{"id":"a9dad323-4c15-4e7d-aa6f-4916fa0b4560","arxiv_id":"2610.37546","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Open Carroll-Weyl null strings have a reflected classical phase space whose boundary algebra is the boundary Carrollian conformal algebra extended by one weight-one current, with D-3 local embedding pairs.","lead":"Tensionless null strings in their full Carroll-Weyl form can now be treated as open strings with reflecting endpoints, at least for origin Dirichlet and linear mixed target gluings. This fixes an open endpoint problem and produces a boundary algebra with one extra current, relevant for Carrollian holography.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"No significant objection identified: the central claim is internally consistent within the explicitly stated smooth reflected domain, and the acknowledged exclusions are scope limits rather than hidden assumptions.","rationale":"The reader's conditional verdict rests on the smooth reflected domain and parity assumptions plus the uninspected companion package. The stress test found no internal flaw: the paper's own limiting statements — smooth reflected domain, exclusion of derivative-jump profiles, characteristic endpoints forced by the fold, restriction to the parity-compatible local diagonal-contact central class, and the open BRST analysis — are stated as conditions, and the central claim is scoped to them. The smooth-domain and parity premises are load-bearing, but they are explicit assumptions rather than unacknowledged gaps. No cited published result is misused, and no parameter fitting or circularity appears. The one unresolved item is external verification of the archived symbolic and analytic checks, so the reader's CONDITIONAL verdict remains appropriate without adjustment.","tokens_in":23100,"tokens_out":18765,"duration_ms":130194,"concrete_test":"Inspect and independently rerun the archived reproducibility package [39]: recompute the projected brackets (4.26) from the circle algebra (4.23) using the normalization factor in Eq. (4.25), re-evaluate the Jacobi identities of Appendix B.3, and verify the smooth right inverse for the gauge slice in Sec. 5.2 together with the symplectic pullback (5.39). If these reproduce exactly, the central claim is supported as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"No significant objection identified. The central claim is explicitly conditional: it asserts a classical reflected realization on a smooth domain with a fixed-point fold, an admissible target involution, fold-compatible connection parity, and an even CW parameter (Proposition 5, Eq. (4.13), Sec. 4.2). The paper states these as input assumptions and explicitly excludes derivative-jump profiles, endpoint-exchanging gluings, and non-null Neumann sectors. Within that domain, the differentiability checks in Appendix B.2, the projected bracket table (4.26), the half-interval symplectic normalization (4.25), the weak first-class closure (5.11), and the regular chart in Sec. 5.2 are mutually coherent; I found no circular step and no fitted parameter. The remaining residual uncertainty is external: the decisive symbolic checks and the smooth right inverse for the gauge slice are archived in the companion package [39], which could not be inspected here. That is a verification gap, not an identified error in the argument.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"The paper constructs a classical phase-space realization of the full Carroll–Weyl (CW) constraint system for open null strings on an interval, by reflecting the half-interval fields to a circle under a fixed-point fold equipped with a constant admissible target involution, fold-compatible connection parity (4.13), and an even CW parameter (Proposition 5, §4.2). Within this explicitly stated domain it claims: the reflected constraint functionals and the complete CW generator are differentiable; their Hamiltonian flows preserve the endpoint gluing; the constraint system is weakly first class on its regular part; the induced boundary algebra is the boundary Carrollian conformal algebra (BCCA) extended by one even weight-one CW current, with the O–P–A table (4.26); and the local embedding count equals the closed-theory value D−3 (5.18). It also exhibits an explicit regular four-dimensional chart realizing one odd canonical pair (§5.2), a separate solution family with nonzero conserved target-space boost charge and nondegenerate symplectic pullback (§5.3), and a displaced-Dirichlet affine cotangent lift with the edge-momentum shift (3.22). All excluded sectors—endpoint-exchanging gluings, derivative-jump profiles, non-null Neumann branches, and quantum/BRST analysis—are stated as such in the text.","tokens_in":23208,"tokens_out":39371,"duration_ms":418797,"significance":"If the claims hold, this is a meaningful step: it supplies the first classical open-string realization of the full CW constraint system, with a clean boundary-algebra statement (BCCA plus one weight-one current) and a preserved D−3 local count. I re-derived the load-bearing algebra directly from the in-text definitions and found it internally consistent: the projected table (4.26) follows from the parent table (4.23)–(4.24) via the projection (4.21) and the symplectic normalization (4.25); the closure identities (5.11) match the bulk brackets (B.2); the zero-mode identities (4.28) and the Appendix B.3 central-term analysis (including the coboundary character of the linear O–A term) are consistent; the reference solution of §5.2 satisfies C1 = C2 = C3 = 0 with the correct reflection parity and reduces to the canonical pair (φ, pφ); and the §5.3 family satisfies P² = 0, P·X = P·X′ = 0 with J01 = −πρq0 and pullback ΩS = dJ01 ∧ dζ (the apparent cosh(2ζ) discrepancy disappears once the contravariant-X / covariant-P index conventions are fixed).","major_comments":[{"comment":"The claim that the constructed patch is a genuine local chart of the reduced surface—i.e., that the gauge-fixing map admits a smooth right inverse in a neighborhood of the reference profile, with the 'finite map and endpoint proof'—is deferred to the companion package [39]. The in-text constraint-rank argument (the dF = 0 computation) and the explicit reduced pair (φ, pφ) are sufficient for the local count (5.18) and for the statement that a canonical pair is realized, but the local-surjectivity of the gauge map, which is what makes the patch a chart 'near the reference profile' in the manifold sense, rests on material not present in the manuscript. Since this is part of the main narrative's regularity claim, I ask that the lemma be stated (hypotheses, statement, and at least a proof sketch) in the text; the archive can retain the machine-checked details.","section":"§5.2, Proposition 5","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The expression 'p0ApA0' is typeset with ambiguous spacing; write p_{0A} p_0^A (or the equivalent with indices lowered/raised consistently) to make the contraction explicit. The same index-spacing issue recurs in (4.29)–(4.32).","section":"§4.4, Eq. (4.30)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence 'Here C_{i,0} denotes the average over the reflected circle' is stranded between the remark on zero-mode normalization and the Fourier-component display; it should be moved into the discussion that follows Eq. (4.30).","section":"§4.4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"At the reference profile the variation of the first gauge-slice condition is δX⁰ = 2fP⁰ = −2ρf (since P⁰ = −ρ), not +2ρf as written in the sentence before Eq. (5.22). The sign does not affect the invertibility conclusion, but the text should state the sign convention so the reader is not misled.","section":"§5.2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The displayed fields X^μ_0 and P_μ use, respectively, contravariant and covariant index conventions that are not stated. A sentence fixing the convention would prevent a reader from mis-deriving Eq. (5.33): I initially obtained ±ρq cosh(2ζ) before resolving the convention, and the correct value −ρq(σ) depends on reading P_μ as covariant while X^μ is contravariant.","section":"§5.3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract's 'full CW constraint system' is precise in context, but it should cross-reference the domain conditions of Proposition 5 (fixed-point fold, admissible involution, connection parity (4.13), even CW parameter) so that the conditional nature of the construction is visible already in the abstract.","section":"Abstract / §6","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The transformation law is typeset densely; separating the Jacobian factor |J|^{−1/2} from the derivative ratio ∂σ′^a/∂σ^b would improve readability. A similar formatting tightening would help (2.2) and (3.8).","section":"§2, Eq. (2.3)","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is self-contained for all claims except the smooth right inverse for the gauge slice and the symbolic audits, which live in the Zenodo archive [39]. If the journal cannot inspect the archive during review, the editorial decision can rest on the in-text derivations, which I checked directly and found consistent. The reference list is dominated by 2026 arXiv preprints, consistent with the pace of this subfield; I verified the quoted closed-CW bracket content internally from the text's own definitions, so no citation-propriety concern arises for the load-bearing tables."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"Quick take: the central claim holds up within the domain the authors state. The genuinely new content is the reflected interval realization — the third CW constraint extended to the boundary, the induced BCCA-plus-one-current algebra, and the D-3 local count. Table 1 is an accurate map of what is new relative to the two-constraint open ILST and the boundaryless closed CW treatments. I agree with the reader's CONDITIONAL verdict and moderate confidence, and the stress-test's \"no significant objection\" survived my own reading.\n\nWhat the paper does well: it states its domain as input rather than hiding it. Smooth fixed-point fold, admissible involution R^2=1 with R^T eta R=eta, fold-compatible connection parity, even CW parameter, and the exclusion of derivative-jump profiles are all explicit (Prop. 5, Sec. 4.2). I hand-checked several load-bearing pieces: the projected O-A bracket (4.26) with the direct interval computation, the zero-mode identities (4.28) under the circle-average convention, the affine-lift cancellation in App. C, and the boost-charge family in Sec. 5.3. The last one has index-convention traps (P is written lowered, then raised in the charge), but the displayed values in (5.33)-(5.39) are consistent once you raise with eta^{mu nu}. The differentiability of the C3 generator is clean: no spatial derivative, no boundary integration-by-parts problem, and the parity of beta = -V^1/V^0 makes the Hamiltonian endpoint term vanish.\n\nSoft spots, in proportion. First, several decisive items live in the Zenodo companion rather than the text: the explicit smooth right inverse for the gauge slice in Sec. 5.2 and the structure-constant audit. That is a verification gap, not an identified error, and it is the main reason confidence should stay moderate. A referee should actually run or at least inspect the package. Second, the central-extension section is explicitly restricted to parity-compatible local diagonal-contact terms; the paper says it is not a cohomology or BRST statement, and the quantum part is deferred. That is an honest partial result, not an overclaim. Third, the smooth reflected domain is load-bearing: a physical boundary condition that produces derivative jumps is outside the construction. The paper acknowledges this, and Prop. 2's vanishing of Carroll flow at non-characteristic endpoints of the minimal theory partially rounds out the picture.\n\nMy recommendation: send it to a serious referee. The math is checkable, the scope claims are honest, and the construction is a real step for the CW endpoint problem. The referee's main job is the companion package.","headline":"Solid, honest construction paper: the reflected CW boundary algebra and D-3 count hold inside the stated smooth domain, with the main open item being verification of the companion package.","tokens_in":23898,"tokens_out":20682,"would_cite":true,"duration_ms":129162,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek/deepseek-v4-flash","headline":"Open null strings can carry the full Carroll–Weyl constraint system to their endpoints on a reflected phase space, extending the boundary Carrollian conformal algebra by one weight-one current and restoring the closed-theory count D−3.","keywords":["Carrollian symmetry","open null string","Carroll–Weyl constraint","boundary Carrollian conformal algebra","constrained Hamiltonian system","boundary conditions","edge modes","reflected phase space"],"falsifier":"Two concrete checks would settle the central claim. First, evaluate the canonical half-interval Poisson bracket $\\{P_n, A_m\\}$ directly from the sine/cosine mode expansions of Appendix A: the paper's table (4.26) predicts $-2(P_{n+m} + P_{n-m})$, with the factor 2 fixed by the circle-to-half-interval normalization, so an independent evaluation giving any other coefficient would break the closing algebra. Second, search for a solution of the bulk equations with a non-characteristic endpoint ($n_a V^a \\neq 0$) and nonzero Carroll flow $Y^\\mu = V^a D_a X^\\mu$: Proposition 2 forbids it for a timelike D$p$ defect with natural tangential variations, so any explicit such solution would disprove the endpoint-selection claim.","tokens_in":27078,"feed_emoji":"🪞","tokens_out":2773,"duration_ms":176944,"temperature":0.7,"pith_summary":"Open (tensionless) null strings are the zero-tension limit of string theory, where the worldsheet becomes Carrollian and the full local symmetry is the Carroll–Weyl (CW) flow; the closed string gauges this consistently with three first-class constraints, but earlier open-string constructions keep only two, leaving the endpoint survival of the third in question. This paper claims the missing symmetry is not lost: on a phase space built by folding the interval across each endpoint and requiring smooth reflected extensions with parity fixed by a target-space involution, all three constraints are differentiable, their Hamiltonian flows preserve the boundary, and the system is weakly first class on its regular part, with a boundary algebra that extends the boundary Carrollian conformal algebra by one even weight-one CW current. The cost is a restricted domain—smooth fold-compatible data only—and the paper shows the restriction has real consequences: smooth folds force characteristic (null) endpoints, and non-characteristic endpoints of a timelike defect carry zero Carroll flow. On the paper's account, the open null string has the same local number of embedding pairs as the closed string ($D-3$), so boundary spectra of the full CW theory must be organized by the enlarged algebra.","feed_headline":"All three Carroll–Weyl constraints survive open null-string endpoints","feed_subtitle":"A smooth fold at each endpoint preserves the full constraint system and restores the closed string's local count D−3.","key_machinery":"The load-bearing object is the reflected phase space: fields and variations on the half-interval $[0,\\pi]$ with smooth extensions to the circle whose parity is fixed by an admissible target involution $R$—an isometric reflection, $R^2 = 1$, $R^T\\eta R = \\eta$—plus fold-compatible auxiliary data ($W^1(-\\sigma) = -W^1(\\sigma)$, even CW parameter). With these parities the constraint densities $C_1 = P^2$, $C_2 = P\\cdot D_1 X$ and $C_3 = P\\cdot X$ become even, odd, and even respectively, and the circle modes fold into the reflection-invariant generators $O_n = \\tfrac12(L_n - L_{-n})$, $P_n = \\tfrac12(M_n + M_{-n})$, $A_n = \\tfrac12(S_n + S_{-n})$ of Eq. (4.21). The central identity is the projected bracket table (4.26), evaluated with the half-interval normalization $\\{\\iota^*F, \\iota^*G\\}_I = 2\\{F,G\\}_{\\mathrm{circle}}\\big|_R$: its O–P sector is exactly the boundary Carrollian conformal algebra, and the bracket $[O_n, A_m] = -m A_{n+m} + m A_{n-m}$ gives $A_n$ weight one. Differentiability and flow preservation are carried by the improved CW generator $G[\\chi] = \\int_0^\\pi d\\sigma\\,(\\chi C_3 - \\chi\\Pi^a V_a - (\\partial_a\\chi) Q^a)$ of Eq. (5.12), whose primary-momentum terms act on the auxiliary fields so that no boundary term obstructs variations on the reflected domain.","core_discovery":"The central result is a classical interval realization of the full Carroll–Weyl constraint system on a smooth reflected phase space, stated for open CW null strings with Dirichlet conditions at the target origin or linear mixed target gluings. The construction folds the half-interval across each endpoint by $\\sigma \\to -\\sigma$ and requires fields and variations to extend smoothly to the circle with parity fixed by an admissible target involution $R$ ($R^2 = 1$, $R^T\\eta R = \\eta$), with fold-compatible connection parity $W^1(-\\sigma) = -W^1(\\sigma)$ and an even CW parameter. In this domain the three constraint densities $C_1 = P^2$, $C_2 = P\\cdot D_1 X$ and $C_3 = P\\cdot X$ have definite parities (even, odd, even), the reflected mode functionals $O_n$, $P_n$, $A_n$ are differentiable, their Hamiltonian flows preserve the gluing, and the system is weakly first class on its regular part. The projected bracket algebra closes with the O–P sector reproducing the boundary Carrollian conformal algebra and $A_n$ acting as an even weight-one current, leaving $D-3$ local embedding pairs—the same count as the closed theory. The construction also determines its own boundary kinematics: the smooth fold forces $n_a V^a = 0$ at both endpoints, a non-characteristic endpoint of a timelike defect has vanishing Carroll flow, and a displaced Dirichlet endpoint requires a canonical affine lift in which the edge momentum shifts by twice the integrated bulk momentum. Two explicit four-dimensional sectors exhibit the regular part: a mixed gluing that reduces to one canonical field pair, and a separate solution family carrying a nonzero conserved target-space boost charge with nondegenerate symplectic pullback.","pith_inferences":["The endpoint-selection results suggest a general diagnostic for Carrollian boundary problems: whenever the bulk equations are first-order transport along a Carroll flow, a non-characteristic boundary condition that leaves the flow free will typically force the flow to vanish at the boundary; applying the same argument to null p-branes or Carroll D-branes could identify which of their endpoint cond","The edge-momentum shift in the affine lift, $\\pi_{I,R} = \\pi_I + 2\\int_0^\\pi P_I\\,d\\sigma$, is a boundary-mode/bulk-momentum mixing of the same type as edge-mode constructions in gauge theory and gravity; a testable extension is to close the algebra of the integrated invariant $\\hat{U}_0 = \\int_0^\\pi d\\sigma\\,P\\cdot X + \\hat{b}\\cdot\\pi$ with the edge pair $(\\hat{b}, \\pi)$, which the paper identifi","Because the classical central terms vanish in the restricted class, the quantum question is now well posed: if a future BRST analysis does find an anomaly, it must come from normal ordering, ghost zero modes, or nonlocal cocycles rather than from the classical bracket table, and the weight-one current $A_n$ is the natural place for a quantum correction to appear.","The identity gluing $R = \\mathbb{1}$ is presented as the minimal completion of the null boundary sector, with no uniqueness claim; a dynamical boundary-state calculation deciding which admissible gluing a particular null defect selects would determine whether the $D-3$ count and the $A_n$ current are universal across gluings or special to the reflected class."],"forward_implications":["The boundary symmetry algebra of the fully gauged open null string is not the bare boundary Carrollian conformal algebra: it is BCCA extended by one even weight-one current $A_n$, so spectra, vertex operators, and boundary states built on the two-constraint algebra are incomplete for the full CW theory.","The closed-theory local count $D-3$ survives the boundary: the two-constraint open theory's count $D-2$ is specific to the ungauged description, and the third constraint removes exactly one more canonical pair without needing new boundary degrees of freedom.","The smooth fold selects characteristic endpoints ($n_a V^a = 0$ at both endpoints), and in the minimal theory a non-characteristic endpoint of a timelike defect has vanishing Carroll flow; a nonzero-flow endpoint therefore requires a different gluing or added boundary structure.","A displaced Dirichlet endpoint must be promoted to a boundary field: the canonical affine lift forces the edge momentum to shift by twice the integrated bulk momentum ($\\pi_{I,R} = \\pi_I + 2\\mathcal{P}_I$), and preserving the original local constraint surface additionally requires $T \\approx 0$.","Within the parity-compatible local diagonal-contact class of central terms, the reflected algebra has no independent central extensions—the O–P and P–A terms vanish and the O–A term is a coboundary—with the paper's own caveat that this is a classical restricted statement, not a quantum anomaly or BRST result."],"supporting_citations":[{"why":"Diagnoses the overlooked local volume-preserving symmetry of null strings, motivating the third Carroll–Weyl constraint whose survival at open endpoints is the paper's central question.","marker":"[2]"},{"why":"Supplies the closed CW three-constraint system, the connection term, and the bulk bracket table that the paper adapts to the interval and projects through the reflection.","marker":"[3, 4]"},{"why":"The ILST action realizing worldsheet diffeomorphisms and common Weyl scaling, the starting point whose CW gauging the open-string construction must preserve.","marker":"[7]"},{"why":"The ungauged open null-string construction with two bulk constraints and the boundary Carrollian conformal algebra; the reflected O–P sector reproduces this algebra and adds one current.","marker":"[12]"},{"why":"Defines the boundary Carrollian conformal algebra (BCCA), the O–P sector that the reflected algebra extends.","marker":"[13]"},{"why":"Closed-string BRST/central-extension analysis whose Weyl–BMS classes are compared in Appendix B.3 and shown not to descend as independent boundary extensions in the restricted classical class.","marker":"[23]"},{"why":"Edge-mode construction in gauge theory, the model for promoting a displaced Dirichlet position to a boundary field with conjugate momentum.","marker":"[32]"},{"why":"The standard Dirac–Bergmann constrained-Hamiltonian algorithm used to derive the three secondary constraints and establish weak first-classness on the regular part.","marker":"[41, 42]"},{"why":"The requirement that Hamiltonian generators on a phase space with boundaries have well-defined variations and flow-preserving boundary conditions, used to build the differentiable CW generator.","marker":"[43, 44]"}],"fun_headline_variants":["Reflected folds let every Carroll–Weyl constraint survive open endpoints","All Carroll–Weyl constraints close on reflected open null-string phase space","Open Carroll–Weyl null strings hold the full constraint algebra at endpoints","Endpoint reflection preserves all three Carroll–Weyl constraints and D-3 count","Reflected phase space restores closed-string constraint count for open null strings"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The load-bearing premise is the smooth reflected domain itself: every field and variation in the construction must have a smooth reflected extension to the circle with parity fixed by an admissible target involution, so profiles with derivative jumps at the endpoint are excluded and the connection must obey the fold-compatible parity $W^1(-\\sigma) = -W^1(\\sigma)$; any physical boundary condition that produces derivative jumps, odd connection parity, or an endpoint-exchanging gluing sits outside the construction, and the reflected algebra, differentiability, and $D-3$ count do not apply to it.","fun_headline_variants_meta":{"raw":{"variants":["Reflected folds let every Carroll–Weyl constraint survive open endpoints","All Carroll–Weyl constraints close on reflected open null-string phase space","Open Carroll–Weyl null strings hold the full constraint algebra at endpoints","Endpoint reflection preserves all three Carroll–Weyl constraints and D-3 count","Reflected phase space restores closed-string constraint count for open null strings"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000142,"raw_usage":{"cost":0.0001421602,"is_byok":false,"cost_details":{"upstream_inference_cost":0.0001421602,"upstream_inference_prompt_cost":3.69642e-05,"upstream_inference_completions_cost":0.000105196},"total_tokens":1757,"prompt_tokens":1179,"completion_tokens":578,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":966,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":491}},"tokens_in":1179,"tokens_out":578,"cost_source":"openrouter_usage","duration_ms":8593,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":491,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-28T03:32:30.454827+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"Two concrete checks would settle the central claim. First, evaluate the canonical half-interval Poisson bracket $\\{P_n, A_m\\}$ directly from the sine/cosine mode expansions of Appendix A: the paper's table (4.26) predicts $-2(P_{n+m} + P_{n-m})$, with the factor 2 fixed by the circle-to-half-interval normalization, so an independent evaluation giving any other coefficient would break the closing algebra. Second, search for a solution of the bulk equations with a non-characteristic endpoint ($n_a V^a \\neq 0$) and nonzero Carroll flow $Y^\\mu = V^a D_a X^\\mu$: Proposition 2 forbids it for a timelike D$p$ defect with natural tangential variations, so any explicit such solution would disprove the endpoint-selection claim.","supporting_citations":[{"cited_title":"An Inconsistency in the Null Strings Literature: The Tale of an Overlooked Symmetry","cited_arxiv_id":"2605.12414","evidence_quote":"Diagnoses the overlooked local volume-preserving symmetry of null strings, motivating the third Carroll–Weyl constraint whose survival at open endpoints is the paper's central question."},{"cited_title":"Classical and Quantized Tensionless Strings","cited_arxiv_id":"hep-th/9307108","evidence_quote":"The ILST action realizing worldsheet diffeomorphisms and common Weyl scaling, the starting point whose CW gauging the open-string construction must preserve."},{"cited_title":"Boundary Carrollian CFTs and Open Null Strings","cited_arxiv_id":"2409.01094","evidence_quote":"The ungauged open null-string construction with two bulk constraints and the boundary Carrollian conformal algebra; the reflected O–P sector reproduces this algebra and adds one current."},{"cited_title":"On the boundary Carrollian conformal algebra","cited_arxiv_id":"2508.21603","evidence_quote":"Defines the boundary Carrollian conformal algebra (BCCA), the O–P sector that the reflected algebra extends."},{"cited_title":"BRST quantization of Carroll-Weyl gauged null strings","cited_arxiv_id":"2608.02731","evidence_quote":"Closed-string BRST/central-extension analysis whose Weyl–BMS classes are compared in Appendix B.3 and shown not to descend as independent boundary extensions in the restricted classical class."},{"cited_title":"Local subsystems in gauge theory and gravity","cited_arxiv_id":"1601.04744","evidence_quote":"Edge-mode construction in gauge theory, the model for promoting a displaced Dirichlet position to a boundary field with conjugate momentum."}],"review_version":1}