{"id":"74d8cae9-3a4a-4452-bf32-6602791ae72b","arxiv_id":"2606.24729","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"A trivariate continuous-time random walk state-space model with state-dependent innovation covariance and Milankovitch forcing reconstructs Cenozoic climate proxies via Kalman filter maximum likelihood.","lead":"The paper develops a continuous-time state-space model to jointly reconstruct δ18O, δ13C, and atmospheric CO2 over the last 67 million years from irregular multi-site proxy data. This allows estimation of how correlations and orbital sensitivities between these indicators changed across the greenhouse-to-icehouse transition.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"State-dependent innovation covariance may make the transition nonlinear, rendering standard Kalman filter likelihood approximate","rationale":"The concern directly engages the reader's weakest assumption (state-dependent innovation covariance in the transition equation) and explains why that assumption is load-bearing for the three empirical claims. Because the abstract supplies no implementation detail on how the dependence is realized or which filter variant is used, the issue cannot be dismissed from the given text.","tokens_in":1736,"tokens_out":312,"duration_ms":28645,"concrete_test":"Re-fit the model to the same data using a particle filter (or unscented Kalman filter) in place of the standard Kalman filter; if the sign of any estimated regime-specific correlation flips or any reported CO2 threshold moves outside the original calibrated bands, the headline empirical claims are sensitive to the filter approximation.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The transition equation lets innovation covariance (and Milankovitch forcing) depend on the prevailing climate state while the latent process is a trivariate continuous-time random walk. If the climate state is a function of the latent variables themselves, the system is nonlinear. The abstract states that all parameters are obtained by maximum likelihood through the Kalman filter with diffuse initialization. The standard Kalman filter supplies the exact likelihood only for linear Gaussian systems with known time-varying coefficients; state-dependent covariance violates this, so the reported ML estimates (and therefore the sign reversal of cross-proxy correlations and the CO2 thresholds) rest on an approximation whose accuracy is not addressed.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript develops a continuous-time state-space framework for joint reconstruction of Cenozoic d18O, d13C, and atmospheric CO2 from multi-site, multi-method proxy data. The latent signals are modeled as a trivariate random walk whose innovation covariance and deterministic La2004 Milankovitch forcing are permitted to depend on the prevailing climate state; all parameters are obtained by maximum likelihood via the Kalman filter with diffuse initialization. The reported results include sign reversal of cross-proxy correlations between greenhouse and icehouse regimes, strengthening orbital sensitivity with ice-sheet growth, and CO2 thresholds for major glaciations placed relative to modern concentrations.","tokens_in":1888,"tokens_out":369,"duration_ms":16010,"significance":"If the modeling and estimation choices are valid, the work supplies a unified reconstruction with calibrated uncertainty bands and documents regime-dependent proxy relationships that bear on Cenozoic climate dynamics. The continuous-time formulation and explicit treatment of irregular sampling and multi-source biases constitute methodological strengths.","major_comments":[{"comment":"Abstract: the transition equation lets innovation covariance (and Milankovitch forcing) depend on the prevailing climate state. Because that state is a function of the latent variables themselves, the system is nonlinear. The standard Kalman filter supplies the exact likelihood only for linear Gaussian systems with known time-varying coefficients; the accuracy of the approximation underlying the reported ML estimates, the sign-reversal claim, and the CO2 thresholds is not addressed.","section":"Abstract"}],"minor_comments":[{"comment":"Clarify the precise functional form by which the climate state enters the innovation covariance and forcing coefficients, including any discretization or approximation steps required for implementation.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful and constructive review. The point on nonlinearity is well taken and we address it directly below.","responses":[{"response":"We agree that state dependence of the innovation covariance and Milankovitch forcing on the latent climate state renders the transition equation nonlinear. The manuscript applies the Kalman filter by evaluating the state-dependent coefficients at the one-step-ahead filtered estimates obtained in a previous iteration, which is an approximation analogous to the iterated extended Kalman filter. Because the paper does not quantify the resulting bias in the likelihood or in the reported regime-dependent correlations and CO2 thresholds, the concern is valid. We will revise the methods and discussion sections to (i) state the approximation explicitly, (ii) report a simulation study that compares the approximate ML estimates against those obtained from a particle filter on the same data-generating process, and (iii) add a brief sensitivity analysis showing how the sign-reversal and threshold results change under modest perturbations of the state-dependent coefficients. These additions will be placed before the results so that readers can judge the robustness of the claims.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the transition equation lets innovation covariance (and Milankovitch forcing) depend on the prevailing climate state. Because that state is a function of the latent variables themselves, the system is nonlinear. The standard Kalman filter supplies the exact likelihood only for linear Gaussian systems with known time-varying coefficients; the accuracy of the approximation underlying the reported ML estimates, the sign-reversal claim, and the CO2 thresholds is not addressed."}],"tokens_in":1299,"tokens_out":316,"duration_ms":14852,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper sets up a continuous-time state-space model for jointly modeling benthic d18O, d13C, and atmospheric CO2 over the Cenozoic. The latent process is a trivariate random walk whose innovation covariance matrix and Milankovitch forcing coefficients are allowed to depend on the current climate state. Parameters come from Kalman filter maximum likelihood.\n\nWhat stands out as new is the state-dependent innovation covariance inside the continuous-time framework for these specific proxies. Standard state-space methods exist, but tying the covariance to the state for this multi-proxy setup appears fresh. The model also incorporates site-specific measurement variances and bias intercepts to align multi-site data.\n\nIt does well at producing a single reconstruction with calibrated uncertainty bands that links CO2 levels to major glaciations. The claim that cross-proxy correlations reverse sign between greenhouse and icehouse periods is the kind of result that could be useful if the model holds.\n\nThe main concern is the one raised in the stress test. Because the innovation covariance depends on the latent state, the system is nonlinear. The standard Kalman filter provides the exact likelihood only when the system is linear or the time-varying coefficients are known in advance. The abstract gives no indication that they used an approximation or a different filter. This means the estimated correlations, orbital sensitivities, and CO2 thresholds rest on potentially biased likelihood values. If the paper does not address the accuracy of this approximation, that is a load-bearing issue for the empirical results.\n\nData exclusion rules and checks against independent records are not visible here either, but the modeling assumption is the bigger question.\n\nThis work is aimed at paleoclimatologists interested in unified proxy reconstructions and changing relationships over deep time. It shows clear thinking on how to handle irregular data and time-varying parameters. I would bring it to a reading group to discuss the filtering step. It deserves peer review so the authors can clarify or fix the nonlinearity issue.","headline":"The state-dependent innovation covariance turns the model nonlinear, so the Kalman ML estimates rest on an unexamined approximation.","tokens_in":2398,"tokens_out":455,"would_cite":false,"duration_ms":19227,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A continuous-time state-space model shows Cenozoic isotope correlations reversing sign as climate shifts from greenhouse to icehouse conditions.","keywords":["Cenozoic","state space model","climate proxies","continuous time","Kalman filter","Milankovitch forcing","d18O","CO2 reconstruction"],"falsifier":"New high-resolution CO2 data from an independent archive that place the Oligocene glaciation threshold outside the model's reported confidence bands would contradict the reconstructed path.","tokens_in":2627,"feed_emoji":"🌡️","tokens_out":709,"duration_ms":20946,"temperature":0.7,"pith_summary":"The paper develops a continuous-time state-space framework to jointly reconstruct benthic d18O, d13C, and atmospheric CO2 over the last 67 million years from unevenly sampled multi-site data. The latent signals are modeled as a trivariate random walk whose innovation covariance and deterministic Milankovitch forcing are allowed to depend on the prevailing climate state. Maximum likelihood estimation through the Kalman filter produces estimates in which cross-proxy correlations change sign between the early greenhouse and later icehouse, orbital sensitivity of the isotopes increases with continental ice-sheet growth, and the CO2 path places atmospheric thresholds for major Cenozoic glaciations relative to present-day concentrations.","feed_headline":"Model shows Cenozoic proxy correlations reverse with climate shift","feed_subtitle":"State-dependent random walk places CO2 thresholds for major glaciations relative to present-day levels","key_machinery":"The trivariate continuous-time random walk whose innovation covariance matrix and La2004 orbital forcing term are permitted to vary with climate state, observed through a measurement model that assigns site-specific error variances to the isotopes and proxy-group variances to CO2 together with bias intercepts, estimated by maximum likelihood via the Kalman filter with diffuse initialization.","core_discovery":"The central claim is that a state-dependent continuous-time trivariate random walk fitted to the joint proxy record reveals sign-reversing correlations between d18O, d13C and CO2 across the Cenozoic greenhouse-to-icehouse transition, increasing orbital sensitivity of the isotopes as ice sheets grow, and a CO2 reconstruction that places the atmospheric thresholds of the major glaciations in calibrated relation to modern levels.","pith_inferences":["The same state-dependent structure could be applied to other proxy sets to test whether similar correlation reversals appear outside the Cenozoic.","Relaxing the random-walk assumption to include regime-switching nonlinear terms would allow the model to capture abrupt transitions more explicitly.","Direct comparison of the model's CO2 bands against independent boron-isotope or stomatal records would provide an external check on the calibrated thresholds."],"forward_implications":["The sign reversal implies that the statistical coupling between the carbon cycle and ice volume changed at the Eocene-Oligocene boundary.","Increasing orbital sensitivity indicates that growing ice sheets amplify the response to Milankovitch forcing.","The CO2 reconstruction supplies quantitative thresholds for the onset of major Cenozoic glaciations expressed relative to present-day concentrations.","Joint modeling borrows strength across proxies to reduce uncertainty in each individual latent history."],"fun_headline_variants":["Cenozoic proxies show reversing correlations in state-dependent model","Trivariate random walk tracks sign flips in Cenozoic proxy relations","Model reveals CO2 thresholds for Cenozoic glaciations vs today","Orbital sensitivity of isotopes rises with growing ice sheets"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The unobserved climate signals behave as a linear random walk in continuous time whose parameters are allowed to switch according to the prevailing climate regime.","fun_headline_variants_meta":{"raw":{"variants":["Cenozoic proxies show reversing correlations in state-dependent model","Trivariate random walk tracks sign flips in Cenozoic proxy relations","Model reveals CO2 thresholds for Cenozoic glaciations vs today","Orbital sensitivity of isotopes rises with growing ice sheets"]},"model":"grok-4.3","cost_usd":0.00418,"raw_usage":{"total_tokens":2103,"prompt_tokens":647,"num_sources_used":0,"completion_tokens":62,"cost_in_usd_ticks":41799500,"prompt_tokens_details":{"text_tokens":647,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1394,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":647,"tokens_out":62,"duration_ms":13448,"temperature":1.0,"reasoning_tokens":1394,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T22:04:35.532819+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"New high-resolution CO2 data from an independent archive that place the Oligocene glaciation threshold outside the model's reported confidence bands would contradict the reconstructed path.","supporting_citations":[],"review_version":1}