{"id":"2b39af3f-51ad-4453-b6d5-b6ff3ec185b1","arxiv_id":"2504.20002","paper_version":3,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using edge tracking in a coupled climate model, the authors compute the unstable AMOC edge state and show that at 460 ppm CO2 the strong AMOC state merges with it in a boundary crisis, producing millennial chaotic transients.","lead":"A climate model of intermediate complexity was used to find the unstable 'edge state' that separates the strong and weakened Atlantic ocean circulation, and to show that at higher CO2 the strong state disappears in a so-called boundary crisis. The result offers a dynamical explanation for why some model ensemble members collapse while others do not under the same emissions scenario.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The boundary crisis at 460 ppm is inferred from finite-time transients and 2D projections; an ON attractor with a small basin is not ruled out.","rationale":"The reader's weakest assumption concerns the edge-tracking observable, a legitimate concern about the computed edge state's validity. I consider a more load-bearing gap: even granting the edge state at 360 ppm, the paper does not demonstrate that the ON attractor is absent at 460 ppm. The boundary crisis is the paper's headline result, and it rests on finite-time transient data and a low-dimensional projection. The two members surviving 7000 years are the strongest finite-time data, and the paper's assertion that they 'eventually collapse' is an assumption, not a result. Because the central claim is that the ON attractor disappears, the burden is to show that no initial condition in the former ON region remains there indefinitely; this is not met. The proposed continuation test directly discriminates between a ghost state (survival probability tending to zero) and a small-basin attractor (some trajectories persist). Thus the verdict should remain CONDITIONAL, with the condition being that the boundary-crisis claim be either directly demonstrated or explicitly softened to a hypothesis.","tokens_in":36583,"tokens_out":10970,"duration_ms":116362,"concrete_test":"Continue the two 460 ppm ensemble members that have not collapsed within 7000 years (Fig. 12) for an additional 20,000 model years and record whether the AMOC strength at 46-66 N ever drops below 3 Sv. If either member avoids collapse for the full extension, the boundary-crisis claim is falsified; if both collapse, the ghost-state interpretation is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that at 460 ppm the ON attractor no longer exists, having merged with the edge state in a boundary crisis. The evidence offered is (i) a 4000-year run initialized from the 360 ppm ON state that collapses after roughly 2700 years, (ii) an 11-member ensemble with long chaotic transients, two members of which have not collapsed within 7000 years, and (iii) an apparent 'touching' of the ON and edge regions in the 2D projection of meridional and vertical salinity gradients (Fig. 11c). None of these establish disappearance. A finite transient is also consistent with a trajectory still in transit, or with an ON attractor whose basin excludes the chosen initial conditions. The survival of two members beyond 7000 years is especially problematic: under the ghost-state hypothesis survival probability should decay to zero, but with 11 members and a finite horizon the data are also consistent with an ON attractor occupying a modest basin fraction. The 'touching' in Fig. 11 is a 2D projection of a roughly 10^5-dimensional state space; disjoint sets can overlap in projection, so this is not evidence of a collision. The paper's own wording in Sec. V B ('we propose') and the abstract's 'reveal a boundary crisis' mark the gap between inference and direct evidence. If the ON attractor persists at 460 ppm, the central claim of monostability and boundary crisis fails, although the model would still show long transients and ensemble splitting.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies the global stability landscape of the Atlantic Meridional Overturning Circulation (AMOC) in the intermediate-complexity climate model PlaSim-LSG. At 360 ppm CO2 the model is bistable with an ON and an OFF AMOC state; the authors apply edge tracking using the 10-year smoothed AMOC strength as the distance measure and obtain a roughly 1400-year edge trajectory that converges to an oscillatory edge state with a period of about 120 years. The edge state has a higher oceanic center of mass than either attractor, exhibits Labrador Sea sea-ice/convection oscillations, and lies in a distinct region of a reduced state space defined by meridional and vertical salinity gradients and deep North Atlantic salinity. At 285 ppm a similar edge state is found, while at 460 ppm a 4000-year run initialized from the former ON state collapses to OFF after a long transient, an 11-member ensemble initialized near the ghost state shows chaotic transients of 400 to over 7000 years, and the ON and edge regions appear to touch in a two-dimensional projection. The authors interpret this as a boundary crisis between 360 and 460 ppm, where the ON attractor collides with the edge state and forms a long-lived ghost state, and they use this framework to explain ensemble splitting under SSP2-4.5 forcing and to compare qualitatively with GISS-E2-1-G simulations.","tokens_in":36818,"tokens_out":3987,"duration_ms":43852,"significance":"If the central claim holds, this is the first explicit computation of an AMOC edge state in a fully coupled climate model, and the first proposal that AMOC collapse in a climate model occurs via a boundary crisis rather than a purely local bifurcation. The paper's strengths include the direct simulation-based edge tracking without fitted parameters, the 1400-year edge trajectory, the physically plausible oscillation mechanism, and the explicit comparison with the GISS ensemble splitting. The data and code availability are also commendable. However, the boundary-crisis claim currently rests on indirect evidence, and the edge-tracking observable is not validated; the significance is therefore conditional on these two points being resolved.","major_comments":[{"comment":"The claim that the ON attractor no longer exists at 460 ppm is not established by the presented evidence. The 4000-year run that collapses after 2700 years, the 11-member ensemble with two survivors beyond 7000 years, and the apparent touching in Fig. 11c are all consistent with alternative interpretations, in particular with a surviving ON attractor whose basin excludes the chosen initial conditions. Under the ghost-state hypothesis the survival probability should decay to zero, but a finite 11-member ensemble with two survivors at 7000 years can also be produced by an ON attractor occupying a modest basin fraction. Because the paper's abstract states that a boundary crisis is 'revealed', the authors should provide a more direct test, for example by continuing the two surviving ensemble members until collapse (or until a statistically significant bound on the ghost-state lifetime is obtained), or by quantifying the basin fraction of the ON state at 460 ppm in the full state space.","section":"Sec. V and Fig. 12"},{"comment":"The edge tracking algorithm uses the 10-year smoothed AMOC strength at 46-66 degrees N as the sole distance measure for bisection and divergence detection. In a roughly 10^5-dimensional system with a possibly fractal basin boundary, this scalar observable is not an injective function of the basin of attraction: two states with identical smoothed AMOC strength can lie on opposite sides of the boundary. The computed 'edge state' may therefore be an artifact of the observable rather than the true invariant set on the basin boundary. Since the boundary crisis is defined as a collision with this edge state, this is a load-bearing methodological choice. The authors should test robustness by repeating the edge tracking with an alternative distance measure, such as a normalized full-state norm or a salinity-based index, and report whether the edge state and its centennial oscillations persist.","section":"Sec. III B and Supplemental S3"},{"comment":"The evidence that the former ON and edge states 'touch' at 460 ppm is based on a two-dimensional projection onto the meridional and vertical salinity gradients. Disjoint sets in the full state space can overlap in a low-dimensional projection, so this touching cannot by itself establish the collision required for a boundary crisis. The authors should either compute distances between the two sets in a higher-dimensional representation of state space, or show that the apparent overlap is not a projection artifact, for example by measuring the minimal distance in a subspace spanned by more than two independent physical fields.","section":"Sec. V B and Fig. 11c"}],"minor_comments":[{"comment":"The wording is inconsistent: the abstract and introduction say the results 'reveal a boundary crisis', while Section V B says 'we propose' and Section V C says the data 'suggests' a crisis. The level of certainty should be aligned with the evidence level throughout.","section":"Sec. I and Sec. V B"},{"comment":"The manuscript contains several typographical errors, including 'greehnouse' in the Introduction, 'Ocillations' in Section V B, and 'Skodowska' in the Acknowledgements. These should be corrected in the final version.","section":"General"},{"comment":"Numerous encoding artifacts appear throughout the manuscript text and figure captions (for example, strings of the form '/uni0000008b/uni00000087...' and missing spaces such as 'statesat 360ppm CO 2'). The camera-ready version must be regenerated without these artifacts.","section":"Figures and text"}],"recommendation":"major_revision","confidential_remarks":"The paper is methodologically interesting and the calculation of an oscillatory edge state in a coupled climate model is a substantial step forward. However, the boundary-crisis claim is the centerpiece of the abstract and title, and I do not think the current evidence is sufficient to establish that the ON attractor has disappeared at 460 ppm. The two long-surviving ensemble members are the most worrying point: they are as consistent with a small surviving ON basin as with a ghost state. The authors should be encouraged to run those two members to collapse, or otherwise quantify the basin fraction, before the paper can be accepted in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth knowing: this is the first explicit edge-state computation in a fully coupled climate model with interactive atmosphere, ocean, and sea ice, and that part is solid. The 120-year oscillatory edge state at 360 ppm is supported by 1400 years of edge tracking, clean energetics, and a plausible physical mechanism centered on the Labrador Sea. The comparison with GISS ensemble splitting in a common reduced state space is suggestive and useful.\n\nThe boundary crisis at 460 ppm is the headline claim, and it is the softest part. The evidence — one 4000-year collapse, an 11-member ensemble where two members survive beyond 7000 years, and a 2D projection in which the ON and edge regions appear to touch — does not establish that the ON attractor has disappeared. A finite transient, a shifted basin boundary, or a small surviving ON basin would each produce similar-looking behavior. The two surviving ensemble members are a real tension with the ghost-state story, though eleven members and a finite horizon cannot rule out a small basin. The paper's own wording in Sec. V B ('we propose') is more honest than the abstract's 'we reveal a boundary crisis.' The stress-test note is correct: this is an inference, not a direct demonstration.\n\nSecond concern: edge tracking uses 10-year smoothed AMOC strength at 46–66°N as the sole distance measure for convergence and divergence. In a 10^5-dimensional system with a fractal boundary, a scalar observable can miss transverse divergence. The authors do not test robustness to another observable. The internal consistency (EOF-based state space, energetics, physical mechanism) gives some confidence, but this is a legitimate gap.\n\nCredit where due: no fitted parameters enter; the computation is direct simulation; data and code are on Zenodo; the process analysis of the oscillations (sea ice, convection, Denmark Strait freshwater) is careful and genuinely useful. The GISS comparison is speculative but stimulating rather than overclaimed.\n\nWho it is for: nonlinear climate dynamics, AMOC tipping, and predictability researchers. The edge state result is worth citing on its own. The crisis claim should be cited as a proposed mechanism, not a demonstrated one.\n\nRecommendation: yes, send to peer review; this deserves referee time. The main point to press is the crisis evidence — either soften the abstract to match the inference, or add tests: extend the surviving members, use a different edge-tracking observable, or look for direct crisis signatures. A conditional accept with those revisions would be reasonable.","headline":"First explicit AMOC edge state in a fully coupled model is a solid computation, but the boundary-crisis headline is a hypothesis the evidence does not yet prove.","tokens_in":37404,"tokens_out":3237,"would_cite":true,"duration_ms":34844,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["37N10","37D45","86A05"],"pacs":[],"model":"deepseek-v4-flash","headline":"The AMOC's strong state in the PlaSim-LSG model disappears between 360 and 460 ppm CO$_2$ through a boundary crisis: a collision with the chaotic edge state leaves only a long-lived transient before collapse.","keywords":["Atlantic Meridional Overturning Circulation","edge state","Melancholia state","boundary crisis","ghost state","transient chaos","edge tracking","climate tipping"],"falsifier":"Run the edge tracking at 360 ppm again with a different convergence observable — for instance the leading salinity EOF scores or a norm of the full Atlantic salinity field — and check whether the pseudotrajectory converges to the same region of the reduced state space with the same roughly 120-year oscillations; a substantially different 'edge state' would show that the AMOC-strength observable alone cannot locate the basin boundary. Independently, at 460 ppm one could measure the distribution of ghost-state lifetimes over many initial conditions and test whether it follows the exponential decay law of transient chaos expected after a boundary crisis, rather than the sharp threshold behaviour of a local saddle-node bifurcation.","tokens_in":36290,"feed_emoji":"🌊","tokens_out":16372,"duration_ms":142864,"temperature":0.7,"pith_summary":"This paper claims that in the PlaSim-LSG climate model the vigorous Atlantic Meridional Overturning Circulation (AMOC) does not lose its stability through the smooth local bifurcation assumed by classical early-warning theory, but through a boundary crisis: as CO$_2$ rises from 360 to 460 ppm, the strong ON attractor collides with the edge state, an unstable chaotic saddle sitting on the basin boundary that separates the strong and weak overturning states. At 460 ppm the ON state no longer exists, and trajectories started near it trace a long-lived chaotic 'ghost state' — alternating between former ON-like and edge-like oscillations — before eventually collapsing to the weak OFF state, with transients that can last thousands of years. This matters because it provides a global dynamical-systems explanation for ensemble splitting under identical forcing: in the intermediate SSP2-4.5 scenario, some PlaSim-LSG members collapse while others persist, mirroring the 'stochastic bifurcation' reported in the comprehensive GISS Earth system model. The paper further shows that the edge state's climate is not simply intermediate between the two attractors: it supports roughly 120-year AMOC oscillations driven by Labrador Sea ice-convection feedbacks, and it exhibits 'excursive' properties — such as a fresher deep North Atlantic — that lie outside the range of both stable states. The authors caution that the result is model-dependent and that whether such a crisis exists in the real climate system remains unknown.","feed_headline":"360-460 ppm: AMOC strong mode dies in a collision","feed_subtitle":"At 460 ppm the strong overturning state merges with the edge state, leaving chaotic transients up to millennia.","key_machinery":"The carrying object is the edge state (Melancholia state): a non-attracting chaotic saddle embedded in the basin boundary between the strong and weak AMOC attractors, which is computed by an edge tracking algorithm that repeatedly bisects pairs of initial conditions interpolated along a straight line in the full roughly $10^5$-dimensional state space and then tracks the two trajectories until they diverge. Convergence, divergence, and bisection are all judged by a single observable — the difference in 10-year smoothed AMOC strength at 46-66°N — and the concatenated, averaged trajectory segments form a pseudotrajectory that populates the edge state's invariant measure. A reduced three-variable state space built from Atlantic salinity structure (meridional salinity gradient, vertical salinity gradient in the 46-66°N band, and deep North Atlantic salinity anomaly) separates the three objects and reveals that at 460 ppm the former ON and edge regions touch and interpenetrate, which is the state-space signature of the proposed boundary crisis. The Grebogi-Ott-Yorke boundary crisis concept supplies the mechanism: the ON attractor is annihilated by collision with the saddle, and the surviving union behaves as a ghost state whose long transient lifetimes explain millennial chaos and ensemble splitting.","core_discovery":"Using an edge tracking algorithm on a coupled intermediate-complexity model with roughly $10^5$ degrees of freedom, the paper constructs the AMOC edge state (Melancholia state) at 285 and 360 ppm CO$_2$: a chaotic saddle on the basin boundary whose pseudotrajectory shows large centennial oscillations (period about 118 years, amplitude up to 10 Sv) driven by interactions between sea ice, deep convection, and freshwater export in the North Atlantic, with the Labrador Sea leading the overturning strength by 6-8 years. When the CO$_2$ level is raised to 460 ppm, simulations initialised from the former ON state no longer settle: one 4000-year run maintains a strong but oscillating AMOC for roughly 1300 years, enters edge-like oscillations, briefly overshoots, and finally collapses to the OFF state, and the edge tracking pseudotrajectory itself loses the boundary and joins this transient. The paper interprets these observations as a boundary crisis: between 360 and 460 ppm the ON attractor collides with the edge state, and their union forms a ghost state in which trajectories chaotically switch between former ON and edge oscillatory modes before escaping to the OFF state, with some ensemble members persisting beyond 7000 years. In the reduced state space of Atlantic salinity gradients, the splitting of PlaSim-LSG ensemble members under SSP2-4.5 forcing occurs exactly in the region occupied by the edge state at 360 ppm and the ghost state at 460 ppm, and the same region is visited by the recovering and collapsing trajectories of the GISS model, which the paper offers as support for the claim that the observed 'stochastic bifurcation' is a signature of an AMOC edge state near a boundary crisis.","pith_inferences":["A reader could test the method's central assumption by re-running the edge tracking at 360 ppm with a different convergence observable — say the leading salinity EOF scores or a norm of the Atlantic salinity field — to see whether the same edge state is recovered; the paper reports no such robustness check.","If the boundary-crisis picture carries over to more complex models, AMOC risk assessment should target the crisis CO$_2$ level and the ghost-state lifetime distribution rather than a single tipping threshold, effectively replacing 'tipping point' with 'tipping window'.","The millennial ghost-state lifetimes imply an attribution problem for observed AMOC behaviour: after the crisis threshold is crossed, a collapse could be delayed so long that its cause — external forcing versus internal chaotic escape — becomes empirically ambiguous.","The GISS comparison could be made quantitative: using the same salinity-gradient coordinates in GISS output, one could test whether the probability of ensemble collapse matches the ghost-state escape statistics computed in PlaSim-LSG."],"forward_implications":["If the AMOC loses stability through a boundary crisis, critical slowing down near the ON state is not the right early-warning signature; instead the approach to the crisis should appear as longer and longer sojourns near the edge state ('sticky' behaviour), a global-stability analogue the paper proposes as an alternative, non-local view of early-warning.","Under intermediate forcing scenarios such as SSP2-4.5, identical time-dependent CO$_2$ can produce qualitatively different AMOC outcomes purely through internal variability, because ghost-state chaos determines which ensemble members escape early and which persist.","Popular stability indicators such as AMOC strength and Atlantic freshwater transport become poor indicators of stability out of equilibrium, since they oscillate strongly on the edge and ghost states even at fixed forcing.","Transition paths passing near the edge state can show non-monotonic excursions in 'excursive' observables, meaning the first detectable signal of an impending collapse can have the opposite sign of the eventual change."],"supporting_citations":[{"why":"introduces the coexistence of attractors, basins, and basic sets that motivates seeking saddles on basin boundaries","marker":"[60]"},{"why":"supplies the edge tracking algorithm (bisection plus parallel tracking) that this paper adapts to PlaSim-LSG","marker":"[61]"},{"why":"establishes edge states (Melancholia states) and fractal basin boundaries as tools for analysing climate stability","marker":"[10]"},{"why":"computes an AMOC edge state in an ocean-only model, the result this paper extends to a fully coupled atmosphere-ocean setup","marker":"[57]"},{"why":"demonstrates edge-state-governed predictability limits and ghost-state transients in a conceptual AMOC model, providing the ghost-state interpretation used here","marker":"[48]"},{"why":"defines the boundary crisis mechanism, an attractor's destruction by collision with a basin-boundary saddle, which is the paper's central mechanism","marker":"[55]"},{"why":"reports the GISS-model 'stochastic bifurcation' under SSP2-4.5 that the paper explains as edge and ghost-state dynamics","marker":"[52]"},{"why":"supplies the restart-file initial conditions used for edge tracking and documents PlaSim-LSG's multicentennial AMOC variability","marker":"[80]"}],"fun_headline_variants":["AMOC's edge state triggers century-long chaos before collapse","Boundary crisis: AMOC's strong state collides with a ghost","At 460 ppm, AMOC's strong mode merges into a chaotic saddle","Ghost states: why AMOC collapse can be unpredictable","AMOC's hidden edge state explains stochastic climate bifurcations"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the 10-year smoothed AMOC strength in the 46-66°N band is a faithful coordinate for separating the two sides of the basin boundary: the edge tracking algorithm decides convergence, divergence, and bisection solely from this one number, so if two trajectories with nearly identical AMOC strength can nevertheless lie on opposite sides of the boundary in the model's roughly $10^5$-dimensional state space, the computed 'edge state' may be an artifact of the chosen observable rather than the true saddle.","fun_headline_variants_meta":{"raw":{"variants":["AMOC's edge state triggers century-long chaos before collapse","Boundary crisis: AMOC's strong state collides with a ghost","At 460 ppm, AMOC's strong mode merges into a chaotic saddle","Ghost states: why AMOC collapse can be unpredictable","AMOC's hidden edge state explains stochastic climate bifurcations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000287,"raw_usage":{"total_tokens":1793,"prompt_tokens":1160,"completion_tokens":633,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":776,"completion_tokens_details":{"reasoning_tokens":544}},"tokens_in":776,"tokens_out":633,"duration_ms":6639,"temperature":1.0,"reasoning_tokens":544,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:37:27.938169+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the edge tracking at 360 ppm again with a different convergence observable — for instance the leading salinity EOF scores or a norm of the full Atlantic salinity field — and check whether the pseudotrajectory converges to the same region of the reduced state space with the same roughly 120-year oscillations; a substantially different 'edge state' would show that the AMOC-strength observable alone cannot locate the basin boundary. Independently, at 460 ppm one could measure the distribution of ghost-state lifetimes over many initial conditions and test whether it follows the exponential decay law of transient chaos expected after a boundary crisis, rather than the sharp threshold behaviour of a local saddle-node bifurcation.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"introduces the coexistence of attractors, basins, and basic sets that motivates seeking saddles on basin boundaries"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the edge tracking algorithm (bisection plus parallel tracking) that this paper adapts to PlaSim-LSG"},{"cited_title":"Lohmann and V","cited_arxiv_id":null,"evidence_quote":"computes an AMOC edge state in an ocean-only model, the result this paper extends to a fully coupled atmosphere-ocean setup"},{"cited_title":"Grebogi, E","cited_arxiv_id":null,"evidence_quote":"defines the boundary crisis mechanism, an attractor's destruction by collision with a basin-boundary saddle, which is the paper's central mechanism"},{"cited_title":"Mehling, K","cited_arxiv_id":null,"evidence_quote":"supplies the restart-file initial conditions used for edge tracking and documents PlaSim-LSG's multicentennial AMOC variability"}],"review_version":1}