{"id":"7a5105be-2af9-417b-9e83-af69f0557bea","arxiv_id":"2511.14679","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A post-processing scheme recovers transition rates and entropy-production bounds from Markov-network trajectories even when forward and backward transitions are randomly missed with unknown, asymmetric probabilities.","lead":"This paper shows how to correct for random “blackouts”—missed transitions—when observing Markov networks, so that entropy production can still be estimated reliably. The method recovers true transition rates from the short-time behavior of waiting-time distributions and then post-processes the observed trajectory to restore bounds like the thermodynamic uncertainty relation.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Hidden parallel transitions between the observed states are observationally equivalent to blackouts, so Eqs. (2)–(6) identify an effective detection probability, not the true η.","rationale":"The reader's weakest assumption—that no hidden transitions lie on the direct path between I+ and I−—is precisely the load-bearing point. The entire inference scheme (Eqs. 2–6) reduces to reading off the coefficients of the short-time WTDs and solving for η and k. If a parallel hidden channel exists, the observed WTDs at leading order cannot distinguish that channel from a blackout: both just remove observable events from the i↔j link. The subsequent post-modification and TUR/WTD estimators are all downstream of this inference, so a failure here invalidates the headline claim for any network with such a channel. The paper does state the condition in the text, but the abstract and concluding perspective present the result without that caveat, and no failure analysis is given. I agree with the reader that this is the most serious concern. The other issues the reader raised—unshown derivations for Eqs. (8)–(11) and missing error bars—are important but secondary: the functional forms are plausible and can be verified analytically, and the missing error bars affect confidence, not conceptual validity. The parallel-channel identifiability issue is a genuine physical scenario that the method cannot handle as stated. Because the paper already receives a CONDITIONAL verdict, my read does not change the verdict: the condition should be made explicit and the failure mode characterized, but the approach is sound under its stated assumption.","tokens_in":10028,"tokens_out":11538,"duration_ms":118123,"concrete_test":"Modify the Fig. 2 simulation by adding a hidden parallel edge between states 1 and 2 with rates q_{12}=q_{21}=0.5, keeping all other rates and η_{I±}=0.8,0.9 fixed. Generate the four observed WTDs, apply Eq. (6) to infer η_{I+},η_{I−},k_{I+},k_{I−}, and compare with true values. If the inferred values match the effective lumped rates (ηk + q) rather than the true η,k, the identifiability claim is falsified; if they still match true values, the concern is resolved. A faster analytic version is to re-derive Eqs. (2)–(5) with an extra hidden channel and show the O(t) coefficients depend only on the sum (1−η)k+q.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central identifiability step, Eqs. (2)–(6), assumes the only undetected channel between i and j is the blackout of the observed link I. The paper states this condition ('these paths contain no hidden transition between I+ and I−') but the abstract's claim that blackout fractions and true rates can be determined is unqualified. If the network has even one additional hidden transition connecting the same two states, the short-time coefficients change: ψ^ex_{I+→I+}(t) = [(1−η_{I−})k_{I−} + q_{ji}] η_{I+}k_{I+} t + O(t^2), and ψ^ex_{I−→I−}(t) = [(1−η_{I+})k_{I+} + q_{ij}] η_{I−}k_{I−} t + O(t^2). Equation (6) then returns not η_{I+} but the fraction of i→j events occurring through the visible channel, i.e. η_{I+}k_{I+}/[η_{I+}k_{I+}+(1−η_{I+})k_{I+}+q_{ij}] (up to the analogous correction), conflating blackouts with genuine hidden channels. Since the post-modification and the TUR/WTD recovery are built on these inferred η and k, the central claim fails whenever such parallel channels exist. The paper neither proves their absence nor characterizes the error when they are present.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper considers a discrete-state Markov network in which one or more transition pairs (\"links\") are observed with unknown, possibly direction-dependent detection probabilities η_{I±}, so that random blackouts compromise the observed currents and thermodynamic inference. The authors propose a three-step strategy: (i) infer the detection probabilities and the true transition rates k_{I±} from the short-time limits of the four waiting-time distributions associated with a link (Eqs. 2–6); (ii) post-modify the observed trajectory by randomly discarding transitions so that the retained trajectory corresponds to a virtual dynamics with symmetric detection probability η ≤ min{η_{I+}, η_{I-}}; (iii) use these post-modified trajectories in TUR/MTUR estimators whose dependence on η is claimed to be a simple rational function (Eqs. 8–10), allowing extrapolation to η=1, i.e., to the blackout-free TUR bound. A waiting-time-based entropy estimator for the post-modified data is also proposed (Eq. 11). The claims are illustrated by analytic and simulated examples on a 4-state network (Figs. 2, 3).","tokens_in":10345,"tokens_out":17341,"duration_ms":172632,"significance":"If the results hold, this is a valuable contribution to thermodynamic inference from incomplete observations. The short-time waiting-time identification is elegant, and the post-modification idea—turning an asymmetric detection loss into a symmetric, thermodynamically consistent virtual dynamics—is likely to be useful beyond the specific TUR/WTD estimators considered here. The paper builds on well-established WTD and TUR frameworks (Refs. [58–70]) and provides analytic and numerical support for the main formulas. However, the significance is currently limited by two load-bearing gaps: the identification of η and k requires a structural assumption (no hidden parallel transitions between the two states of an observed link) that is not stated in the abstract, and the exact rational forms of the TUR/MTUR estimators are asserted rather than derived. Both issues are fixable in revision, but they are central to the paper's claims.","major_comments":[{"comment":"The inference of η_{I±} and k_{I±} relies on the condition, stated just before Eq. (2), that the paths between I+ and I− contain no hidden transition. This condition is not highlighted as a limitation in the abstract or conclusion. If a hidden transition with rates q_{ij}, q_{ji} connects the same two states, Eq. (2) acquires an additional term q_{ji} η_{I+} k_{I+} t, and Eq. (5) acquires q_{ij} η_{I-} k_{I-} t. Equation (6) then returns η_{I+} k_{I+}/(k_{I+}+q_{ij}) rather than η_{I+}, conflating blackouts with genuine hidden channels. Since the post-modification and the TUR/WTD recovery are built on these inferred values, the central claim fails whenever such parallel channels exist. The paper should either prove identifiability under weaker conditions or, at minimum, state this assumption prominently and characterize the error when it is violated.","section":"Inference of blackouts and restoring transition rates, Eqs. (2)–(6)"},{"comment":"The universal form σ_TUR(η)=aη/(1+bη) is stated with the justification \"as argued below\" and \"theoretically, we find these dependencies by using the first cumulants extracted from the dominant eigenvalue λ(z) of the tilted generator,\" but no derivation or explicit calculation is given. The entire extrapolation to the blackout-free value η=1 hinges on this exact functional form; the same applies to the multi-current form (9) and the MTUR form (10). Without a derivation (or at least a clearly stated conjecture supported by a proof sketch), the claim that σ_TUR(1) is recovered is not established. Please provide the derivation in the Letter or a supplement.","section":"Entropy estimators, Eq. (8) (and Eqs. (9)–(10))"},{"comment":"The claim that σ_WTD(η) is \"a non-trivial lower bound\" of σ_M for post-modified data is asserted. The cited WTD bound was derived for complete blackout-free observations with one pair of transitions between two adjacent states; here the post-modified process has two parallel channels (the visible channel and the hidden blackout channel) between the same states. The paper should provide a proof or a rigorous argument that the lower-bound property remains valid in this setting, or state the conditions under which it does.","section":"Entropy estimators, Eq. (11)"}],"minor_comments":[{"comment":"The abstract and the concluding paragraph claim that \"the unknown frequency of blackouts and the true underlying transition rates can be determined\" without mentioning the no-hidden-parallel-transition assumption. Please qualify these statements.","section":"Abstract and Conclusion"},{"comment":"The right-most network in the caption contains duplicated labels \"ηI ηI\" and \"1 − ηI 1 − ηI\"; this appears to be a typesetting error.","section":"Figure 1 caption"},{"comment":"The phrase \"as argued below\" is misleading because no argument follows. Either remove it or place the derivation immediately after the equation.","section":"Eq. (8)"},{"comment":"The tilde notation in ψpm_{fJs→ eIr} is not defined clearly; please explain which transitions are reversed and how the sum over I_r J_s is meant.","section":"Eq. (11) and surrounding text"},{"comment":"The sentence \"Using the steady-state probabilities, e.g., obtained as the eigenvector of the generator or by p_s^i = ν_ex_{I+}/η_{I+} k_{I+}\" is slightly circular: to obtain the eigenvector one already needs the full generator, which was just reconstructed. This is correct but should be phrased more carefully.","section":"Inference of blackouts and restoring transition rates"}],"recommendation":"major_revision","confidential_remarks":"The paper has a promising core idea and the numerical examples are convincing, but the two load-bearing issues—the unqualified identifiability claim in the presence of hidden parallel channels and the missing derivation of the rational TUR/MTUR forms—need to be addressed before publication. If the authors can clearly delimit the validity of the method and provide the missing derivation, the paper would be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the short-time WTD trick is real: for a link with asymmetric random blackouts, the four short-time coefficients in Eqs. (2)–(5) do determine the detection probabilities and the true rates, and the post-modification plus the rational TUR forms give a sensible route to restoring the blackout-free TUR bound. Second, the identifiability result depends on there being no genuine hidden transition between the two states of the observed link. The paper states this assumption in the inference section, but the abstract presents the recovery of 'true underlying transition rates' without that qualification. The stress-test note is right: if a parallel hidden channel with rates q exists, Eq. (6) returns η k / (k+q), an effective visibility fraction, not the true detection probability, and the downstream TUR recovery is built on that misidentified η. So the scope is narrower than the abstract suggests.\n\nThe paper does several things well. Attributing blackouts to a second channel is a clean formal move. The short-time expansions are physically transparent. The post-modification to equalize η+ and η− is simple and should work in simulations and experiments. The rational form of σ_TUR(η) is plausible and the simulations in Fig. 3 support it, though I would have liked to see error bars and at least one asymmetric-η case with a known ground truth.\n\nWhere it's soft: the derivations of Eqs. (8), (10), and (11) are asserted rather than shown. In a Letter that's acceptable, but a referee should ask for a supplement or a clear citation. The claim that σ_WTD remains a lower bound after post-modification is not proven and deserves scrutiny. The numerical section is a single 4-state example; that's suggestive, not a stress test. And, again, the parallel-channel caveat is not in the abstract.\n\nBottom line: the central machinery holds under its stated assumptions. The paper deserves a serious referee. The fix is easy—sharpen the abstract, add a limitation paragraph, and provide the missing derivations or references. I'd recommend sending it to review with moderate revision expected.","headline":"A genuinely useful blackout-compensation scheme for Markov-network inference, provided the no-hidden-parallel-channel assumption holds; the abstract overstates that assumption.","tokens_in":10956,"tokens_out":3775,"would_cite":true,"duration_ms":35100,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60J27","82C05","82C31"],"pacs":["05.70.Ln","05.40.-a","82C05"],"model":"deepseek-v4-flash","headline":"Random detection blackouts in Markov networks can be fully corrected, restoring true rates and entropy bounds.","keywords":["Markov networks","random blackouts","detection probability","waiting-time distributions","entropy production","thermodynamic uncertainty relation","stochastic thermodynamics","partial observation"],"falsifier":"Simulate a simple three- or four-state Markov network where, in addition to the observed link, a hidden channel (with small but finite rate) connects the same two states, while all transitions are perfectly detected. Apply Eqs. (2)–(6) to the observed waiting times: the method will report nonzero blackout probabilities and incorrect rates even though no blackouts exist. This directly tests the identifiability assumption.","tokens_in":9792,"feed_emoji":"⚛️","tokens_out":1360,"duration_ms":18796,"temperature":0.7,"pith_summary":"This paper tackles a practical breakdown in stochastic thermodynamics: when an experimenter randomly misses transitions in a Markov network, with different miss rates for forward and backward jumps, standard inference tools fail—observed currents can even make an equilibrium system look driven. The authors show that the short-time limits of four waiting-time distributions around each observed link reveal both the unknown detection probabilities and the true transition rates. They then post-process the observed trajectories, randomly discarding transitions to equalize effective detection in both directions, and prove that this modified data restores the full thermodynamic uncertainty relation bound and preserves a waiting-time-based entropy estimator. The result matters because real measurements of molecular motors, colloids, and biochemical networks often suffer asymmetric detection gaps, and until now these gaps were assumed absent or benign.","feed_headline":"Blackout-corrected trajectories restore entropy bounds","feed_subtitle":"Random missed detections in Markov networks no longer hide true transition rates or the TUR entropy bound.","key_machinery":"The central object is the four-way short-time expansion of the experimentally observed waiting-time distributions for forward and backward transitions of a link, together with the binomial-splitting picture of blackouts as a second hidden channel. The short-time linear term in ψ_{I+→I+} and ψ_{I-→I-} encodes the missed transitions of the opposite direction, which is what makes the detection probabilities identifiable from the ratios of the four limits. The post-modification step then restores thermodynamic consistency by equalizing detection probabilities, and the rational-form dependence of the TUR/MTUR estimators on the remaining common detection probability η provides the analytic bridge","core_discovery":"The paper establishes that for a Markov network whose transitions are seen through random, time-asymmetric blackouts, the loss of information is not irretrievable. Writing the observed waiting-time densities ψ_{I+→I+}, ψ_{I+→I-}, ψ_{I-→I+}, ψ_{I-→I-} for a link I=(I+,I-), the short-time expansions contain exactly enough structure to solve for the detection probabilities η_{I±} and the bare rates k_{I±}. In particular, the ratio appearing in Eq. (6) isolates η_{I+} as t→0. With all rates and η's known, the observer can distinguish equilibrium (zero net current) from a nonequilibrium steady state, reconstruct the full generator if every link is observable, and, by randomly deleting observed tr","pith_inferences":["A natural testable extension is to apply the short-time ratio estimator to experimental single-molecule data with known ground-truth detection efficiencies (e.g., fluorophore blinking in motor-protein assays) to see whether the inferred η_{I±} match the independently measured miss rates.","The rational-form assumption for σ_TUR(η) depends on the underlying process being a stationary, irreducible Markov network; for networks with absorbing states or multiple disconnected components, the functional form (8) may fail, and the two-point fitting procedure would need modification.","The 'hidden parallel channel' reading of blackouts suggests a symmetry with genuine hidden states: if an observed link is in reality accompanied by a second physical pathway between the same two states, the short-time equations would absorb its rate into the blackout terms, and the inferred η would no longer be a true detection probability—an ambiguity the paper does not resolve.","One could push the post-modification idea further: instead of discarding transitions randomly, a deterministic thinning rule that preserves higher-order statistics might allow recovery of full trajectory statistics, not just the first two cumulants used in TUR."],"forward_implications":["If a Markov network's observable links all suffer asymmetric random blackouts, the full generator (all transition rates) can be recovered from waiting-time data alone, giving access to steady-state probabilities and to a rigorous equilibrium-versus-NESS test.","Entropy-production bounds from thermodynamic uncertainty relations can be evaluated at their blackout-free values even though the raw trajectories never contain a single blackout-free transition.","Post-modified trajectories remain valid input for waiting-time-based entropy estimators, which can yield a lower bound stronger than the TUR bound.","The inference scheme requires no symmetry or homogeneity in the blackout probabilities—each link and each direction may miss events at its own arbitrary rate.","The correction strategy transfers directly to multidimensional TUR estimates built from several observable links, including their covariance structure.","The same post-processing idea should extend to time-dependent driving, cycle-affinity inference, and other thermodynamic estimators that share the requirement of unbiased observations."],"fun_headline_variants":["Fix detection blackouts, restore entropy bounds","Unmask hidden rates from blackout-ridden data","Random blackouts? Entropy bounds still emerge","Recover true rates despite random detection gaps","From blackouts to full entropy inference"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The short-time waiting-time expansions assume that the two states of each observed link are connected only by that link, with no hidden transition lying on the direct path between them; if another channel connects the same two states, the inferred detection probabilities and rates become contaminated.","fun_headline_variants_meta":{"raw":{"variants":["Fix detection blackouts, restore entropy bounds","Unmask hidden rates from blackout-ridden data","Random blackouts? Entropy bounds still emerge","Recover true rates despite random detection gaps","From blackouts to full entropy inference"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001152,"raw_usage":{"total_tokens":4588,"prompt_tokens":693,"completion_tokens":3895,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":437,"completion_tokens_details":{"reasoning_tokens":3827}},"tokens_in":437,"tokens_out":3895,"duration_ms":26750,"temperature":1.0,"reasoning_tokens":3827,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:31:34.587212+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate a simple three- or four-state Markov network where, in addition to the observed link, a hidden channel (with small but finite rate) connects the same two states, while all transitions are perfectly detected. Apply Eqs. (2)–(6) to the observed waiting times: the method will report nonzero blackout probabilities and incorrect rates even though no blackouts exist. This directly tests the identifiability assumption.","supporting_citations":[],"review_version":1}