{"id":"3bb9ad26-22e1-443e-8133-caa9ddccba00","arxiv_id":"2610.38372","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"Running the Dirac-Bergmann algorithm on all nine classes of Newer General Relativity, the authors report physical degree-of-freedom counts between 4 and 10, with no first-class constraints in any class.","lead":"A Dirac-Bergmann constraint analysis assigns a physical degree-of-freedom count to each of nine parameter classes of Newer General Relativity, a five-parameter family of nonmetricity-based gravity theories. The counts decide which of these cosmological alternatives to general relativity carry ghost-like extra modes, so the table matters to anyone testing modified gravity against data.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"Type 1's own formulas are singular at the STEGR point: Eq. (18) satisfies Table I, but c1+c3=0 makes Eq. (44) divide by zero and makes π_i of Eq. (42) primary constraints, so Table II's 9-dof entry cannot cover the class it claims to determine.","rationale":"I read the central claim as a class-level statement: for each coefficient class in Table I, the Dirac-Bergmann chain terminates at the primary-plus-secondary level and Table II gives the definitive physical degree-of-freedom count. The reader's REJECT verdict is therefore appropriate, but the sharpest form of the problem is more specific than the delta-derivative truncation emphasized in the reader's weakest_assumption. The Type 1 analysis itself contains an algebraic singularity at the STEGR coefficients. Eq. (18) satisfies Table I's Type 1 conditions exactly, yet Eq. (42) shows that the coefficient of Ṅ_a in π_i is 2(c1+2c3), which vanishes at STEGR because c1+c3=0. Eq. (44) then divides by 2(c1+c3). So the paper's Type 1 treatment silently assumes c1+c3 ≠ 0 and does not cover the full Type 1 class. At the STEGR point, π_i is velocity-independent and therefore supplies three additional primary constraints, so the single-primary-constraint count used for Type 1 is already incorrect there. This is an internal inconsistency in the paper's own equations, not a disagreement with an external consensus. The external STEGR/GR equivalence, which the paper itself cites, then supplies the decisive check: that branch must propagate the two GR degrees of freedom, not the nine listed in Table II. The delta-derivative truncation acknowledged in b46, b47, and b105 remains a genuine concern, but it is explicitly deferred; the STEGR branch singularity is not acknowledged anywhere. Secondary issues also remain: Eqs. (65)-(66) drop the {σ_i, σ_j} bracket without argument, and the LU decompositions assume nonzero leading principal minors without mapping those conditions onto the coefficient parameter space. These reinforce the rejection but are not needed to establish the core problem. The paper deserves credit for its systematic per-type presentation, for using xAct, and for stating the delta-derivative limitation in the conclusions; none of that repairs the unhandled exceptional branch inside Type 1. Because the headline result is a definitive class-level table and the STEGR point is a counterexample to its Type 1 row, the appropriate verdict is REJECT. A revision that explicitly excludes or separately analyzes exceptional sub-branches such as c1+c3=0 could salvage a restricted version of the claim, but that is not the claim currently made.","tokens_in":44951,"tokens_out":7459,"duration_ms":51056,"concrete_test":"Run the check at the STEGR point without any delta-derivative truncation: set c1=-1/4, c2=1/2, c3=1/4, c4=0, c5=-1/2 in Eqs. (41)-(43), compute the Hessian rank with respect to (ṅ, ṅ_i, γ̇_ij), and count the primary constraints. The prediction from Eqs. (42) and (44) is that the rank drops by at least four (π_N and π_i all become velocity-independent), not by one as assumed for Type 1. Then run the Dirac-Bergmann chain for this branch, retaining all delta-derivative terms or with a covariant regulator; if the constraint algebra contains first-class Hamiltonian and momentum constraints and yields 2 pDoF, the Type 1 entry of Table II is refuted. If instead one wants to claim generic-branch validity only, the test is to state the additional condition c1+c3≠0 explicitly and re-derive Table II with all such exceptional sub-branches separated.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim (b22, b95) is that each of the nine classes has a definitive constraint count. The most load-bearing defect is not the acknowledged delta-derivative truncation (b46, b47) but an unacknowledged singularity inside the Type 1 analysis. The STEGR coefficients in Eq. (18), c1=-1/4, c2=1/2, c3=1/4, c4=0, c5=-1/2, satisfy the Type 1 conditions of Table I: c4 = -c1-c2+c3 = 0 and c5 = -2c3 = -1/2. Yet in the Type 1 momenta, Eq. (42) has coefficient (2c1+2c3) multiplying Ṅ_a, and at the STEGR point 2c1+2c3=0. The paper nevertheless inverts this relation in Eq. (44), dividing by 2(c1+c3). Consequently the whole Type 1 Dirac chain is derived only on the open submanifold c1+c3 ≠ 0, with a single primary constraint φ_N (Eq. 46). At the STEGR point, π_i no longer depends on any velocity, so π_i - f_i(N,γ,∂N,∂γ)=0 are three further primary constraints. The primary-constraint count (Table I) is already wrong there, and the subsequent algorithm cannot be applied. This is not a matter of disagreeing with a consensus: STEGR is dynamically equivalent to GR, and the cited geometric-trinity literature states that equivalence; a correct Hamiltonian analysis of this branch must find the two GR degrees of freedom, not the nine of Table II. The paper never mentions that Eq. (18) lies in Type 1 or that c1+c3=0 is an exceptional sub-branch. Because the headline table is a class-level statement with no caveat, this single branch failure invalidates the claim that the pDoF are determined unambiguously for Type 1, and by extension for the intersections that inherit the same exceptional conditions.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"The paper presents a Dirac–Bergmann Hamiltonian analysis of Newer General Relativity, a five-parameter quadratic nonmetricity theory, split into nine coefficient classes according to the rank of the kinetic Hessian. For each class the authors compute conjugate momenta, identify primary constraints, solve consistency conditions with LU decompositions of the Dirac matrices, and report the numbers of second-class constraints and physical degrees of freedom in Table II: 9, 7, 5, 4, 4, 7, 5, 4, 4, and 10 for Types 1–9. The stated conclusion (b95) is that the analysis determines unambiguously the physical degrees of freedom of each class, and the paper explicitly acknowledges that spatial derivatives of the Dirac delta distribution are neglected throughout (b46, b47, b105).","tokens_in":45363,"tokens_out":3728,"duration_ms":27851,"significance":"If the class-level constraint counts were correct, the paper would fill a real gap: a systematic Hamiltonian treatment of the nine Hessian-types of Newer GR, with explicit secondary-constraint chains and multiplier solutions. The systematic enumeration of cases, the use of smeared constraints, and the candid statements about the delta-derivative truncation are commendable features, as is the proposed future test retaining the neglected terms. However, the central claim is not established. The Type 1 analysis breaks down precisely on the STEGR subbranch, the delta-derivative truncation is load-bearing for the first/second-class split rather than a harmless boundary regularization, and the secondary-secondary Poisson brackets are dropped without proof. The headline Table II therefore cannot be regarded as a definitive determination of the degrees of freedom for all nine classes.","major_comments":[{"comment":"The Type 1 analysis is singular on the STEGR sub-branch without the paper acknowledging it. The coefficients of Eq. (18), c1=-1/4, c2=1/2, c3=1/4, c4=0, c5=-1/2, satisfy the Type 1 conditions of Table I, c4=-c1-c2+c3 and c5=-2c3. But at these coefficients the factor 2(c1+c3) multiplying \\dot{N}_a in the momentum \\pi_i of Eq. (42) vanishes, so Eq. (44), which divides by 2(c1+c3), is not defined on this branch. On the same branch \\pi_i ceases to depend on any velocity, so \\pi_i - f_i(N,\\gamma,\\partial N,\\partial\\gamma)=0 are three additional primary constraints, contradicting the single primary constraint reported for Type 1. Since Eq. (18) is the STEGR point, whose equivalence to GR is cited in the paper itself, a correct Hamiltonian analysis of this branch cannot give the nine degrees of freedom listed in Table II. The class-level claim in Table II therefore fails for a physically central member of Type 1, independently of the validity of the delta-derivative truncation.","section":"Sec. V.A, Eqs. (41)–(46), Table I, Table II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The decision to discard Poisson-bracket terms containing spatial derivatives of the Dirac delta is not a benign boundary regularization for this problem: those terms are precisely what distinguishes first-class from second-class constraints in a diffeomorphism-invariant theory, and every class in Table II ends up with zero first-class constraints. The authors acknowledge the assumption and defer a complete treatment to future work, but they provide no estimate or consistency check of its effect, and the conclusions (b22, b95) are asserted without this caveat. The proposed future computation retaining the derivative terms is the right test, but until it is performed the first/second-class split, and hence every pDoF count in Table II, remains conditional.","section":"Sec. III, b46–b47 and Sec. VI, b105","authors_acknowledge":"A complete Hamiltonian analysis retaining these spatial deriva- tivesofDiracdeltadistributionisleftforfuturework,anditmightprovideadirecttestoftheassumptionsadoptedinthepresentwork.","authors_acknowledge_p":0.8},{"comment":"The consistency conditions for the secondary constraints contain terms of the form \\lambda'_j {\\bar{\\sigma}_i, \\bar{\\sigma}_j}, but in each case the next displayed equation omits these terms without proving {\\bar{\\sigma}_i, \\bar{\\sigma}_j}=0. For example, Eq. (65) writes the \\lambda' term explicitly and then Eq. (66) drops it, stating only that {\\bar{\\sigma}_i, \\bar{\\phi}_j}=A_{ij}\\delta^{(3)}. If {\\bar{\\sigma}_i, \\bar{\\sigma}_j} is nonzero, the multiplier equations change, the LU decomposition with the displayed matrices is no longer the relevant consistency system, and the termination of the algorithm is not established. The paper never states or derives the vanishing of these secondary-secondary brackets.","section":"Sec. V.B, Eq. (65); analogous Eqs. (80), (102), (129)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The solver strategy assumes that every leading principal minor of every Dirac matrix is nonzero, stated as 'the determinant of each \\Delta^{(P)}_Q are assumed to be nonzero.' This is a condition on the coefficient parameters of each class, but the paper does not check where it holds within the nine classes. On sub-branches where a minor vanishes, the displayed multiplier solutions and the resulting constraint counts do not apply. Since Table II is presented as a class-level statement with no exclusions, the analysis is at best valid on an open submanifold of each class, and the extent of that submanifold is not determined.","section":"Sec. V.B and subsequent LU decompositions, e.g. Eq. (69)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The multiplier solutions in the Type 8 section use the symbols B(6)_{2233} and B(6)_{3322} from the Type 6 analysis instead of the corresponding B(8) entries; this appears to be a copy-paste error and makes the displayed solution inconsistent with the immediately preceding matrix D(12).","section":"Sec. VIII (Type 8), Eqs. (261)–(262)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The action for Newer GR is introduced only in the coincident gauge, while the connection is described as an independent dynamical variable in Eq. (15). The paper should state explicitly that the analysis is performed in the coincident gauge from the outset and that relaxing it is deferred, as the conclusion already indicates.","section":"Sec. II, Eqs. (13)–(18)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Reference [44] lists the author as 'L. Hersenberg' instead of L. Heisenberg, and references [12] and [13] are identical entries; these should be corrected.","section":"References","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"There are numerous grammatical and typographical issues that impede reading, including 'we also taking the same assumption' (b46), 'we obtains' before Eq. (16), 'constriants' in the Type 8 conclusion, and inconsistent notation for the Lagrange multipliers (\\bar{\\lambda} versus \\lambda^i and \\lambda^{ij}) that should be standardized.","section":"Throughout, Sec. III and Sec. V","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The paper states that the Hamiltonian analysis was carried out with the xAct package, but no code or reproducibility notebook is provided. Given that most displayed f_i coefficients are not written out, a supplemental file with the xAct computations would be valuable for checking the constraint chains.","section":"Sec. V, header comment before Eq. (35)","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"reject","confidential_remarks":"The most serious problem is the unacknowledged singularity at the STEGR point inside Type 1: because Eq. (18) satisfies the Type 1 conditions and makes the inversion in Eq. (44) singular, the paper's own Table II cannot be correct for that branch. Combined with the load-bearing delta-derivative truncation and the unproven vanishing of secondary-secondary brackets, the central claim of an unambiguous degree-of-freedom count is not supported. A revision that adds an exceptional-branch analysis for STEGR and justifies the neglected brackets could potentially salvage the generic-branch results, but that is substantial additional work beyond the current manuscript. The journal may also wish to check the provenance of Table I, since the classification is imported from refs. [54], [55], and [57], with [57] listed as a preprint."},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"The one thing you should know: Table II's mode counts are the new result, and they fail at the one point in parameter space that is independently checkable. STEGR, whose coefficients are given in Eq. (18), satisfies the Type 1 conditions of Table I, and the Type 1 analysis divides by c1+c3, which vanishes at the STEGR point.\n\nWhat is actually new: the secondary-constraint chain per class and the per-class counts. The nine-way taxonomy comes from D'Ambrosio-Heisenberg and the primary constraints from refs. 54-57; the paper credits both and states clearly that a complete Dirac-Bergmann analysis was missing (b18). The continuation is done systematically, per type, using xAct and LU decompositions, and the counting arithmetic is internally consistent with pDoF = 10 minus half the second-class total.\n\nThe problem is that the headline table is never checked against the one case with a known answer, and the Type 1 branch is singular exactly there. The STEGR coefficients satisfy c4 = -c1-c2+c3 = 0 and c5 = -2c3. Eq. (42) has (2c1+2c3) multiplying the Ndot_a term, and Eq. (44) divides by 2(c1+c3), so the whole Type 1 chain exists only for c1+c3 not equal to zero. At the STEGR point, pi_i no longer depends on any velocity, so three further primary constraints appear and Table I's \"one primary constraint\" is wrong already. The paper does not mention the overlap, and Table II's 9 degrees of freedom for Type 1 sits next to the introduction's own citation that STEGR is dynamically equivalent to GR, which carries two. That looks like a misidentified branch structure, not a patchable caveat.\n\nThe other soft spots are ones the authors flag. The delta-derivative truncation (b46, b47) is acknowledged and deferred, but it is doing load-bearing work: every class comes out with zero first-class constraints, which is suspicious for generally covariant theories, and GR would supply first-class diffeomorphism constraints. The secondary-secondary brackets are dropped without demonstration (e.g., Eqs. (65)-(66)), and the nonzero-minor assumption on the LU decompositions is stated once in passing with no parameter-space analysis. Minor: the f_i coefficients are never listed, so the explicit brackets are not independently checkable.\n\nWho it is for: the f(Q) and symmetric-teleparallel community, as a caution about which branches to take seriously and which to discard. I would send it to a referee — the STEGR point gives a concrete target and the calculation is checkable — but I would not take Table II as a reliable determination, and I would not cite these counts.","headline":"The per-class mode counts in Table II are the new result, and they fail at the STEGR point, which sits inside Type 1 exactly where the paper's own inversion divides by zero.","tokens_in":46039,"tokens_out":6145,"would_cite":false,"duration_ms":46254,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":["83D05","83C05","70H45"],"pacs":["04.50.Kd","04.20.Fy"],"model":"deepseek/deepseek-v4-flash","headline":"Every branch of Newer General Relativity propagates a fixed number of gravitational degrees of freedom, from 10 down to 4, with all constraints second-class and no gauge freedom left.","keywords":["Newer General Relativity","symmetric teleparallel gravity","Dirac-Bergmann algorithm","Hamiltonian constraint analysis","physical degrees of freedom","nonmetricity","second-class constraints","ADM decomposition"],"falsifier":"Recompute the Type 1 constraint algebra without the truncation: retain the delta-derivative terms in $\\{\\bar{\\phi}_N,\\bar{\\sigma}_N\\}$ and in the smeared bracket of Eq. (54), then check whether the secondary constraint's consistency condition still determines the multiplier uniquely and whether the two constraints remain second-class. If the retained terms change the rank of the Dirac matrix or create a null vector, the Type 1 count of 9 fails, and by the same mechanism every row of Table II is at risk. The authors themselves name exactly this computation as the direct test of their assumption.","tokens_in":46247,"feed_emoji":"🌀","tokens_out":13567,"duration_ms":82198,"temperature":0.7,"pith_summary":"Newer General Relativity is a five-parameter family of quadratic nonmetricity theories that extends symmetric teleparallel gravity, and its coefficient space splits into nine types according to which velocities become non-invertible in the Legendre map. The paper runs the Dirac–Bergmann algorithm on every type and claims that the constraint chain always terminates at the primary-plus-secondary level, with every constraint second-class and none first-class. The resulting physical degree-of-freedom counts are 9, 7, 5, 4, 4, 7, 5, 4, 4 and 10 for Types 1 through 9, computed as $10-\\tfrac{1}{2}N_2$ with $N_2$ the number of second-class constraints. If correct, this settles how many gravitational modes each member of the family carries, the quantity that marks a modified-gravity theory as viable or strongly coupled. The authors state plainly that the whole determination rests on dropping Poisson-bracket terms containing spatial derivatives of the Dirac delta distribution, following an earlier coincident-$f(Q)$ analysis, and defer a full treatment to future work.","feed_headline":"Nine Newer-GR branches carry fixed 4–10 degrees of freedom","feed_subtitle":"A full Dirac–Bergmann sweep across all nine classes fixes how many gravitational modes each branch carries.","key_machinery":"The carrying mechanism is the Dirac–Bergmann algorithm applied to the singular Lagrangian of Newer GR. The central objects are the nine-type Hessian classification of the coefficient space; the primary constraints that appear wherever a velocity cannot be inverted in the Legendre map; the consistency conditions that promote some of them to secondary constraints; and the Dirac matrix of Poisson brackets among constraints, whose rank decides whether every Lagrange multiplier is fixed or a new constraint must be added. The decisive step is the truncation of all terms containing spatial derivatives of the Dirac delta distribution: under that truncation each Dirac matrix attains full rank at the secondary level, which forces the all-second-class conclusion. The counting identity is $10-\\tfrac{1}{2}N_2$ physical degrees of freedom, with ten the number of configuration degrees of freedom in the ADM variables (lapse, shift, and spatial metric) and $N_2$ the number of second-class constraints.","core_discovery":"The central claim is a complete constraint census of Newer General Relativity. Starting from the ADM-decomposed action, the paper derives the conjugate momenta for each of the nine Hessian classes, reads off the primary constraints from the degenerate velocity–momentum relations, and iterates their consistency conditions. In every class the iteration stops at the secondary level: the Dirac matrix of constraint brackets reaches full rank, all Lagrange multipliers are determined uniquely, and no tertiary constraints arise. The full constraint set is therefore entirely second-class in all nine types, which the paper interprets as the absence of Hamiltonian gauge freedom, and the physical degrees of freedom follow from the standard counting rule as 9, 7, 5, 4, 4, 7, 5, 4, 4 and 10. The authors call the determination unambiguous, with the explicit caveat that it assumes delta-derivative surface terms do not change the symplectic structure.","pith_inferences":["The most direct test of the paper's central claim is to recompute a single branch — cheapest for Type 1 with its two constraints — keeping every delta-derivative term; those terms are exactly what separates first-class from second-class behaviour in covariant theories, so a change in $\\{\\bar{\\phi}_N,\\bar{\\sigma}_N\\}$ for Type 1 would cascade through all nine rows of Table II.","Because general covariance normally appears in a Hamiltonian analysis as first-class constraints, the all-second-class outcome may be an artefact of the coincident gauge, which freezes the connection; the paper itself leaves relaxing that gauge as an open direction.","If the counts survive the truncation test, most of the parameter space (9 or 10 degrees of freedom) describes gravity that is strongly coupled by comparison with general relativity's 2, so only the 4-degree branches would be plausible as STEGR-like phenomenology."],"forward_implications":["The nine types collapse into five distinct counts — 10, 9, 7, 5 and 4 degrees of freedom — so the mode content is not uniform across the parameter space and jumps between nearby coefficient branches.","Because every constraint in every type is second-class and none is first-class, none of the nine theories possesses gauge freedom of the kind diffeomorphism invariance would generate; each branch is a constrained system whose multipliers are fully fixed.","For each type the Dirac–Bergmann chain ends at the primary-plus-secondary level, so no tertiary or higher constraints exist in any branch and the analysis is complete in the algorithm's own sense.","The generic Type 9 branch, whose Legendre map is fully invertible, propagates the maximum of 10 degrees of freedom, while the most constrained branches (Types 4, 7 and 8) propagate 4."],"supporting_citations":[{"why":"Supplies the projections of the non-metricity tensor onto the ADM hypersurface that the paper uses to build the expanded action.","marker":"[54]"},{"why":"Provides the Hessian-based classification of Newer GR into nine types; the per-type coefficient assumptions in Table I come from here.","marker":"[55]"},{"why":"The coincident-$f(Q)$ Hamiltonian analysis from which the assumption about neglecting delta-derivative surface terms is adopted.","marker":"[43]"},{"why":"Provides the consistency-condition framework and the smeared-constraint bracket formalism used throughout the Dirac–Bergmann iterations.","marker":"[44]"},{"why":"Defines symmetric teleparallel gravity and the coincident gauge in which the Newer-GR action is written.","marker":"[56]"},{"why":"The geometric-trinity account that frames Newer GR as the nonmetricity-side analogue of New General Relativity.","marker":"[8]"},{"why":"Supplies the ADM decomposition conventions (foliation, lapse, shift, induced metric) on which the 3+1 split is based.","marker":"[12]"},{"why":"The canonical-structure analysis of the torsional three-parameter analogue that this work mirrors in the nonmetricity sector.","marker":"[51]"}],"fun_headline_variants":["Newer GR constraint census: nine classes, all second-class, 4–10 DOF","Hamiltonian sweep fixes Newer GR modes at 4 to 10 per class","All nine Newer GR branches lack Hamiltonian gauge freedom","Newer GR: no tertiary constraints, all second-class, 4–10 DOF","Nine Newer GR types, no gauge freedom, DOF 4–10"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The entire degree-of-freedom table rests on dropping every Poisson-bracket term that contains a spatial derivative of the Dirac delta distribution, an assumption the paper takes over from an earlier coincident-$f(Q)$ analysis and explicitly leaves untested.","fun_headline_variants_meta":{"raw":{"variants":["Newer GR constraint census: nine classes, all second-class, 4–10 DOF","Hamiltonian sweep fixes Newer GR modes at 4 to 10 per class","All nine Newer GR branches lack Hamiltonian gauge freedom","Newer GR: no tertiary constraints, all second-class, 4–10 DOF","Nine Newer GR types, no gauge freedom, DOF 4–10"]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.000409,"raw_usage":{"cost":0.0004088812,"is_byok":false,"cost_details":{"upstream_inference_cost":0.0004088812,"upstream_inference_prompt_cost":2.85012e-05,"upstream_inference_completions_cost":0.00038038},"total_tokens":3000,"prompt_tokens":910,"completion_tokens":2090,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":746,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":1998}},"tokens_in":910,"tokens_out":2090,"cost_source":"openrouter_usage","duration_ms":14243,"image_pages":[],"temperature":1.0,"billed_attempts":1,"reasoning_tokens":1998,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-31T07:14:39.860602+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"falsifier":"Recompute the Type 1 constraint algebra without the truncation: retain the delta-derivative terms in $\\{\\bar{\\phi}_N,\\bar{\\sigma}_N\\}$ and in the smeared bracket of Eq. (54), then check whether the secondary constraint's consistency condition still determines the multiplier uniquely and whether the two constraints remain second-class. If the retained terms change the rank of the Dirac matrix or create a null vector, the Type 1 count of 9 fails, and by the same mechanism every row of Table II is at risk. The authors themselves name exactly this computation as the direct test of their assumption.","supporting_citations":[{"cited_title":"ADM formulation and Hamiltonian analysis of Coincident General Relativity","cited_arxiv_id":"2007.03261","evidence_quote":"Supplies the projections of the non-metricity tensor onto the ADM hypersurface that the paper uses to build the expanded action."},{"cited_title":"Journal of High Energy Physics2021, 170","cited_arxiv_id":null,"evidence_quote":"Provides the Hessian-based classification of Newer GR into nine types; the per-type coefficient assumptions in Table I come from here."},{"cited_title":"The European Physical Journal C84, 349","cited_arxiv_id":null,"evidence_quote":"The coincident-$f(Q)$ Hamiltonian analysis from which the assumption about neglecting delta-derivative surface terms is adopted."},{"cited_title":"Fortschritte der Physik71, 2300185","cited_arxiv_id":null,"evidence_quote":"Provides the consistency-condition framework and the smeared-constraint bracket formalism used throughout the Dirac–Bergmann iterations."},{"cited_title":"Phys. Rev. D98, 044048","cited_arxiv_id":null,"evidence_quote":"Defines symmetric teleparallel gravity and the coincident gauge in which the Newer-GR action is written."},{"cited_title":"The Geometrical Trinity of Gravity","cited_arxiv_id":"1903.06830","evidence_quote":"The geometric-trinity account that frames Newer GR as the nonmetricity-side analogue of New General Relativity."},{"cited_title":"Physical Review D112, 084052","cited_arxiv_id":null,"evidence_quote":"The canonical-structure analysis of the torsional three-parameter analogue that this work mirrors in the nonmetricity sector."}],"review_version":1}