{"id":"af1efed3-6666-4d9f-b612-ab8a11a86f95","arxiv_id":"2508.03106","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Minimal Hořava gravity must be restricted to constant-mean-curvature slices to remove a pathological mode, and spherical dust-shell collapse shows its time-dependent sector has an ill-posed Cauchy problem.","lead":"An analysis of the last observationally viable slice of Hořava gravity, a Lorentz-violating competitor to general relativity, finds that a pathological mode forces the theory onto constant-mean-curvature slices, and that the time-dependent branch of this restricted theory fails to predict the future from initial data. The result matters because it further narrows, and may disqualify, the surviving parameter space of a long-studied modified gravity candidate.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's central no-go claim cannot be checked because the supplied full text is a different arXiv submission; the load-bearing Hamiltonian mode analysis is missing.","rationale":"The reader's weakest assumption correctly identifies the Hamiltonian mode analysis as the foundation of the paper's central claim. The supplied full text is a different arXiv submission, so that foundation cannot be inspected. The reader's UNVERDICTED verdict is therefore appropriate, and my stress-test does not move it. The load-bearing concern is not a specific technical flaw in the physics but the absence of the derivations needed to assess one: the necessity and sufficiency of the CMC condition and the claimed undetermined evolution after the shell's first contraction. These are exactly the points that would need to be checked if the correct manuscript were available. The proposed concrete test—re-deriving the mode analysis and the thin-shell solution from the actual text—would settle whether the concern lands. Until then, the claim remains unverified rather than refuted.","tokens_in":1595,"tokens_out":2604,"duration_ms":31219,"concrete_test":"Obtain the actual full text of arXiv:2508.03106. In the Hamiltonian formalism, expand the constraints to quadratic order around a homogeneous background and compute the dispersion relation of the extra scalar mode; verify that the high-frequency instability and low-frequency strong coupling appear exactly as claimed. Then test whether the constant-mean-curvature condition is both necessary and sufficient by counting independent constraint equations with and without CMC imposed. Finally, reproduce the thin-shell collapse solution step-by-step up to the shell's first contraction and check whether the subsequent evolution is actually undetermined or just not uniquely extended across the shell-crossing singularity. If any step fails, the m²Hg Cauchy-problem failure does not follow.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract's central conclusion—that m²Hg's time-dependent mean-curvature sector fails the Cauchy problem—rests on two claims: (1) eliminating a pathological mode forces the constant-mean-curvature restriction, and (2) after the first contraction of a thin dust shell, a spherical mode with undetermined evolution appears. Neither claim is inspectable from the supplied text: the full text is arXiv:2508.03108 (a cs.LG paper on out-of-distribution detection), not arXiv:2508.03106. In particular, there is no derivation of the Hamiltonian mode analysis, no dispersion relation for the would-be pathological mode, and no equation for the elliptic lapse or the shell matching conditions. The weakest point is the necessity/sufficiency of the CMC condition: the abstract asserts that eliminating the mode 'must' restrict to CMC slices, but without the constraint algebra one cannot tell whether CMC is a genuine requirement or merely a sufficient simplification. If the CMC condition is not strictly required, the 'minimal minimal' theory is not uniquely defined and the claimed Cauchy failure could be an artifact of the chosen restriction. This is not a disagreement with the physics; it is a statement that the evidence needed to verify the central claim is absent.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript, as evidenced by its abstract, claims a Hamiltonian analysis of minimal Hořava gravity (mHg), identifying a pathological mode whose elimination forces a constant-mean-curvature (CMC) restriction, yielding \"minimal minimal Hořava gravity\" (m²Hg). The paper then claims that the time-dependent mean-curvature sector has an elliptic lapse equation (infinite propagation speed) and that spherical collapse of a thin dust shell exhibits a spherical mode with undetermined evolution after first contraction, demonstrating a failure of the Cauchy problem. However, the provided full text is not the paper under review; it is a machine-learning paper on out-of-distribution detection (arXiv:2508.03108). None of the derivations, equations, or calculations on which the abstract's conclusions rest are available for inspection.","tokens_in":1797,"tokens_out":4392,"duration_ms":49893,"significance":"If the claims were correct, the paper would substantially narrow the viable sector of Hořava gravity and provide a concrete physical scenario (thin-shell collapse) where the theory's initial-value problem is ill-posed. That would be an important result for the quantum-gravity phenomenology community. The abstract states a clear, falsifiable prediction—failure of the Cauchy problem—that could be checked once the derivation is supplied. However, the significance cannot currently be assessed because the supporting technical content is absent; there are no machine-checked proofs, reproducible code, or derivations to verify.","major_comments":[{"comment":"The full text provided is arXiv:2508.03108, a cs.LG paper on out-of-distribution detection, not the gr-qc paper announced in the abstract. The manuscript therefore contains none of the Hamiltonian analysis, constraint algebra, dispersion relation, elliptic lapse equation, or thin-shell matching conditions on which the abstract's conclusions rest. Without these derivations, the central claim is unverifiable. This is a load-bearing omission that must be corrected before the paper can be refereed.","section":"Full text (mismatched manuscript)"},{"comment":"The abstract states that eliminating the pathological mode 'must' restrict the theory to constant-mean-curvature slices. This necessity claim requires a constraint-algebra computation showing that the pathological mode cannot be decoupled by any other means. If CMC is only a sufficient condition, the theory m²Hg is not uniquely defined, and the subsequent Cauchy-failure result could be an artifact of a particular restriction. The derivation must spell out the full mode content and the precise sense in which CMC is required.","section":"Abstract, claim on CMC restriction"},{"comment":"The conclusion that the thin-shell collapse exhibits a spherical mode with undetermined evolution after first contraction rests on the behavior of the elliptic lapse equation and the shell matching conditions. The supplied material contains no equations for these, so one cannot check whether the mode is physical, whether the ambiguity is a gauge artifact, or whether the matching conditions are imposed correctly. The paper should present these equations and the boundary/matching problem explicitly.","section":"Abstract, claim on Cauchy failure"}],"minor_comments":[{"comment":"The abbreviations mHg and m²Hg are defined in the abstract, but the reader would benefit from a one-sentence explanation of what 'minimal' means in terms of the parameter restrictions, rather than only the name.","section":"Abstract, notation"},{"comment":"The phrase 'instantaneously propagating spherical mode' is ambiguous: it could mean an infinite-speed mode, a zero-speed mode, or a mode whose speed is undefined. The paper should clarify this terminology and distinguish it from standard notions of instantaneous propagation in nonlocal theories.","section":"Abstract, propagation claim"},{"comment":"The claim that the time-independent-mean-curvature sector is 'equivalent to a particular foliation of GR with nonzero cosmological constant' needs a concrete statement of the dictionary between the Hořava parameters and the GR cosmological constant; as written, the equivalence cannot be checked.","section":"Abstract, GR equivalence"}],"recommendation":"major_revision","confidential_remarks":"This review is made difficult by an apparent submission error: the provided full text is a different arXiv submission (a cs.LG paper on out-of-distribution detection), not the Hořava-gravity paper announced in the abstract. I have assessed the material as submitted. The central claims are uninspectable, and the manuscript must be replaced with the actual paper before any technical evaluation can proceed. The recommendation of major revision is based on the need to provide the complete derivation and to address the specific necessity/sufficiency concerns about the CMC restriction and the Cauchy-failure argument."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know one thing before reading further: the full text attached to this review is not the Hořava gravity paper. It is arXiv:2508.03108, a cs.LG paper on out-of-distribution detection. So none of the claims in the abstract can be checked against a derivation. I can only speak to the abstract as a statement of results.\n\nWhat the abstract claims is coherent and, if true, important within modified gravity: the pathological mode forces a constant-mean-curvature restriction, the time-independent sector is equivalent to a foliation of GR with cosmological constant, and the time-dependent sector has an elliptic lapse, infinite speed, and a dust-shell collapse that leaves an undetermined mode after first contraction. These are concrete, checkable claims. The CMC condition is specific enough that a referee with the right machinery could verify necessity and sufficiency. The paper also does a good job of framing the remaining viable sector of the theory.\n\nThe soft spot is not a physics argument; it is a complete absence of evidence. The abstract asserts the mode and its pathologies, and asserts that CMC is necessary to eliminate it, but without the constraint algebra, dispersion relation, or shell matching conditions there is no way to tell whether CMC is genuinely required or merely sufficient. The stress-test note is right about that. The 'failure of the Cauchy problem' is also a strong claim; the abstract only sketches the post-contraction behavior.\n\nAs submitted, this is not a reviewable paper. The editor should return it and ask for the correct full text. If that text is supplied, the paper deserves a serious referee: the subfield is narrow but this would be an important no-go result, and the claims are specific enough to be falsified. I would not cite it or put it on the reading group until I see the Hamiltonian analysis. My verdict is unverdictable, not wrong.","headline":"The abstract describes an important-sounding no-go result for minimal Hořava gravity, but the supplied full text is a cs.LG OOD paper, so the load-bearing Hamiltonian derivation is missing and the paper cannot be evaluated as submitted.","tokens_in":2302,"tokens_out":2897,"would_cite":false,"duration_ms":32423,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The time-dependent sector of minimal Hořava gravity is ill-posed.","keywords":["Hořava gravity","constant mean curvature","Cauchy problem","thin-shell collapse","preferred foliation","Lorentz violation"],"falsifier":"A concrete calculation that would settle the claim is to construct two explicit solutions in the time-dependent sector of m²Hg that agree on a full spacelike slice before the dust shell contracts but diverge afterwards, satisfying all equations of motion; alternatively, a numerical evolution showing that the post-collapse spherical mode is uniquely fixed by the constraints and matching conditions would refute the claimed failure of the Cauchy problem.","tokens_in":1394,"feed_emoji":"","tokens_out":4597,"duration_ms":50734,"temperature":0.7,"pith_summary":"Minimal Hořava gravity must be further restricted to eliminate a pathological mode: the slices of the preferred foliation must each have constant mean curvature (CMC). The paper shows that the resulting theory, m²Hg, splits into two regimes. When the mean curvature is time independent, the theory is just a particular foliation of general relativity with a nonzero cosmological constant. When the mean curvature is time dependent, a thin-shell collapse calculation reveals an instantaneously propagating spherical mode with undetermined evolution, demonstrating a failure of the Cauchy problem. If this is correct, only the static sector of m²Hg is a viable gravitational theory.","feed_headline":"Time-dependent minimal Hořava gravity is ill-posed","feed_subtitle":"A collapsing dust shell leaves an undetermined instantaneous mode, so only the static sector survives.","key_machinery":"The argument rests on a Hamiltonian analysis of minimal Hořava gravity that identifies a pathological scalar mode, unstable at high frequencies and strongly coupled at low frequencies. Requiring constant mean curvature on every slice of the preferred foliation eliminates this mode, yielding m²Hg. In the time-dependent regime the lapse satisfies an elliptic equation, which is the mechanism producing instantaneous propagation. The thin-shell collapse model then serves as the probe that exposes the failure of uniqueness after the shell reaches a point.","core_discovery":"The central claim is that the time-dependent mean-curvature sector of minimal minimal Hořava gravity (m²Hg) has an ill-posed initial value problem. This is shown by studying the spherical collapse of a thin dust shell: the solution is uniquely determined from initial conditions until the shell first contracts to a point, after which an instantaneously propagating spherical mode appears whose evolution is not fixed by the data. Because the lapse is governed by an elliptic equation in this sector, information propagates at infinite speed, making the theory nonlocal and unpredictive.","pith_inferences":["The ill-posedness may not be limited to dust shells: any time-dependent configuration that develops a point-like focus might trigger the instantaneous undetermined mode, which could be tested with scalar-field collapse models.","The CMC condition might be interpreted as a gauge fixing that merely hides the pathological mode in this particular slicing, so the ill-posedness could resurface in other gauge choices.","If the time-independent sector is indeed equivalent to GR with a cosmological constant, then the nontrivial content of m²Hg is confined to the nonlocal, unpredictive sector, leaving little new physics that is both viable and predictive."],"forward_implications":["If the paper is correct, the only cleanly viable sector of m²Hg is the time-independent one, which is equivalent to a particular foliation of general relativity with a nonzero cosmological constant.","The time-dependent sector of m²Hg is nonlocal and unpredictive: its Cauchy problem fails, so generic dynamical processes cannot be uniquely evolved from initial data.","Observational constraints that pick out minimal Hořava gravity are not sufficient to make the theory predictive; the additional CMC restriction and the static condition are needed for a well-posed theory.","Attempts to use minimal Hořava gravity to model gravitational collapse in the dynamic regime will encounter this ill-posedness unless additional physical input or a different formulation is introduced."],"supporting_citations":[],"fun_headline_variants":["Time-varying minimal Hořava gravity is ill-posed","Dynamic minimal Hořava gravity has no well-posed Cauchy problem","Spherical collapse exposes ill-posedness in minimal Hořava gravity","Time-dependent sector of minimal Hořava gravity fails predictivity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the Hamiltonian mode analysis correctly identifies a pathological mode in minimal Hořava gravity and that imposing constant mean curvature is both necessary and sufficient to eliminate it.","fun_headline_variants_meta":{"raw":{"variants":["Time-varying minimal Hořava gravity is ill-posed","Dynamic minimal Hořava gravity has no well-posed Cauchy problem","Spherical collapse exposes ill-posedness in minimal Hořava gravity","Time-dependent sector of minimal Hořava gravity fails predictivity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000331,"raw_usage":{"total_tokens":1834,"prompt_tokens":928,"completion_tokens":906,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":544,"completion_tokens_details":{"reasoning_tokens":833}},"tokens_in":544,"tokens_out":906,"duration_ms":7976,"temperature":1.0,"reasoning_tokens":833,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T04:40:02.421715+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete calculation that would settle the claim is to construct two explicit solutions in the time-dependent sector of m²Hg that agree on a full spacelike slice before the dust shell contracts but diverge afterwards, satisfying all equations of motion; alternatively, a numerical evolution showing that the post-collapse spherical mode is uniquely fixed by the constraints and matching conditions would refute the claimed failure of the Cauchy problem.","supporting_citations":[],"review_version":1}