an open problem in the same explicit way the paper flags the uncomputed alpha1 and alpha2.","section":"§4.2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Refs. 11, 20, 28, 29, and 34 are listed as unpublished or in preparation and carry results discussed in the text. Please update their status at proof stage, and where a result has since appeared, cite the published version.","section":"References","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"This is a Deserfest proceedings review, and judged as a review it is careful, well organized, and honest about its open problems; the physics I could check is internally consistent. My reservation is bibliographic rather than technical: several numbers that carry the paper's summary conclusions (the §6.2.1 positivity inequalities, the §6.1 energy flux integral, the §7 black-hole existence claim, and the §2 field-redefinition law) come from the authors' own unpublished or in-preparation work. That is a normal pattern for a talk reporting work in progress, but the editor may wish to ensure the proceedings version distinguishes clearly between results the reader can verify from the cited literature and results that are not yet available."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"This is the standard short reference for Einstein-Aether theory, and it earns that status. If you want the action, the field equations, the five-mode wave spectrum with speeds and polarizations, the static PPN result, and the cosmological reduction in one place, this is it. The bookkeeping is clean and the authors are unusually willing to say what they don't know. Two things are genuinely new: footnote b corrects their own earlier equivalence claim from Ref. 18 (the Barbero-Villasenor conditions), and section 2 pushes the c1 + c3 = 0 field-redefinition framing as the right way to describe the theory so that nonzero couplings always mean real deviation from GR. That second point is a small but real service to anyone working in the framework. Correcting your own published error in a proceedings footnote is the kind of thing I want to see more of, not less. The wave section is the strongest part: Table 1 is concrete, the stability conditions are stated, and footnote h is honest that they aren't yet observational constraints. Where I'd push back on the framing: section 6.3's 'plenty of parameter space' is a linearized statement, and the specific inequalities in 6.2.1 come from Ref. 20, listed as in preparation. You can't check them here. That's a real gap, and it's the one worth flagging. The sharper issue is section 5. The paper says outright that alpha1 and alpha2 have not been computed, then guesses from Will's vector-tensor results that alpha2 is nonzero generically. If that guess holds, the 10^-7 bound on alpha2 doesn't just 'yield constraints of this order' — it plausibly kills generic ci and leaves only the c13 = 0 slice. That inference deserves to be made explicit, and it isn't. On the other side, I don't think the reader should penalize the paper for not establishing nonlinear energy positivity. The authors disclaim it twice, in plain terms, in 6.2 and 6.3. That's a survey doing its job, not an unstated assumption. Section 7's black hole existence claim rests on unpublished Ref. 34, so treat it as a progress report. Who should read it: anyone entering Lorentz-violating gravity, and anyone who needs the wave-speed constraints for gravitational-wave work. Worth a serious referee pass if it came in fresh — the content is checkable and the open problems are named rather than buried.","headline":"A useful, honest snapshot of Einstein-Aether theory as of 2005 — the framework and wave spectrum are checkable, but the observational viability half leans on unpublished work and uncomputed PPN parameters.","tokens_in":15610,"tokens_out":926,"would_cite":true,"duration_ms":14856,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["04.50.+h","11.30.Cp","04.30.-w","98.80.-k"],"model":"selfhosted/deepseek-v4.1-flash","headline":"A gravity theory with a preferred rest frame at every point can keep general covariance and still match general relativity's static post-Newtonian predictions, while predicting extra wave modes and modified cosmology.","keywords":["Einstein-Aether theory","Lorentz symmetry violation","preferred frame","unit timelike vector field","post-Newtonian parameters","gravitational wave modes","black hole horizons","cosmological helium abundance"],"falsifier":"Compute the two preferred-frame post-Newtonian parameters $α_1$ and $α_2$ for generic couplings and compare with the measured limits of order $10^{-4}$ and $10^{-7}$; a value outside those bounds, or a binary-pulsar inspiral rate inconsistent with the five-mode energy loss, would rule the theory out for that parameter region.","tokens_in":15851,"feed_emoji":"🧭","tokens_out":2872,"duration_ms":49566,"temperature":0.7,"pith_summary":"This paper reviews a theory in which gravity is coupled to a dynamical unit-timelike vector field, the 'æther', that picks out a preferred rest frame at every spacetime point. The point is not to abandon general covariance — the action is fully diffeomorphism invariant — but to give up local Lorentz symmetry, the assumption that no local frame is special. The authors argue this is the minimal, honest way to describe a preferred frame: a scalar cosmic time would smuggle in an extra clock rate and force the frame to be hypersurface-orthogonal, whereas a unit vector carries exactly the three pieces of information a frame needs. The review then gathers what is known: the linearized spectrum has five massless modes with calculable speeds, the static post-Newtonian parameters $[abstract:s0]$ come out identical to general relativity, and cosmology reduces to a rescaling of Newton's constant plus a curvature-like fluid. Open problems, chiefly whether positive energy survives beyond linear order, are stated plainly rather than hidden.","feed_headline":"Gravity with a preferred rest frame still passes solar-system tests","feed_subtitle":"A unit timelike vector breaks local Lorentz symmetry but still reproduces general relativity's static post-Newtonian numbers.","key_machinery":"The load-bearing object is the quadratic derivative action $S=-1/(16πG)∫d^4x√(-g)(R+K^{abmn}∇_a u_m ∇_b u_n+λ(u^a u_a-1))$, where $K^{abmn}=c_1 g^{ab}g^{mn}+c_2 δ^{a}{}_{m}δ^{b}{}_{n}+c_3 δ^{a}{}_{n}δ^{b}{}_{m}+c_4 u^a u^b g^{mn}$. The unit-norm constraint is what makes the vector field behave unlike a generic massive vector: it removes the timelike polarization from the variations and thereby the ghost. A second piece of machinery is the field-redefinition freedom $g'_{ab}=g_{ab}+(B-1)u_a u_b$, $u'^a=Bu^a$-normalized, which leaves the action in the same form with shifted couplings; it lets one choose a representative with $c_1+c_3=0$ so that any nonzero coupling is a genuine departure from general relativity, and it underlies the known special cases that reduce exactly to general relativity.","core_discovery":"The claim the review builds toward is that a generally covariant theory with a dynamical unit timelike vector — the action of Eq. (1), with four dimensionless couplings $c_1,c_2,c_3,c_4$ and a Lagrange multiplier enforcing $u^a u_a = 1$ — is a viable competitor to general relativity rather than a straw man. Three results carry that claim. First, the unit constraint means every variation of the æther is spacelike, so the usual ghost problem of a non-gauge vector field need not arise. Second, the static, spherically symmetric weak-field solution reproduces $g_{00}=1-2U_N+2U_N^2+...$ and $g_{ij}=(1+2U_N+...)$ with the same Eddington–Robertson–Schiff parameters as general relativity, so the theory is indistinguishable from it at that order. Third, the linearized spectrum around flat space contains two spin-2, two spin-1 and one spin-0 mode, each with its own speed set by the couplings, and the requirement of positive energy and stability restricts the couplings to a region — roughly $c_1>0$, $c_{14}>0$, $c_{123}>0$ for small couplings — that is far from empty. The review's stated purpose, per its abstract, is to report status and stress open questions rather than to announce a single new derivation.","pith_inferences":["If the extra spin-1 and spin-0 modes couple to ordinary matter only through the metric, their direct detection is hopeless at terrestrial scales, but their indirect signature in binary inspiral is a clean, mode-counting test that distinguishes this theory from general relativity without needing strong-field data.","The field-redefinition freedom suggests the four couplings overcount the physics: the space of physically distinct theories is the quotient by the rescaling, so a future constraint plot should be quoted in redefinition-invariant combinations rather than in raw $c_i$.","The caustic problem that kills the Maxwell-like special case ($c_1+c_3=0$, $c_2=c_4=0$) is a warning that any unit-vector theory whose frame is a pure gradient will form shocks; a useful diagnostic for the general theory is whether generic initial data drive $u_{[a}∇_b u_{c]}$ toward zero.","The paper's own admission that nonlinear energy positivity is unproven is the natural place for a numerical collapse study: evolving a spherical æther wave to see whether total energy stays positive would test the viability claim directly rather than by extrapolation."],"forward_implications":["If the theory is right, gravitational radiation from inspiraling binaries carries energy in five modes rather than two, including a monopolar 'trace' mode, so binary pulsar timing should show a modified inspiral rate that can be used to bound the couplings.","Cosmology is altered without new matter: the æther acts as a conserved fluid with $p=-ρ/3$ plus a shift of the gravitational constant, $G_{cosmo}=G/(1+(c_{13}+3c_2)/2)$, which the authors note is constrained by primordial helium abundance.","Black holes can exist with a regular horizon even though the æther cannot be invariant at a bifurcation surface, because the æther stress tensor need only stay regular there.","Because the spin-2 mode speed is $1/(1-c_{13})$, gravitational waves need not travel at the speed of light defined by the metric, which opens a route to constraints from gravitational Čerenkov emission by cosmic rays."],"supporting_citations":[{"why":"Establishes the Maxwell-like special case, its equivalence to Einstein–Maxwell plus charged dust, and the shock/caustic obstruction that motivates the general action.","marker":"[15]"},{"why":"Supplies the static post-Newtonian calculation showing the Eddington–Robertson–Schiff parameters agree with general relativity, and the asymptotic form of the spherical solution used for the energy argument.","marker":"[18]"},{"why":"Works out the linearized wave spectrum — the five modes, their speeds and polarizations in Table 1 — which is the backbone of the stability and positivity constraints.","marker":"[19]"},{"why":"Provides the Newtonian limit, the relation $G_N=G/(1-c_{14}/2)$, and the cosmological reduction to a rescaled gravitational constant plus a $p=-ρ/3$ fluid.","marker":"[13]"},{"why":"Gives the general relation between couplings under the metric field redefinition, which justifies choosing $c_1+c_3=0$ as the canonical representative.","marker":"[11]"},{"why":"Identifies the special parameter combination for which the theory is equivalent to general relativity by field redefinition, fixing the boundary of the genuinely distinct theories.","marker":"[10]"},{"why":"Analyses subluminality of the modes and the decoupling limit, and begins the study of cosmological perturbations and the CMB signature.","marker":"[14]"},{"why":"Supplies the gravitational Čerenkov bound on the difference between the maximum speed of cosmic rays and the speed of gravitational waves, used to constrain mode speeds.","marker":"[27]"},{"why":"Provides the Noether-charge computation of the æther contribution to total energy, Eq. (13), which underpins the total-energy result $E=(r_0/2G)(1-c_{14}/2)$.","marker":"[28]"},{"why":"Shows the Maxwell-like case admits negative-energy configurations, the objection the review must answer for the general theory.","marker":"[9]"}],"fun_headline_variants":["Einstein-Aether review: unit timelike vector means no usual ghost","Preferred rest frame, same solar-system numbers as general relativity","Abstract stresses open questions; review weighs Einstein-Aether against GR","No new derivation; review maps Einstein-Aether viability and constraints","Linearized spectrum: two spin-2, two spin-1, one spin-0 mode"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The viability verdict rests on linearized positivity and stability conditions carrying over to the full nonlinear theory; the authors state they cannot make a definite statement about nonlinear energy, so the extrapolation is theirs to make and is not established here.","fun_headline_variants_meta":{"raw":{"variants":["Einstein-Aether review: unit timelike vector means no usual ghost","Preferred rest frame, same solar-system numbers as general relativity","Abstract stresses open questions; review weighs Einstein-Aether against GR","No new derivation; review maps Einstein-Aether viability and constraints","Linearized spectrum: two spin-2, two spin-1, one spin-0 mode"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1985,"prompt_tokens":856,"completion_tokens":1129,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":1048}},"tokens_in":856,"tokens_out":1129,"duration_ms":19530,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":1048,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T16:36:22.916411+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"Compute the two preferred-frame post-Newtonian parameters $α_1$ and $α_2$ for generic couplings and compare with the measured limits of order $10^{-4}$ and $10^{-7}$; a value outside those bounds, or a binary-pulsar inspiral rate inconsistent with the five-mode energy loss, would rule the theory out for that parameter region.","supporting_citations":[{"cited_title":"Gravity with a dynamical p referred frame,","cited_arxiv_id":null,"evidence_quote":"Establishes the Maxwell-like special case, its equivalence to Einstein–Maxwell plus charged dust, and the shock/caustic obstruction that motivates the general action."},{"cited_title":"Static post-Newtonian equivalence of GR and gravity with a dynamical preferred frame","cited_arxiv_id":"gr-qc/0310044","evidence_quote":"Supplies the static post-Newtonian calculation showing the Eddington–Robertson–Schiff parameters agree with general relativity, and the asymptotic form of the spherical solution used for the energy argument."},{"cited_title":"Einstein-Aether Waves","cited_arxiv_id":"gr-qc/0402005","evidence_quote":"Works out the linearized wave spectrum — the five modes, their speeds and polarizations in Table 1 — which is the backbone of the stability and positivity constraints."},{"cited_title":"Lorentz-Violating Vector Fields Slow the Universe Down","cited_arxiv_id":"hep-th/0407149","evidence_quote":"Provides the Newtonian limit, the relation $G_N=G/(1-c_{14}/2)$, and the cosmological reduction to a rescaled gravitational constant plus a $p=-ρ/3$ fluid."},{"cited_title":"Foster, to be published","cited_arxiv_id":null,"evidence_quote":"Gives the general relation between couplings under the metric field redefinition, which justifies choosing $c_1+c_3=0$ as the canonical representative."},{"cited_title":"Lorentz Violations and Euclidean Signature Metrics","cited_arxiv_id":"gr-qc/0307066","evidence_quote":"Identifies the special parameter combination for which the theory is equivalent to general relativity by field redefinition, fixing the boundary of the genuinely distinct theories."},{"cited_title":"Can We See Lorentz-Violating Vector Fields in the CMB?","cited_arxiv_id":"astro-ph/0407437","evidence_quote":"Analyses subluminality of the modes and the decoupling limit, and begins the study of cosmological perturbations and the CMB signature."},{"cited_title":"Lower Bound on the Propagation Speed of Gravity from Gravitational Cherenkov Radiation","cited_arxiv_id":"hep-ph/0106220","evidence_quote":"Supplies the gravitational Čerenkov bound on the difference between the maximum speed of cosmic rays and the speed of gravitational waves, used to constrain mode speeds."},{"cited_title":"Foster, unpublished","cited_arxiv_id":null,"evidence_quote":"Provides the Noether-charge computation of the æther contribution to total energy, Eq. (13), which underpins the total-energy result $E=(r_0/2G)(1-c_{14}/2)$."},{"cited_title":"Causality, shocks and instabilities in vector field models of Lorentz symmetry breaking","cited_arxiv_id":"gr-qc/0104103","evidence_quote":"Shows the Maxwell-like case admits negative-energy configurations, the objection the review must answer for the general theory."}],"review_version":1}