{"id":"6050357a-68f1-4fcc-b9e1-40336a03e6c3","arxiv_id":"2610.03495","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"On Carrollian target spaces with a homothetic kernel generator, the CW-gauged null string action equals the ILST action off shell, making the two theories classically equivalent.","lead":"This paper shows that on degenerate Carrollian target spaces admitting a homothetic structure, null string theory with Carroll-Weyl gauge symmetry reduces identically to the simpler ILST theory on the same target. The result links tensionless strings to black hole horizon geometry and to the recent null string holography program.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"Off-shell identity (3.8) is correct, but its force as 'ILST describes a null string' rests on the contested CW-gauged definition of NST; under the ILST-based definition the equivalence is vacuous by construction, so the iff (3.9) is definition-bound rather than definition-independent.","rationale":"The reader's weakest_assumption is the contested definition of NST, and I agree it is the single most load-bearing concern. My stress test independently confirms the off-shell identity S_NST = S_ILST (3.8): (3.7) is pure algebra under kernel alignment, (3.6) gives CW invariance under homothety, (3.10) shows the W-connection fully decouples, and the necessity direction of (3.9) via (3.12) is correct — separating terms by derivative order in X forces h_mu_nu K^nu = 0 then L_K h = 2h. Correctness risk on the central identity is genuinely low. The concern is that this identity's force as a statement about null string theory is contingent on the CW-gauged definition [16] contested by [13-15]; under the ILST-defined null string, the equivalence is vacuous by construction and (3.9) is unnecessary. The paper is internally disciplined: it honestly cites [13-15], narrows the claim in Sec 3.4 to 'locally classically equivalent within this normalized class,' and in Appendix A records the irregular quadratic constraint, the vanishing pulled-back presymplectic form, and the non-establishment of canonical degrees of freedom (b237, b278), so the abstract's claim (b4) that NST is 'well-defined and described by ILST' overstates what is established even within the paper's own framework. The shear-free homothetic restriction (K=fV, L_V h = (2/f)h) is a real scope limit, acknowledged. None of this is a mathematical flaw; together it keeps the verdict at CONDITIONAL. My concrete test targets whether (3.9) is definition-bound by rechecking the equivalence under the competing definition; nothing I found moves any element of the reader's verdict (UNCHANGED).","tokens_in":22594,"tokens_out":19387,"duration_ms":106601,"concrete_test":"Re-derive the necessity claim (3.9) and the equivalence (3.8) under the competing definition of null strings adopted in [13-15], namely the ILST action (3.1) on the Carrollian worldsheet with no CW connection and no requirement of off-shell CW invariance. If under that definition the two theories coincide by construction on every CTS and (3.9) never needs to be imposed, the paper's iff is specific to the CW-gauged definition and the headline significance collapses; if a nontrivial analogue of (3.9) survives, the classification generalizes beyond the preferred definition. This is a definitional stress test, not a re-derivation of a published theorem: it settles whether the paper's central condition is definition-bound or unavoidable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central algebra is sound and I verify it independently: with kernel alignment h_mu_nu K^nu = 0 the cross and quadratic W-terms in (3.7) drop out, so S_NST = S_ILST is a literal identity of functionals, and delta S_NST/delta W_a = 0 in (3.10) shows the CW connection is pure redundancy on these targets; L_K h = 2h then gives off-shell CW invariance via (3.6), and the necessity direction of (3.9) is argued correctly by splitting (3.12) into second-derivative and first-derivative terms in X. The load-bearing concern is the meaning of the theorem, not the algebra. The 'only if' in (3.9) — that ILST describes a null string only on homothetic-kernel targets — is derived as the condition for off-shell CW invariance of the ILST action, which is a requirement only under the authors' definition of NST as the CW-gauged theory ([16], contested in [13-15], cited honestly). Under the competing definition where null strings are given directly by the ILST action without the W-connection, the equivalence holds by construction on every CTS and (3.9) is never needed; the iff has no force outside the contested definition. The paper's own text confirms the scope is narrower than the abstract's (b4) 'well-defined and described by ILST': Sec 3.4 narrows to 'locally classically equivalent within this normalized class,' and Appendix A records the irregular quadratic constraint with vanishing pulled-back presymplectic form (A.6-A.7) and states the d-3 profile count does not establish canonical physical degrees of freedom (b237, b278). The shear-free homothetic restriction (3.9 with K=fV, L_V h = (2/f)h) excludes sheared Carrollian targets. These are acknowledged limitations, but together they make the headline claim definition-dependent and its physical content underdetermined, which is exactly why the verdict should remain CONDITIONAL.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"This paper studies the classical relation between two worldsheet actions on a Carrollian worldsheet with a Carrollian target space (CTS): the minimal null string theory (NST) of [16], defined by gauging 2d diffeomorphisms, Weyl and Carroll–Weyl (CW) scalings, and the ILST action, which lacks CW gauging. The main result, Eq. (3.8), is an off-shell algebraic identity: on a CTS (h,V) admitting a homothetic kernel generator K with L_K h = 2h and h_μν K^ν = 0, the CW-gauged NST action equals the ILST functional identically, because the cross and quadratic W terms drop out of Eq. (3.7); Eq. (3.9) states that homothety and kernel alignment are also necessary for the ILST action to be off-shell CW invariant, argued by splitting (3.12). The paper further constructs equivalence classes of such theories (Sec. 3.4), analyzes classical solutions (Sec. 3.5), studies beyond-minimal deformations via clock one-forms and connections (Sec. 4), gives a Schwarzschild-horizon example (Sec. 5), and records the irregular canonical structure in Appendix A.","tokens_in":22922,"tokens_out":9205,"duration_ms":59389,"significance":"If it holds, the result supplies a clean, checkable criterion — homothetic kernel alignment — for when minimal NST on a CTS reduces to ILST, with consequences for null string holography and horizon-probing strings. The central derivation is a genuine functional identity, not a fit: I verified independently that the W-terms drop out of (3.7) under h_μν K^ν = 0 and that the necessity direction of (3.9) follows from (3.12) by the stated integration-by-parts argument. The paper is also unusually candid: it cites the competing definition of null strings [13–15] honestly, narrows the equivalence to 'locally classically equivalent within this normalized class' (Sec. 3.4), and discloses that the d−3 profile count is not a canonical physical mode count (Sec. 5 and App. A). The main reservation is that the significance of the iff (3.9) is definition-bound: it has force only under the CW-gauged definition of NST from the authors' own [16], and under the ILST-based definition the equivalence is vacuous by construction.","major_comments":[{"comment":"The off-shell identity S_NST = S_ILST and the 'if and only if' in (3.9) are algebraically correct, but their physical force is contingent on the CW-gauged definition of NST from [16], a definition the manuscript itself records as contested in [13–15]. Under an alternative definition in which a null string theory is given directly by the ILST action (3.1) without gauging the CW connection W_a, equality (3.8) holds by construction on every CTS and the conditions (3.9) are never needed; the iff then has no content outside the authors' definition. The abstract's claim (b4) that NST 'is well-defined if the background admits a homothetic kernel generator and ... is described by the ILST theory' should state explicitly that 'well-defined' and 'described by' are relative to the CW-gauged definition of [16]. The paper's own Sec. 3.4 narrowing of the equivalence to 'locally classically equivalent within this normalized class' and the honest citation of [13–15] are commendable, but the abstract and Sec. 1 framing should match that narrowed scope.","section":"§3.3, Eqs. (3.8)–(3.12)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The manuscript repeatedly calls NST on homothetic-kernel CTS 'well-defined,' but its own constraint analysis in Appendix A.1 shows the theory is irregular: depending on the quadratic constraint by independent linear constraints changes its generated transformations, the pullback of the canonical two-form vanishes on the constraint surface (A.6–A.7), and ordinary Dirac counting is not justified. Consequently the 'd−3 physically independent configurations' stated in §3.5 and at the start of §5 are, by the authors' own caveat in [b237], not canonical physical degrees of freedom, and the radial profile variation of the periodic family (A.8) is asserted not to be generated by the displayed symmetries. The abstract and Sec. 1 framing of 'well-defined' should be reconciled with this irregularity, e.g., by stating that well-definedness is meant at the level of the off-shell gauge-invariant action, not of a regular canonical phase space; as written, the running 'well-defined' terminology overstates what the analysis establishes.","section":"Abstract (b4), §3.5, App. A.1","authors_acknowledge":"We note that this profile count does not establishd−3canonical physical degrees of freedom: the transverse momenta vanish on the real constraint surface and the quadratic constraint is irregular, as explained in Appendix A The above analyses can be, essentially verbatim, extended to generic Kerr or Reissner-Nordström black hole horizons, that we do not present here.","authors_acknowledge_p":0.85},{"comment":"For the principal beyond-minimal deformation, the ruled-clock term β(U·P + w)², the CW connection equation (4.21) eliminates w through (4.22) and returns exactly the β=0 minimal action; the paper states this honestly. Given that the leading nonminimal examples — the clock deformation and the kernel-flow-invariant connection — either reduce to the minimal theory or fall into the multiplier branch (with g_V = 0 from V^μ R_μν = 0 in (4.24) when ∇V = 0), the reader is left without a clear statement of what, if anything, survives as a genuinely new class of NST on CTS. A closing summary in §4 distinguishing the vacuous reductions (clock term, connection equation) from the surviving cases (such as the effective CTS Ĝ of (4.13) when g_V ≠ 0) would sharpen the section's contribution and prevent the discussion in Sec. 6 from implying more than the deformation analysis supports.","section":"§4, Eqs. (4.16)–(4.22)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The sentence 'Ddimensional Lorentzian manifolds, however, allow allow for codimension-1 null hypersurfaces' contains a duplicated 'allow allow'.","section":"§1, p. 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence 'In early 1990s the Isberg–Lindström–Sundborg–Theodoridis (ILST) work [6, 7] it was put in a more rigorous mathematical setting' is ungrammatical; suggest rewording, e.g., 'In the early 1990s the ILST work [6, 7] placed this in a more rigorous mathematical setting'.","section":"§1, p. 2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The passage '...which follows from the kernel identity h_μν V^ν = 0 alone. and LVh = (2/f)h.' contains a sentence fragment ('and LVh = (2/f)h') that should be attached to the preceding sentence or completed.","section":"§3.5, after Eq. (3.18)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The consistency relation λ = f̃ / (f(1 + f V(F))) is stated tersely; one clarifying sentence on how λ is determined (and on the role of the condition 1 + f V(F) ≠ 0) would make the equivalence-class construction easier to follow.","section":"§3.4, Eq. (3.16)","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The significance of the central equivalence rests entirely on the contested CW-gauged definition of NST introduced in the authors' own works [10–12, 16, 19]; under the competing ILST-based definition of [13–15], the equivalence is vacuous by construction. The citation of the opposition is honest and specific, which counts strongly in the paper's favor, but the abstract's headline claim (b4) still overstates the scope relative to what the paper itself concedes in Sec. 3.4 and Appendix A. The self-citation pattern is dense, though not improper given the subject matter. The editorial decision hinges on whether a careful, definition-relative statement of the result, with 'well-defined' tempered by the irregular-constraint analysis, is acceptable for JHEP; I believe it is, after the requested revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"The central algebraic claim is correct and the paper deserves a careful read. On a shear-free Carrollian target with homothety aligned with the kernel, h_mu_nu K^nu = 0 makes the W and cross terms drop out in (3.7), so S_NST = S_ILST off-shell, eq. (3.8). I verified this independently; it is a genuine identity, not a fit. The necessity argument (3.9), by integrating the delta-chi term by parts and requiring vanishing for arbitrary second derivatives of X, is sound. That off-shell decoupling, and the explicit kernel-alignment condition, are new relative to the prior ILST and null string papers. The paper is also honest about dissenting literature [13-15] instead of ignoring it, and it flags its own limitations clearly: Appendix A records the irregular quadratic constraint with vanishing pulled-back presymplectic form, and the authors state that the d-3 profile count does not establish canonical physical degrees of freedom (b237, b278). The horizon examples are described as geometric realizations, not as a dynamical sector (b242). That transparency is a genuine strength.\n\nThe soft spot is definitional. The paper defines null string theory as the CW-gauged theory from their earlier work [16]. Under that definition, the equivalence (3.8) is a substantive statement. But Lindström and others define null strings directly as the ILST action without gauging CW; on that definition the equivalence holds on every CTS by construction and the iff in (3.9) has no force. So the significance of the result is contingent on the disputed definition, and the paper itself narrows the abstract's claim in Sec. 3.4 to \"locally classically equivalent within this normalized class.\" Relatedly, the irregular constraint structure means the physical content is underdetermined: the authors acknowledge that the profile count does not yield canonical modes, and no independent argument is given that the remaining transverse profiles are gauge-inequivalent. These are acknowledged limitations, but they keep the paper's headline claim from being fully established.\n\nThis should go to a referee. The algebra is checkable, the scope is clearly stated, and the connection to the debated definition of NST is honest. The referee should press on whether the CW-gauged definition is the right one and whether the irregular constraint analysis can be upgraded to a physical statement about degrees of freedom. I would accept it conditionally, expecting the authors to either strengthen the interpretation or sharpen the conditional wording.","headline":"Clean off-shell identity, but its physical significance rests on a contested definition of null string theory; still worth a referee.","tokens_in":23718,"tokens_out":1984,"would_cite":false,"duration_ms":15458,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["11.25.-w"],"model":"deepseek/deepseek-v4-flash","headline":"On a Carrollian target space with a homothetic kernel generator, the CW-gauged null string action equals the ILST action identically off shell, and both conditions — kernel alignment and homothety — are necessary for the equality.","keywords":["null string theory","Carrollian worldsheet","Carrollian target space","Carroll-Weyl gauge symmetry","ILST tensionless string","homothetic kernel generator","shear-free Carrollian geometry","black hole horizon"],"falsifier":"Take an explicit shear-free homothetic CTS, such as $V=\\partial_u$, $h=e^{2u}q_{AB}(y)\\,dy^A dy^B$, $K=\\partial_u$ with $\\mathcal{L}_K h = 2h$, insert it into Eq. (3.12), and demand $\\delta_{\\chi} S_{\\rm ILST}=0$ for an arbitrary local parameter $\\chi(\\sigma)$ without using the field equations; the paper claims strict off-shell cancellation of the two terms in (3.12). Finding any kernel-aligned homothetic background on which $\\delta_{\\chi} S_{\\rm ILST}\\neq 0$, or any configuration where $S_{\\rm NST}-S_{\\rm ILST}$ is nonzero off shell, would falsify the equivalence.","tokens_in":23893,"feed_emoji":"🧵","tokens_out":7584,"duration_ms":46305,"temperature":0.7,"pith_summary":"This paper claims that null string theory (NST), the tensionless string whose worldsheet gauges diffeomorphisms, Weyl, and Carroll–Weyl (CW) scaling, coincides exactly with the older ILST tensionless string whenever it probes a Carrollian target space — a degenerate-metric 'zero signature' manifold — that admits a homothetic kernel generator. The equivalence is an off-shell identity: the gauged NST action and the ILST action are equal as functionals precisely when the homothety vector generating the CW transformation is aligned with the degenerate kernel direction and scales the metric by two, and each condition is necessary. This matters because it fixes when the disputed extra CW gauge symmetry of NST actually changes the classical physics, and it underpins the authors' null string holography picture in which strings probing black hole horizons are described as NST on Carrollian targets. The paper further shows the minimal theory is stable: adding a clock one-form, a ruling, or a flow-invariant connection does not create new bulk dynamics.","feed_headline":"Null strings and ILST coincide on Carrollian targets","feed_subtitle":"Gauging Carroll-Weyl scaling changes nothing when the target's degenerate metric admits a homothetic kernel.","key_machinery":"The load-bearing object is the Carroll–Weyl covariant derivative $D_a X^{\\mu} = \\partial_a X^{\\mu} + W_a K^{\\mu}$, where $K$ is the homothety vector and $W_a$ the CW gauge field. It does two jobs: the homothety condition $\\mathcal{L}_{K}h=2h$ makes the CW-gauged action (3.5) invariant under $\\delta_{\\chi} X^{\\mu} = \\chi K^{\\mu}$, $\\delta_{\\chi} V^{a}=-\\chi V^{a}$, and the kernel-alignment condition $h_{\\mu\\nu}K^{\\nu}=0$ makes every $W_a$-dependent term vanish from $h_{\\mu\\nu} D_a X^{\\mu} D_b X^{\\nu}$, so the connection decouples and the action collapses to the ILST functional.","core_discovery":"The central claim is that on a Carrollian target space $(h,V)$, whose metric $h$ is positive-semidefinite of rank $D-1$ with kernel spanned by $V$, the CW-gauged null string action $S_{\\rm NST}$ equals the ILST action $S_{\\rm ILST}$ identically off shell, Eq. (3.8), whenever the homothety vector $K$ obeys $h_{\\mu\\nu}K^{\\nu}=0$ (kernel alignment) and $\\mathcal{L}_{K}h=2h$ (homothety). Because the kernel is one-dimensional, a nonvanishing $K$ of this type is a rescaled kernel vector $K=fV$, which forces the background to be shear-free, $\\mathcal{L}_{V}h=(2/f)h$. Alignment makes the CW connection $W_a$ drop out of the kinetic term algebraically — its equation of motion is identically zero, so the reduced theory carries no secondary Gauss-law constraint — while homothety is precisely what guarantees the action is invariant under the local CW transformation. Conversely, the ILST action is CW-invariant off shell if and only if the same two conditions hold, so the reverse implication holds too: an ILST theory on a shear-free CTS is a null string theory exactly when it admits a homothetic kernel generator.","pith_inferences":["If the classical equivalence survives quantization, the distinction between null string theory and ILST would collapse precisely on homothetic Carrollian backgrounds, which would blunt the contested CW-gauging definition of NST: the extra gauge symmetry would be classically redundant exactly where the target is degenerate.","Because the physical phase space appears singular (zero transverse momenta, vanishing presymplectic form), the $d-3$ profiles may be best understood as boundary or bond data rather than bulk modes; testing that reading against the celestial and Carrollian holography dictionaries the authors invoke would sharpen the claim.","The shear-free homothety restriction is strong: generic Carrollian backgrounds carry shear and fail the equivalence. This predicts that any genuinely new null-string physics beyond ILST, should it exist, must come from shear or from homotheties not aligned with the kernel."],"forward_implications":["On any shear-free Carrollian target with a homothetic kernel generator, minimal null string theory and ILST are classically identical; gauging Carroll–Weyl scaling adds no new dynamics.","The CW connection is algebraically decoupled in the minimal theory: its equation of motion is identically zero and it generates no Gauss-law constraint, so it may be completely gauge-fixed away.","Quadratic clock or ruling couplings $\\beta\\,(U\\cdot P+w)^2$ do not create new bulk dynamics: the CW field equation fixes $w=-U\\cdot P$ and the $\\beta$-term drops out of the reduced action.","On a Schwarzschild-like horizon the reduced theory describes $d-3$ transverse profiles $\\theta^A(\\sigma)$ modulo $\\sigma$-reparametrization — a configuration count the paper explicitly declines to call a canonical mode count because transverse momenta vanish and the quadratic constraint is irregular.","Minimal NST/ILST theories on CTS backgrounds related by the rescalings (3.14)–(3.16) form equivalence classes, so not every such theory is physically distinct."],"supporting_citations":[{"why":"Supplies the contested definition of null string theory as requiring Carroll-Weyl scaling to be gauged, which the paper's central equivalence is relative to.","marker":"[16]"},{"why":"Supplies the ILST action that NST is shown to equal on Carrollian targets.","marker":"[7]"},{"why":"Motivates the study through null string holography and supplies the homothety condition $\\mathcal{L}_K g = 2g$ for CW invariance on generic targets.","marker":"[19]"},{"why":"Establishes that null strings carry Carroll-Weyl gauge symmetry, the property the paper's NST definition rests on.","marker":"[12]"},{"why":"The authors' consistency analysis of the null string literature, framing the CW symmetry as previously overlooked.","marker":"[10]"},{"why":"The competing treatment of (anti-)de Sitter null strings and Carroll-Weyl symmetry that contests the authors' definition of NST.","marker":"[13]"},{"why":"Supplies the framework of irregular constrained systems used to classify the singular phase space of the reduced theory.","marker":"[29]"},{"why":"The Carrollian geometry review the paper leans on for metricity, torsion, and connection facts.","marker":"[4]"}],"fun_headline_variants":["Homothetic kernel makes null strings and ILST identical","Null string theory equals ILST on shear-free Carrollian targets","CW-gauged null strings reduce to ILST with kernel alignment","When a Carrollian target admits homothetic kernel, NST is ILST"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The result rests on the authors' definition of null string theory as a theory in which Carroll–Weyl scaling is a gauge symmetry — a definition stated in their own prior work and explicitly contested by other groups (cited in the paper as refs [13–15]) — so if NST were instead defined as ILST without CW gauging, the equivalence would hold trivially by construction.","fun_headline_variants_meta":{"raw":{"variants":["Homothetic kernel makes null strings and ILST identical","Null string theory equals ILST on shear-free Carrollian targets","CW-gauged null strings reduce to ILST with kernel alignment","When a Carrollian target admits homothetic kernel, NST is ILST"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000164,"raw_usage":{"cost":0.000164248,"is_byok":false,"cost_details":{"upstream_inference_cost":0.000164248,"upstream_inference_prompt_cost":0.000115528,"upstream_inference_completions_cost":4.872e-05},"total_tokens":1204,"prompt_tokens":1030,"completion_tokens":174,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":256,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":97}},"tokens_in":1030,"tokens_out":174,"cost_source":"openrouter_usage","duration_ms":2856,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":97,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-05T03:43:30.145082+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"Take an explicit shear-free homothetic CTS, such as $V=\\partial_u$, $h=e^{2u}q_{AB}(y)\\,dy^A dy^B$, $K=\\partial_u$ with $\\mathcal{L}_K h = 2h$, insert it into Eq. (3.12), and demand $\\delta_{\\chi} S_{\\rm ILST}=0$ for an arbitrary local parameter $\\chi(\\sigma)$ without using the field equations; the paper claims strict off-shell cancellation of the two terms in (3.12). Finding any kernel-aligned homothetic background on which $\\delta_{\\chi} S_{\\rm ILST}\\neq 0$, or any configuration where $S_{\\rm NST}-S_{\\rm ILST}$ is nonzero off shell, would falsify the equivalence.","supporting_citations":[{"cited_title":"What is Classical Null String Theory?","cited_arxiv_id":"2609.04844","evidence_quote":"Supplies the contested definition of null string theory as requiring Carroll-Weyl scaling to be gauged, which the paper's central equivalence is relative to."},{"cited_title":"Classical and Quantized Tensionless Strings","cited_arxiv_id":"hep-th/9307108","evidence_quote":"Supplies the ILST action that NST is shown to equal on Carrollian targets."},{"cited_title":"Null String Holography, Null Strings Probe Projective Boundary of Their Target Spaces","cited_arxiv_id":"2609.10432","evidence_quote":"Motivates the study through null string holography and supplies the homothety condition $\\mathcal{L}_K g = 2g$ for CW invariance on generic targets."},{"cited_title":"Null Strings Gauged and Reloaded, I: Null Strings Have Carroll-Weyl Gauge Symmetry","cited_arxiv_id":"2605.25817","evidence_quote":"Establishes that null strings carry Carroll-Weyl gauge symmetry, the property the paper's NST definition rests on."},{"cited_title":"An Inconsistency in the Null Strings Literature: The Tale of an Overlooked Symmetry","cited_arxiv_id":"2605.12414","evidence_quote":"The authors' consistency analysis of the null string literature, framing the CW symmetry as previously overlooked."},{"cited_title":"(Anti-)De Sitter null strings and Carroll-Weyl symmetry","cited_arxiv_id":"2609.07765","evidence_quote":"The competing treatment of (anti-)de Sitter null strings and Carroll-Weyl symmetry that contests the authors' definition of NST."},{"cited_title":"Dynamical Structure of Irregular Constrained Systems","cited_arxiv_id":"hep-th/0302033","evidence_quote":"Supplies the framework of irregular constrained systems used to classify the singular phase space of the reduced theory."},{"cited_title":"Foundations of Carrollian Geometry","cited_arxiv_id":"2510.21651","evidence_quote":"The Carrollian geometry review the paper leans on for metricity, torsion, and connection facts."}],"review_version":1}