{"id":"36be3248-c881-4906-a0d6-e9ec41e87f26","arxiv_id":"2603.07081","paper_version":3,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Single real scalars minimally coupled to a Carrollian connection and invariant under supertranslations cannot propagate on-shell.","lead":"On the Carrollian plane, any first-order single-scalar theory that is minimally coupled to a Carrollian connection and invariant under supertranslations has zero momentum density and static energy on-shell, so its fields are frozen and cannot propagate. This no-go result redirects attempts to build propagating Carrollian physics toward multi-field, higher-derivative, or non-minimal models.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sec. 2.4's supertranslation argument assumes an active symmetry of the fixed-background action; this fails for magnetic/mixed Lagrangians, and the paper's own Example 2.3 (A=0, wave equation) contradicts the claimed P=0.","rationale":"The reader's weakest assumption identifies the same general area: the supertranslation current argument requires supertranslations to be genuine symmetries of the action. I agree that this is the load-bearing point. However, the concern is not merely an unverified assumption: it fails explicitly, and the failure is visible inside the paper's own Example 2.3. With A=0, the mixed Lagrangian L=1/2 y_t^2-1/2 ŷ_x^2 produces the standard wave equation, admits the solution ϕ=sin(t-x), and yields P=-∂_tϕ∂_xϕ≠0. This is a direct counterexample to the central no-go statement for the class (2.6), unless one imposes the additional requirement that supertranslations be active symmetries of the fixed-background action—which, for magnetic/mixed Lagrangians, they are not. The temporal-translation part of the Noether analysis (2.10) is sound, but the step d(fJ)=0 for all f is not justified. Because the main title claim 'single Carrollian scalars cannot propagate' is contradicted by the paper's own allowed theory, the verdict should move from CONDITIONAL to REJECT for the central claim, while acknowledging that a restricted electric-type statement may survive.","tokens_in":8135,"tokens_out":28645,"duration_ms":272985,"concrete_test":"For Example 2.3 with A=0 and V=0, take the on-shell solution ϕ=sin(t-x) on a compact region and choose f(x)=x^2/2. Directly compute (jAϕ)*P=-∂_tϕ∂_xϕ=cos^2(t-x). Then d(f(jAϕ)*J)=τ∧df (jAϕ)*P=f'(x)P dt∧dx=x cos^2(t-x)dt∧dx, which is nonzero, contradicting Sec. 2.4's assertion that this vanishes for all smooth f. Equivalently, compute the off-shell variation of the action under δt=-εf(x), δϕ=εf∂_tϕ; for this Lagrangian δS≠0, showing the action is not invariant under active supertranslations with fixed A. Either computation decides the concern.","verdict_should_be":"REJECT","load_bearing_attack":"The load-bearing step is the claim in Sec. 2.4 that invariance under supertranslations t'=t-γf(x) gives d(f(jAϕ)*J)=τ∧df (jAϕ)*P=0 for every f, hence P=0 on-shell. This requires the fixed-background action S_A[ϕ]=∫τ∧dx L(ϕ,∂_tϕ,∇_xϕ) to be invariant under the active diffeomorphism Ψ_f(t,x)=(t-γf(x),x) with A held fixed. But Ψ_f^*τ=dt-[A(t-γf(x),x)+γf'(x)]dx, which equals τ=dt-A(t,x)dx only if A(t-γf(x),x)+γf'(x)=A(t,x). For arbitrary f this condition fails. The transformation law (2.5), A'=A-∂_x t', is a passive coordinate transformation of the connection, not an active symmetry of a fixed background. Thus supertranslations are not Noether symmetries of the general class (2.6). The paper's Example 2.3 makes this concrete: with A=0, V=0, L=1/2 y_t^2-1/2 ŷ_x^2 gives the wave equation ∂_t^2ϕ-∂_x^2ϕ=0, whose solution ϕ=sin(t-x) has P=-∂_tϕ∂_xϕ=cos^2(t-x)≠0. The claimed identity d(fJ)=f'P dt∧dx=0 for all f is simply false. Therefore the conclusion P=0 is not established for magnetic/mixed theories; the no-go theorem is contradicted unless restricted to electric-type Lagrangians, where P=0 is trivial.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs first-order scalar field theories on the Carrollian plane using jet-bundle geometry, with Lagrangians L(φ, ∂_t φ, ∇_x φ) minimally coupled to a Carrollian connection A. It claims that the extended Carroll group, including supertranslations t' = t − γ f(x), is a symmetry of these theories, and that Noether's theorem then forces the on-shell momentum density to vanish and the energy density to be static, thereby precluding propagation. The paper further states a higher-dimensional no-go theorem for minimally coupled single Carrollian scalars.","tokens_in":8583,"tokens_out":13615,"duration_ms":118694,"significance":"The jet-bundle construction is clearly presented, and the time-translation Noether current (2.9) and its continuity equation (2.10) are correct. If the supertranslation no-go result were valid, it would sharpen the electric/magnetic dichotomy and justify the need for extra structure (multi-fields, higher derivatives, or non-minimal couplings) in propagating Carrollian theories. The paper also provides explicit examples that are instructive. However, the central claim is not established: the supertranslation argument rests on an invalid identification of passive coordinate invariance with active Noether symmetry, and the paper's own mixed-type example contradicts the claimed P = 0 result. As it stands, the advertised conclusion is not supported.","major_comments":[{"comment":"The step d(f (j_A φ)^* J) = τ∧df (j_A φ)^* P = 0 for all f requires f∂_t to be a symmetry of the fixed-background action S_A[φ] with A held fixed. This is false for arbitrary f: from (2.5), A' = A − (β + γ f'), so an active supertranslation changes A unless f' = 0 or A satisfies a special relation. The invariance of the Lagrangian density (2.6) under coordinate changes is a passive statement in which A transforms as well; it does not make the action S_A[φ] invariant. Consequently the 'need only multiply the expression by f' passage does not follow from Noether's theorem, and P = 0 is not established for magnetic/mixed Lagrangians.","section":"§2.4, Eq. (2.10)"},{"comment":"The paper's own mixed-type Lagrangian L = ½ y_t² − ½ ŷ_x² − V(y) with A = 0 and V = 0 gives the wave equation ∂_t² φ − ∂_x² φ = 0. The solution φ = sin(t − x) has P = ∂_t φ ∂L/∂ŷ_x |_{j_A φ} = cos²(t − x) ≠ 0. This directly contradicts the §2.4 claim that (j_A φ)^* P = 0 for every solution. Since this example is explicitly presented as a legitimate member of the constructed class, the no-go theorem is false as stated for magnetic/mixed theories.","section":"Example 2.3"},{"comment":"The displayed Euler–Lagrange equation is missing the term −F ∂L/∂(∇_x φ), with F = ∂_t A, which arises when the A∂_t part of ∇_x is integrated by parts. The correct equation is EL = ∂_φ L − ∂_t L_{∂_t φ} − ∇_x L_{∇_x φ} − F L_{∇_x φ} = 0. The examples in §2.4 implicitly use this corrected form (their F terms have the corresponding signs), so the displayed equation should be fixed.","section":"§2.3, Eq. (2.8)"}],"minor_comments":[{"comment":"The title contains a spacing typo: 'PROP AGATE' should be 'PROPAGATE'.","section":"Title"},{"comment":"'Forbenius condition' should be 'Frobenius condition'.","section":"§2.2"},{"comment":"'The continuity equation ... is is the closure' contains a duplicated 'is'.","section":"§2.4"},{"comment":"The higher-dimensional no-go theorem is stated without proof. The 2D argument does not automatically generalize: the supertranslation algebra and the connection transformation law in higher dimensions require a separate derivation. As a central advertised result, this should be proved or explicitly labeled as a conjecture.","section":"§3, No-Go Theorem"},{"comment":"The Aside treating A as dynamical is a different theory from the fixed-background minimal coupling used elsewhere. The condition δS/δA = 0 does not rescue the fixed-background no-go claim; the manuscript should distinguish these two frameworks explicitly.","section":"§2.4, Aside"}],"recommendation":"reject","confidential_remarks":"The core theorem is contradicted by the manuscript's own Example 2.3, and the Noether argument fails because supertranslations are not symmetries of the fixed-background action for magnetic/mixed theories. This is a load-bearing error that cannot be fixed by local edits within the current scope. A substantially revised manuscript that correctly distinguishes passive coordinate invariance from active symmetries, and that restricts the no-go claim to genuinely supertranslation-invariant fixed backgrounds or to electric-type theories, might be viable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The paper's construction is genuinely nice: using a Carrollian connection to build first-order scalar Lagrangians on the plane, and requiring independence from spacetime coordinates, gives a broad class of theories that are covariant under the extended Carroll group in a passive sense. The Noether current for time translations is computed correctly, and the continuity equation (2.10) is fine. That is real content.\n\nBut the headline result does not survive scrutiny. In Sec. 2.4 the author claims that because the theory is invariant under supertranslations, the current fJ is conserved for every f, giving τ∧df P = 0 and hence P = 0. This assumes the action is invariant under the active diffeomorphism t → t - γ f(x) with the background A held fixed. It isn't. The transformation law (2.5) shows that A changes to A - ∂_x t' under the coordinate change; the invariant coframe τ = dt - A dx is preserved only if A is transformed at the same time. For a fixed background, a generic supertranslation is not a symmetry unless A(t-γf(x),x)+γf'(x)=A(t,x), which is a very restrictive condition. The paper's own Example 2.3 with A=0 makes this precise: L = 1/2 y_t^2 - 1/2 ŷ_x^2 yields the wave equation ∂_t^2 φ - ∂_x^2 φ = 0, and the solution φ = sin(t-x) has P = - (∂_t φ)(∂_x φ) = cos^2(t-x) ≠ 0. That directly contradicts the claim that P=0 for all solutions. So the no-go theorem is not true as stated.\n\nThere are also smaller correctness issues. Eq. (2.8) in the EL equation is missing a -F ∂L/∂(∇_x φ) term; the worked examples require that term, and Example 2.4 has the F term with the opposite sign. The higher-dimensional theorem is asserted without proof, so that is also unsupported.\n\nWhat is worth keeping? The jet-bundle framework, the observation that passive extended Carroll covariance forces the Lagrangian to be of the form L(y, y_t, ŷ_x), and the correct time-translation continuity equation. If the author restricts the theorem to backgrounds for which the supertranslation is an active symmetry, or weakens the claim to electric-type Lagrangians, the result becomes trivial or much narrower.\n\nMy verdict: this deserves a serious referee, but not because the main theorem is sound. It deserves one so that the active/passive issue is caught clearly, and so the author has a chance to reframe the paper around what actually holds. I would not cite the no-go claim in my own work. It is a useful cautionary example about how easy it is to confuse coordinate transformations with symmetries in a background field theory.","headline":"Neat jet-bundle framework, but the central no-go theorem is spoiled by a symmetry mistake — the paper's own A=0 example propagates, so P=0 is false.","tokens_in":9005,"tokens_out":10636,"would_cite":false,"duration_ms":95723,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["70G45","70S10","81R10"],"pacs":[],"model":"deepseek-v4-flash","headline":"Supertranslations force the on-shell momentum density to vanish, so single minimally coupled Carrollian scalar fields cannot propagate.","keywords":["Carrollian field theory","supertranslations","Noether current","momentum density","ultra-locality","jet bundles","no-go theorem","Carrollian plane"],"falsifier":"Check the conservation identity $d(fJ)=0$ for the flat mixed-type Lagrangian $L = 1/2 y_t^2 - 1/2 \\hat{y}_x^2$. The Euler–Lagrange equation $\\partial_t^2 \\phi - \\partial_x^2 \\phi = 0$ admits the non-static local solution $\\phi = \\cos(t-x)$, whose momentum density $P = -\\partial_t \\phi \\partial_x \\phi = \\cos^2(t-x)$ does not vanish. If this solution also satisfies $d(fJ)=0$ for all smooth $f$, the paper's conclusion is falsified; if not, the paper's identification of the supertranslation current is the point to scrutinise.","tokens_in":8052,"feed_emoji":"❄️","tokens_out":12644,"duration_ms":107495,"temperature":0.7,"texified_at":"2026-08-05T21:00:29.882840+00:00","pith_summary":"First-order scalar field theories defined intrinsically on the Carrollian plane are extremely flexible: the Lagrangian can be any function of the field and its temporal and covariant spatial derivatives. But if the action is required to be invariant under supertranslations — coordinate shifts $t' = t - \\gamma f(x)$ with arbitrary smooth $f$ — then the Noether current for these symmetries forces the momentum density to vanish identically on-shell and the energy density to be static. The paper proves this for all minimally coupled single scalars, so no choice of Lagrangian can produce propagating solutions. This establishes a no-go theorem: propagating intrinsic Carrollian field theories must involve additional structure beyond a single minimally coupled first-order scalar. The result matters because it redirects the search for Carrollian dynamics away from exotic Lagrangians and toward multi-field, higher-derivative, or non-minimally coupled models.","texify_model":"deepseek-v4-flash","texify_usage":{"total_tokens":7541,"prompt_tokens":872,"completion_tokens":6669,"prompt_tokens_details":{"cached_tokens":0},"prompt_cache_hit_tokens":0,"prompt_cache_miss_tokens":872,"completion_tokens_details":{"reasoning_tokens":5821}},"feed_headline":"Carrollian scalars cannot propagate: supertranslations freeze momentum","feed_subtitle":"A new no-go theorem shows supertranslation invariance forces zero momentum and static energy, blocking wave solutions for single scalars.","key_machinery":"The central object is the Noether one-form for time translations, $J = dx E - \\tau P$, where $E = y_t \\partial L/\\partial y_t + \\hat{y}_x \\partial L/\\partial \\hat{y}_x - L$ is the energy density and $P = y_t \\partial L/\\partial \\hat{y}_x$ the momentum density, expressed in the invariant coframe defined by the clock form $\\tau = dt - dx A_t^x$. The argument multiplies this current by an arbitrary smooth function $f(x)$ to obtain the supertranslation current; on-shell conservation of $f J$ for every $f$ yields $\\tau \\wedge df P = 0$, hence $P = 0$ and $\\partial_t E = 0$. This mechanism — arbitrary smooth supertranslations forcing the spatial component of the Noether current to vanish — is what carries the no-go theorem.","core_discovery":"On the Carrollian plane ($R^2$ with degenerate metric $dx^2$ and kernel vector $\\partial_t$), consider any first-order scalar Lagrangian of the form $L(y, y_t, \\hat{y}_x)$ that is independent of spacetime coordinates and minimally coupled via a Carrollian connection. The paper shows that the Noether current for a temporal shift is $J = dx E - \\tau P$. Because supertranslations $t' = t - \\gamma f(x)$ are symmetries for every smooth $f$, the corresponding current is $f J$, and its on-shell conservation forces $d(f J) = \\tau \\wedge df P = 0$ for all $f$. Since $f$ is arbitrary, the momentum density $P$ must vanish identically on-shell; the continuity equation then forces the energy density $E$ to be static. Hence every solution is frozen: eithe","pith_inferences":["The obstruction is purely symmetry-driven and does not depend on the interaction potential, so it applies equally to free and interacting theories; a testable extension would be to check whether promoting the Carrollian connection to a dynamical field can evade the vanishing of the momentum density.","The argument uses the infinite-dimensional freedom in choosing f∈C^∞(R); on a compact spatial circle with only Fourier modes available, the conclusion would still hold by density, but a discrete symmetry group might weaken the obstruction — a possible analogue worth exploring.","Because supertranslations of this kind are the hallmark of asymptotically flat boundary symmetries, the same Noether-based obstruction may constrain attempts to couple Carrollian matter at null infinity; a non-minimal coupling to the boundary geometry might be required for propagating matter.","The dual Galilean statement suggests a new way to understand why the standard single-field Galilean-invariant wave equation cannot be real: its complex structure is not a convenience but a necessity forced by boost invariance."],"forward_implications":["On-shell, the momentum density vanishes and the energy density is static for every solution of every supertranslation-invariant single-scalar Lagrangian of the form (2.6).","Propagating (wave-like) solutions are impossible; any attempt to build a hyperbolic-like equation of motion results in solutions that are nevertheless frozen by the symmetry.","The electric/magnetic dichotomy of Carrollian limits persists in intrinsic theories: either the solutions are static (magnetic-type) or the Lagrangian is independent of the spatial covariant derivative (electric-type).","The no-go theorem generalises to higher-dimensional Carrollian manifolds with flat spatial metric and to the dual Galilean case, where it implies that a real single-scalar Galilean-invariant first-order theory cannot propagate — providing a geometric rationale for the necessity of complex wavefunctions in the quantum-mechanical wave equation.","To obtain propagating Carrollian field theories, one must go beyond minimal coupling of a single scalar: consider multiple fields, higher derivatives, or non-minimal couplings."],"fun_headline_variants":["Supertranslations freeze Carrollian scalars: no waves","Carrollian scalars can't propagate: supertranslations do it","Zero momentum, static energy: Carrollian scalars frozen","No-go: supertranslations block Carrollian scalar motion","Frozen by symmetry: Carrollian scalars can't travel"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The argument assumes that each supertranslation generated by $f(x)\\partial_t$ is a genuine symmetry of the action and that its Noether current is exactly $f$ times the temporal-shift current $J$, so that the on-shell conservation $d(f J)=0$ holds for every smooth $f$; if that identification fails, the conclusion $P=0$ does not follow.","fun_headline_variants_meta":{"raw":{"variants":["Supertranslations freeze Carrollian scalars: no waves","Carrollian scalars can't propagate: supertranslations do it","Zero momentum, static energy: Carrollian scalars frozen","No-go: supertranslations block Carrollian scalar motion","Frozen by symmetry: Carrollian scalars can't travel"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001072,"raw_usage":{"total_tokens":4289,"prompt_tokens":671,"completion_tokens":3618,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":415,"completion_tokens_details":{"reasoning_tokens":3533}},"tokens_in":415,"tokens_out":3618,"duration_ms":24642,"temperature":1.0,"reasoning_tokens":3533,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T18:38:43.303122+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Check the conservation identity $d(fJ)=0$ for the flat mixed-type Lagrangian $L = 1/2 y_t^2 - 1/2 \\hat{y}_x^2$. The Euler–Lagrange equation $\\partial_t^2 \\phi - \\partial_x^2 \\phi = 0$ admits the non-static local solution $\\phi = \\cos(t-x)$, whose momentum density $P = -\\partial_t \\phi \\partial_x \\phi = \\cos^2(t-x)$ does not vanish. If this solution also satisfies $d(fJ)=0$ for all smooth $f$, the paper's conclusion is falsified; if not, the paper's identification of the supertranslation current is the point to scrutinise.","supporting_citations":[],"review_version":2}