{"id":"87f0509f-287a-4f23-adfd-853cdf7b33e7","arxiv_id":"hep-ph/0611184","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Three torsion-balance runs found the gravitational inverse-square law holds down to 56 micrometers at 95% confidence, bounding any single extra dimension to 44 micrometers or smaller.","lead":"A torsion-balance experiment tested whether gravity follows an exact inverse-square law at separations down to 55 micrometers, finding no confirmed deviation. The result pushes constraints on extra spatial dimensions and on new forces below the dark-energy length scale of about 85 micrometers.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The 95% CL limits rest on the detector-bow correction (Delta z = 3.5 and 3.9 micrometers) used to absorb the small-s excess in Experiments I and III; the text does not make clear whether Delta z is an independently measured, fixed parameter or a fitted nuisance degenerate with a short-range Yukawa.","rationale":"The reader's weakest_assumption correctly identifies the detector-bow model and the excess small-s noise as the soft spot, and the CONDITIONAL verdict is defensible. I sharpen the concern in one respect: the load-bearing question is not simply 'if the bow model is wrong' but whether Delta z is an independently measured, fixed parameter or a fitted nuisance degenerate with a short-range Yukawa in the small-s data. The text does not settle this for Experiment I, where the bow was discovered after the data and 'modeled.' I also note that the Experiment II control, which the reader treats as clean support for the bow interpretation, is confounded by simultaneous changes in fiber and rotation frequencies, so the disappearance of the anomaly there is not attributable to flattening alone. Against this, the paper has genuine independent support that the reader underweights: the same-sign anomaly in Experiments I and III is the opposite of what a lambda << 1 mm Yukawa would produce given the over-/under-cancellation design, and the combined Newtonian fit (chi-squared = 407 for 421 dof) shows no significant deviation, with the best Yukawa fit improving chi-squared by only 3.5 for two parameters. The apparatus parameters are cross-checked against independent CMM and balance metrology (Eq. 2), and the torque scale is continuously calibrated by the gravitational octupole, so there is no circularity that forces the result. The Casimir background rests partly on private communications (Jaffe, Chesler, Andreev, Yaffe), which is a citation gap, but the paper supplies independent physical reasoning (membrane thickness, 1.6 kHz drum-head mode) that does not depend on those communications, so this is a minor point rather than the load-bearing one. On balance the quoted limits are conservative and the exclusion is likely to survive, but the bow-model degeneracy is a specific, checkable item that a critical reader would want closed before treating 56 and 44 micrometers as final. I therefore leave the verdict at CONDITIONAL/UNCHANGED rather than moving to ACCEPT or REJECT.","tokens_in":7550,"tokens_out":7777,"duration_ms":126013,"concrete_test":"Re-fit the Experiment I and III data with Delta z fixed at its independently measured value (from the profilometry that established Delta z <= 1.0 micrometers in Experiment II and 3.9 micrometers in Experiment III) rather than floated, and with a conservative upper bound on any 21 omega component of the excess small-s noise. Report the profile likelihood for lambda. If the 95% CL lower bound on lambda (56 micrometers) and the corresponding R bound (44 micrometers) shift by more than about 10% relative to the published fit, the limits are not robust to the bow/noise modeling and the concern lands; if they are stable, it does not.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is an exclusion (|alpha| <= 1 down to lambda = 56 micrometers; R <= 44 micrometers). The characteristic failure mode of an exclusion is a systematic that absorbs a real signal, making the bound too aggressive. The detector-bow model is exactly such a systematic: it is introduced to explain the small-s excess attraction in Experiments I and III. The text is ambiguous about its status. For Experiment I it says the bow was 'discovered' after the data and that the outer and inner hole sets were 'modeled at different average heights, Delta z = 3.5 micrometers' -- phrasing that does not distinguish an independent profilometric measurement from a parameter floated in the fit. If Delta z is floated alongside alpha and lambda, it is partially degenerate with a short-range Yukawa precisely in the small-s data where the anomaly appears, and the quoted 56 micrometer bound could be optimistic. Two features mitigate this. First, Experiment II, taken with a flattened ring (Delta z <= 1.0 micrometers), shows no anomaly, which is what the bow interpretation predicts. Second, the anomaly in Experiments I and III is same-sign ('increased attraction, similar to that seen in Experiment I'), whereas a lambda << 1 mm Yukawa would show opposite signs in Experiment I (over-canceled) versus Experiment III (under-canceled); the same-sign pattern favors a systematic over a Yukawa. But the Experiment II control is confounded: it simultaneously changed the fiber (20 to 17 micrometers), the attractor frequency (omega_0/28 to omega_0/7.5) and the calibration frequency (49 omega/3 to 6 omega), so the disappearance of the anomaly cannot be cleanly attributed to flattening alone. Separately, the excess small-s torque noise (about four times thermal in Fig. 2) is not explained, and its 21 omega content is not bounded; if it has a 21 omega component it would bias the same small-s points. The concern is real but substantially mitigated, not fatal.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript reports three torsion-balance ('missing-mass') experiments testing the gravitational inverse-square law over separations from 9.53 mm down to 55 µm, i.e. below the dark-energy length scale λ_d ≈ 85 µm. A 21-fold symmetric molybdenum detector ring with machined holes is rotated above a two-plate attractor whose hole pattern is designed to null the Newtonian 21ω torque; a short-range Yukawa interaction V(r) = −Gm₁m₂/r [1 + α exp(−r/λ)] would not be nulled and would appear with opposite sign in Experiment I (over-cancelled) versus Experiments II and III (under-cancelled). Torques at 21ω and 42ω are fitted jointly with apparatus parameters η constrained by independent electronic-balance and coordinate-measuring-machine measurements (Eq. 2), with a vertical-position error term in Eq. (3). A combined Newtonian fit gives χ² = 407 for ν = 421; adding a Yukawa improves χ² by only 3.5. The resulting 95% CL exclusion (Fig. 6) is quoted as |α| ≤ 1 for λ ≥ 56 µm, and, via the single-extra-dimension mapping α = 8/3, λ = R, as R ≤ 44 µm; a 2σ limit M* ≥ 3.2 TeV/c² is quoted for the two-large-extra-dimension scenario.","tokens_in":7850,"tokens_out":4638,"duration_ms":75103,"significance":"If it holds, this is a substantial advance: the quoted reach of 56 µm at |α| = 1 improves on the authors' own 2004 result and on the Irvine, Colorado and Stanford bounds by up to two orders of magnitude, and it is the first inverse-square-law test to penetrate the dark-energy length scale, which is precisely where several motivated scenarios (fat gravitons, extra time dimensions, large extra dimensions) predict departures. The experimental design is genuinely strong: the three-experiment configuration with opposite-sign response to a short-range Yukawa, the continuous gravitational octupole calibration of the torque scale, the independent CMM/AFM and electronic-balance determination of the apparatus geometry, and the 21ω nulling scheme together constitute a real systematic-error discriminator rather than a single-measurement claim. The result is falsifiable and is presented with an explicit exclusion curve rather than a single number, which is the right form for a null test.","major_comments":[{"comment":"The 95% CL bound is quoted from a fit in which the small-s excess attraction in Experiments I and III is absorbed by modelling the outer and inner hole sets at different mean heights above the attractor. The text does not state whether Δz is an independently measured quantity held fixed in the fit, or a parameter floated within the η vector of Eq. (2) with some prior. This distinction is load-bearing: if Δz is floated, it is partially degenerate with a short-range Yukawa precisely in the s < 100 µm data where the anomaly appears, and the quoted λ = 56 µm could be optimistic. The manuscript should state explicitly (i) how Δz was determined (profilometry, CMM, AFM scan), (ii) its uncertainty and whether that uncertainty entered Eq. (2) as a prior, and (iii) whether Δz was free or fixed in the Yukawa fits that produce Fig. 6. A short demonstration that the exclusion curve is unchanged when Δz is floated within its measured uncertainty, or when the s < 100 µm points are removed, would settle the point.","section":"Experiments I and III, detector-bow correction (Δz = 3.5 µm and 3.9 µm)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The reach to 55 µm is the central claim, and the dominant conceivable background at those separations is the Casimir force. The manuscript dismisses it on the basis of private communications from Jaffe, Chesler, Andreev and Yaffe plus a qualitative argument that the 1.6 kHz lowest drumhead mode of the beryllium-copper membrane makes m = 21 deformations insignificant. Neither the private communications nor the mode-frequency argument is accompanied by a number. A quantitative upper bound on the Casimir-induced 21ω torque, expressed in the same units as the data points of Figs. 3–5 and compared with the thermal noise floor, should be given, or a published source containing that calculation should be cited. The same request applies, more briefly, to the electrostatic and magnetic backgrounds, which are asserted to be negligible by reference to Ref. [11] without an estimate specific to the present, smaller separations.","section":"Backgrounds at the smallest separations (Casimir and electrostatic), text preceding the combined fit","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The manuscript states that torque noise at s < 100 µm exceeds the thermal expectation by about a factor of four (Fig. 2), and separately that a 'marginally significant short-range anomaly corresponding to an increased attraction' is present in Experiments I and III. The reader is not told how the excess noise is propagated into ΔN_m of Eq. (3), nor how significant the anomaly actually is once the inflated noise is accounted for. Since the exclusion at small λ is driven by exactly these points, the manuscript should quote the significance of the excess (in σ, for the 21ω channel, per experiment and combined), state whether the errors used in Eq. (2) are the measured point-to-point scatter or the thermal prediction, and confirm that the global χ² = 407 for ν = 421 is not masking a local mismatch at small s. A plot of normalized residuals versus s would make this transparent.","section":"Fig. 2 and Eq. (3); Experiments I and III small-s excess","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The body states that the results 'yield a model-independent upper limit on the size of a compact extra dimension', and the abstract states without qualification that 'an extra dimension must have a size R ≤ 44 µm'. The 44 µm number follows from the specific mapping α = 8/3, λ = R for a single flat extra dimension taken from Ref. [9]; it is model-independent only in the sense that it is a direct re-reading of the α(λ) exclusion, not in the sense that it applies to compact extra dimensions generically. The abstract in particular should carry the qualifier ('a single flat extra dimension of the ADD type'), and the phrase 'model-independent' in the body should be replaced by a precise statement of what is assumed. The same care should be applied to the M* ≥ 3.2 TeV/c² limit, which is specific to the two-extra-dimension scenario and to the definition of M* in Ref. [11].","section":"Abstract and final paragraph: 'model-independent' extra-dimension bound","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The title is rendered 'Dar k-Energy' and several author names are broken or misspelled in the arXiv version ('Senjanov ´ ıc', 'Kolanov ´ ıc', 'Dimopoulis', 'Bennet', 'E¨ ot-Wash'); these should be corrected in the final version, along with 'inadvertantly', 'slighter higher' and 'preceeding' in the body.","section":"Title and author list","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The η vector of Eq. (2) should be enumerated explicitly, with a note on which components carry experimental priors and which are floated freely, so that the reader can see which parameters are constrained by the CMM/balance measurements and which by the torque data alone. The second term of Eq. (3), δs_j ∂Ñ_m/∂s_j, should be defined in words; the typesetting of the square root in the arXiv version is garbled.","section":"Eq. (2) and Eq. (3)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that the results 'improve on previous work by a factor of up to 100' should specify the λ at which the factor of 100 applies; at large λ the improvement over Ref. [11] is much smaller. The goodness-of-fit of the combined Newtonian fit (χ² = 407, ν = 421) should be accompanied by its p-value.","section":"Combined fit, paragraph beginning 'A combined Newtonian fit'","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The caption should state the range of α covered by the plotted exclusion and confirm that the |α| > 1 region at large λ is excluded as well, so that the figure can be read without consulting the text. The mapping from the plotted α(λ) curve to the R ≤ 44 µm number would be clearer if the α = 8/3 horizontal line were drawn on the figure.","section":"Fig. 6","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Reference [13] (Svetovoy and Lokhanin) does not appear to be cited anywhere in the text; either cite it where relevant to the Casimir discussion or remove it.","section":"Reference list","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The over-cancellation/under-cancellation argument that distinguishes a short-range Yukawa from a systematic is the strongest feature of the design, but it is conveyed only in prose. A small table giving, for each experiment, the lower-plate thickness and the predicted sign and magnitude of the 21ω response to a representative short-range Yukawa would let the reader verify the discrimination directly.","section":"Experiment I description","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"The physics is sound and the experimental design is exemplary; my major comments are requests for documentation of choices that were very likely made correctly (the status of Δz, the Casimir estimate, the treatment of the small-s noise) rather than indications of an error. The one item I would insist on before publication is an explicit statement of whether Δz was fixed by measurement or floated in the Yukawa fits, since that is the single point on which the headline number depends and it is currently ambiguous. The 'model-independent' phrasing in the abstract should be tightened; it is the kind of sentence that gets quoted out of context."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Bottom line: this is a real result. The Eöt-Wash group pushed their torsion balance down to 55 µm and moved the gravitational-strength Yukawa range bound to 56 µm, roughly a hundredfold improvement over Hoyle 2004, with the 44 µm extra-dimension bound following from the standard α = 8/3 mapping. If you work on short-range gravity or large extra dimensions, this is the number to beat now. The abstract claim [abstract:s1] is supported by the data as presented, though the phrasing 'inverse-square law holds (|α| ≤ 1)' is loose — what is actually bounded is the range of a unit-strength Yukawa, not α itself at all λ.","headline":"A genuine hundredfold improvement in short-range gravity bounds, with one ambiguity — whether the detector-bow correction is measured or fitted — that a careful reader should press on.","tokens_in":8651,"tokens_out":1212,"would_cite":true,"duration_ms":17776,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["04.80.-y","95.36.+x","04.80.Cc","12.38.Qk"],"model":"selfhosted/deepseek-v4.1-flash","headline":"A torsion balance finds no deviation from Newtonian gravity at separations down to 55 micrometers, so any gravitational-strength Yukawa force must have a range shorter than 56 micrometers and any single compact extra dimension must be no 44","keywords":["gravitational inverse-square law","torsion balance","Yukawa interaction","extra dimensions","dark-energy length scale","short-range gravity","Casimir background"],"falsifier":"A repeat measurement with a demonstrably flat, rigid detector at the same 55–100 µm separations would settle it: if the excess attraction persists with the bow model removed, the quoted $λ = 56~$µm and $R = 44~$µm limits would have to be revised downward in strength or reinterpreted as a real short-range force.","tokens_in":8908,"feed_emoji":"⚖️","tokens_out":2307,"duration_ms":33673,"temperature":0.7,"pith_summary":"The paper asks whether gravity's $1/r^2$ law survives at distances smaller than the dark-energy length scale, $85~$µm, the scale set by the observed cosmic acceleration. A short-range failure of the inverse-square law is what several proposals for the cosmological constant problem predict, and what theories with extra spatial dimensions require in the opposite direction. Using an upgraded torsion balance whose attractor and detector are patterned with 21-fold-symmetric holes, the authors measure gravitational torques at separations from 9.53 mm down to 55 µm and fit the data with a Newtonian model plus one Yukawa term. They report no significant violation, and at 95% confidence bound the range of any gravitational-strength Yukawa interaction to at most 56 µm and the size of a single compact extra dimension to at most 44 µm. The interest is that a laboratory experiment now reaches the distance scale cosmologists associate with dark energy, closing a window that had been open by a factor of up to 100.","feed_headline":"Gravity still follows the inverse-square law down to 56 µm","feed_subtitle":"Torsion-balance tests find no extra force and cap any single compact extra dimension at 44 micrometers.","key_machinery":"The instrument is a ``missing mass'' torsion balance: a molybdenum detector ring with 42 machined holes in two 21-fold-symmetric circles hangs above an attractor built from a thin molybdenum disc with 42 holes atop a thicker tantalum disc with 21 holes, and the gravitational coupling between the holes produces a torque that oscillates 21 times per attractor revolution. The lower attractor holes are offset by $360/42$ degrees so that, if the inverse-square law holds, the $21ω$ torque nearly cancels, while a short-range Yukawa interaction with $λ$ below the 1 mm disc thickness is not cancelled. Running with the lower disc at two thicknesses (differing by 0.140 mm) makes a genuine short-range force flip sign between experiments while a systematic error would not, and a separate three-sphere gravitational octupole driven by a turntable provides a continuous absolute calibration of the torque scale.","core_discovery":"The authors claim that Newtonian gravity, augmented by nothing, fits their measured torques across three separate experiments spanning 9.53 mm to 55 µm. Parameterizing a deviation as $V(r) = -G m_1 m_2 [1 + α e^{-r/λ}]/r$, they find at 95% confidence that $|α| ≤ 1$ requires $λ ≤ 56~$µm, so no gravitational-strength Yukawa force with a range above that value survives. Translated into extra dimensions, the same data exclude a single compact dimension larger than $R ≤ 44~$µm, and for the two-large-extra-dimension scenario they require a $2σ$ lower limit on the unification mass $M_* ≥ 3.2$ TeV/$c^2$. The combined Newtonian fit gives $χ^2 = 407$ for 421 degrees of freedom, and adding a Yukawa term improves the fit by only $Δχ^2 = 3.5$, at $α = -0.0037$, $λ = 2$ mm, with no $2σ$ effect at any range.","pith_inferences":["The bound is set by the smallest separation achieved, so the natural next step is engineering: a flatter, more rigid detector and a thinner membrane would move the 56 µm limit toward the 20 µm scale where thermal and electrostatic backgrounds begin to dominate.","Because the same data can be recast as a bound on any power-law or finite-range modification once the geometry integral is redone, the exclusion is broader than the single Yukawa curve shown; the authors say as much by deferring other functional forms to a separate publication.","The persistent excess torque noise at the smallest separations, roughly four times thermal, is the practical ceiling on this generation of the experiment; if it is instrumental rather than statistical, better vibration and patch-potential control would tighten the limit more than extra data at large separation.","A laboratory bound at the dark-energy length scale invites the reverse question: if no new force appears exactly where cosmic acceleration suggests one might, the coincidence between $\\lambda_d$ and the reachable laboratory range becomes a constraint on model building rather than a hint."],"forward_implications":["Any gravitational-strength Yukawa force mediating a new long-range interaction must have a range below 56 µm, which removes a wide band of parameter space for light scalar or vector mediators coupled to mass.","A single compact extra dimension must be smaller than 44 µm, and in the two-large-extra-dimension picture the unification mass must exceed 3.2 TeV/$c^2$ at $2σ$.","Scenarios in which gravity weakens for separations below the dark-energy length scale, such as a graviton with a size near 85 µm, are pushed to sizes below the experiment's reach.","The techniques demonstrated here — patterned nulled torques, multiple attractor thicknesses, and in-situ autocollimator linearity mapping — set a template for pushing torsion-balance tests to smaller separations."],"supporting_citations":[{"why":"Supplies the analysis strategy, the geometry integration that turns the Yukawa potential into predicted torques, and the fitting procedure this work extends.","marker":"[11]"},{"why":"Provides the mapping from a single extra dimension to a Yukawa interaction with $α = 8/3$ and $λ = R$, and summarizes the theoretical expectations plotted against the new bound.","marker":"[9]"},{"why":"Defines the two-large-extra-dimension scenario whose unification mass the paper bounds at $M_* ≥ 3.2$ TeV/$c^2$.","marker":"[8]"},{"why":"The doctoral thesis describing the upgraded instrument, its components, and its commissioning.","marker":"[12]"},{"why":"The earlier torsion-balance inverse-square-law test whose apparatus and limits this work improves on.","marker":"[10]"},{"why":"Cosmological measurements supplying the dark-energy density $ρ_d$ from which the 85 µm dark-energy length scale is computed.","marker":"[1, 2, 3]"},{"why":"The proposal that a graviton of size near the dark-energy length scale would weaken gravity below that scale, one of the hypotheses being tested.","marker":"[6]"},{"why":"The extra-time-dimension scenario predicting a similar short-distance weakening of gravity.","marker":"[7]"}],"fun_headline_variants":["Torsion tests find no extra gravity down to 56 µm","Newtonian gravity holds from 9.53 mm to 55 µm","No gravitational-strength Yukawa force above 56 µm","Single extra dimension capped at 44 µm by torsion tests","Gravity data fit Newtonian form across 9.53 mm to 55 µm"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The 95% confidence bound depends on the modeled bow of the detector ring, which the authors invoke to explain the marginally significant excess attraction seen at the smallest separations in Experiments I and III.","fun_headline_variants_meta":{"raw":{"variants":["Torsion tests find no extra gravity down to 56 µm","Newtonian gravity holds from 9.53 mm to 55 µm","No gravitational-strength Yukawa force above 56 µm","Single extra dimension capped at 44 µm by torsion tests","Gravity data fit Newtonian form across 9.53 mm to 55 µm"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1872,"prompt_tokens":868,"completion_tokens":1004,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":925}},"tokens_in":868,"tokens_out":1004,"duration_ms":15189,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":925,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T15:37:36.322817+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A repeat measurement with a demonstrably flat, rigid detector at the same 55–100 µm separations would settle it: if the excess attraction persists with the bow model removed, the quoted $λ = 56~$µm and $R = 44~$µm limits would have to be revised downward in strength or reinterpreted as a real short-range force.","supporting_citations":[{"cited_title":"Hoyle et al., Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the analysis strategy, the geometry integration that turns the Yukawa potential into predicted torques, and the fitting procedure this work extends."},{"cited_title":"Ann. Rev. Nucl. Part. Sci. 53, 77","cited_arxiv_id":null,"evidence_quote":"Provides the mapping from a single extra dimension to a Yukawa interaction with $α = 8/3$ and $λ = R$, and summarizes the theoretical expectations plotted against the new bound."},{"cited_title":"Phys. Lett. B 436, 257","cited_arxiv_id":null,"evidence_quote":"Defines the two-large-extra-dimension scenario whose unification mass the paper bounds at $M_* ≥ 3.2$ TeV/$c^2$."},{"cited_title":"PhD thesis, Univ. of Washington, unpub- lished","cited_arxiv_id":null,"evidence_quote":"The doctoral thesis describing the upgraded instrument, its components, and its commissioning."},{"cited_title":"Hoyle et al., Phys","cited_arxiv_id":null,"evidence_quote":"The earlier torsion-balance inverse-square-law test whose apparatus and limits this work improves on."},{"cited_title":"Phys. Rev. D 69, 044014","cited_arxiv_id":null,"evidence_quote":"The proposal that a graviton of size near the dark-energy length scale would weaken gravity below that scale, one of the hypotheses being tested."},{"cited_title":"G. Gabadadze and G. Senjanov ´ ıc, hep-ph/9919297","cited_arxiv_id":null,"evidence_quote":"The extra-time-dimension scenario predicting a similar short-distance weakening of gravity."}],"review_version":1}