{"id":"2d3377e3-e906-453b-9f4c-e89ba693aeb2","arxiv_id":"2603.12573","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Derives upper bounds on pointwise mutual information in terms of stochastic Fisher information that recover known averaged bounds.","lead":"The paper derives general upper bounds on pointwise mutual information expressed via stochastic Fisher information. These bounds average to existing mutual information bounds and are tested classically with a quantum extension, potentially setting limits for single-shot information extraction in sensing and dynamics.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest assumption correctly flags the two conditions (finiteness of stochastic Fisher information and validity of averaging) that must hold for the general claim. Because the paper is a derivation with zero free parameters and the abstract states the bounds are tested classically and generalized quantumly, the absence of any reported counter-example or special-case failure supports leaving the UNVERDICTED verdict unchanged pending full-text inspection of the explicit inequalities.","tokens_in":1589,"tokens_out":261,"duration_ms":22220,"concrete_test":"Pick a simple bivariate Gaussian with known closed-form mutual information and Fisher information; compute the stochastic Fisher information explicitly, evaluate the proposed pointwise bound at several sample points, then numerically integrate to confirm it recovers the known mutual-information bound within integration error.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on deriving a pointwise inequality between pointwise mutual information and stochastic Fisher information whose expectation recovers a known mutual-information/Fisher-information bound. The abstract and reader's summary indicate the construction uses standard definitions and the averaging step follows directly from the integral representation of mutual information. No internal inconsistency, hidden circularity, or unsupported interchange of limits is apparent from the provided description.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript derives general upper bounds to pointwise mutual information in terms of stochastic Fisher information and shows that these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. The results are claimed to hold in general cases, with tests in classical systems and a quantum generalization provided. Applications to stochastic dynamics and quantum sensing are discussed.","tokens_in":1653,"tokens_out":351,"duration_ms":32295,"significance":"If the central derivation holds, the work strengthens connections between pointwise information measures and Fisher information by providing bounds applicable to single realizations rather than ensembles. The averaging consistency with established mutual-information/Fisher-information bounds serves as an external anchor, and the quantum extension broadens potential utility in quantum sensing where single-shot limits are relevant.","major_comments":[],"minor_comments":[{"comment":"The definition and independence of stochastic Fisher information (relative to the pointwise mutual information) should be stated explicitly early in the manuscript, e.g., in the section introducing the main inequality, to allow direct verification that the bound is non-tautological.","section":"Introduction / main derivation section"},{"comment":"The averaging identity that recovers the known mutual-information bounds should include an explicit interchange-of-integral step or dominated-convergence argument if the support or differentiability conditions are non-trivial.","section":"Averaging / expectation step"},{"comment":"In the classical numerical tests, specify the exact distributions or parameter ranges used so that readers can reproduce the tightness of the pointwise bound.","section":"Numerical tests section"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their positive assessment of our work and for recommending minor revision. We appreciate the recognition that our bounds on pointwise mutual information recover known averaged results and that the quantum generalization may be relevant for single-shot quantum sensing. Since the report contains no specific major comments requiring point-by-point replies, we focus on preparing the minor revisions.","responses":[],"tokens_in":1026,"tokens_out":88,"duration_ms":22472,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that the authors have derived general upper bounds to pointwise mutual information in terms of stochastic Fisher information. They show that these bounds average to the known bounds on mutual information in terms of Fisher information from the literature. This pointwise approach is what stands out as new. It builds on the established program of using Fisher information to bound mutual information but moves it to the level of individual points rather than averages. The paper does well by including tests in classical systems and providing a quantum generalization, which helps make the abstract claims more concrete. The focus on applications to stochastic dynamics and quantum sensing is appropriate, since those areas often involve single realizations where ensemble averages are not available. The soft spots are in the details of the derivation. The abstract does not include the explicit steps or the precise definition of stochastic Fisher information, so it is hard to judge if the bound is non-trivial or if it relies on particular assumptions about differentiability or support of the distributions. The averaging identity is presented as a consistency check, which is helpful, but verifying that the stochastic version is defined independently would strengthen the case. No major circularity is apparent from the description, but the full proof would clarify this. The work is aimed at researchers in quantum information and statistical physics interested in fundamental limits for information extraction. A reader familiar with Fisher information bounds would get value from seeing how the pointwise version is constructed and applied. I recommend sending this to peer review for a thorough check of the mathematics and the quantum extension.","headline":"This paper derives pointwise bounds on mutual information using stochastic Fisher information that average to known results.","tokens_in":2132,"tokens_out":364,"would_cite":false,"duration_ms":40833,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information... i(x, θ) = log p(x|θ)/p(x), ι(x, θ) = (∂θ log p(x|θ))², Λ₂(x, θ) = ι(x, θ)p(θ)² + ṗ(θ)² + 2∂θ log p(x|θ)ṗ(θ)p(θ)"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/RealityFromDistinction.lean","rs_theorem":"reality_from_one_distinction","paper_passage":"recovering the average bounds... I(X,Θ) ≤ log(∫ √(F(θ)f(θ)² + ḟ(θ)²) dθ) - ∫ p(θ) log f(θ) dθ"}],"headline":"Standard information-theoretic bounds on PMI via SFI; no RS cost or distinction-forcing machinery","alignment":"orthogonal","rationale":"The paper's core construction (Theorems 1-3, eqs. 3-5, 17-18) defines PMI as log-ratio of conditionals and SFI/CQFI as squared score, then applies FTC + triangle inequality + Jensen to obtain pointwise upper bounds whose ensemble average recovers the known MI-FI result of Gorecki et al. This is classical/quantum information geometry on trajectories, with no appearance of the RS reciprocal cost J(x)=½(x+x⁻¹)-1, the functional equation uniqueness theorem, φ-ladder, 8-tick periodicity, or the reality_from_one_distinction forcing chain. The zero-parameter aspect noted in the reader verdict is incidental and does not invoke RS parameter-free derivation of constants.","tokens_in":47281,"confidence":"moderate","tokens_out":440,"duration_ms":17461,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Pointwise mutual information is upper-bounded by stochastic Fisher information.","keywords":["pointwise mutual information","stochastic Fisher information","Fisher information","mutual information","quantum sensing","stochastic dynamics","information bounds"],"falsifier":"A numerical example or analytical counterexample in a simple probability distribution where pointwise mutual information exceeds the derived bound from stochastic Fisher information.","tokens_in":2460,"feed_emoji":"","tokens_out":348,"duration_ms":38804,"temperature":0.7,"pith_summary":"The paper derives general upper bounds on pointwise mutual information using stochastic Fisher information. These bounds are shown to average to known bounds on mutual information from Fisher information. The connection holds for general cases in both classical and quantum settings. This is relevant for understanding limits on information extraction from single realizations in stochastic dynamics and quantum sensing.","feed_headline":"Stochastic Fisher information bounds pointwise mutual information","feed_subtitle":"Upper limits on single-shot information extraction that recover standard mutual information bounds when averaged, for classical and quantum ","key_machinery":"Stochastic Fisher information, which is used to derive upper bounds on pointwise mutual information.","core_discovery":"We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These results deepen the connection between information-theoretical quantities and are shown to hold in general cases. We test the bounds in classical systems and provide a quantum generalization.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Stochastic Fisher info bounds pointwise mutual info","Pointwise mutual info bounded by stochastic Fisher info","Upper bounds link stochastic Fisher info to pointwise mutual info","Bounds on pointwise mutual info from stochastic Fisher information"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The stochastic Fisher information is well-defined and finite for the probability distributions or quantum states under consideration, and the averaging recovers the known bounds without additional restrictions.","fun_headline_variants_meta":{"raw":{"variants":["Stochastic Fisher info bounds pointwise mutual info","Pointwise mutual info bounded by stochastic Fisher info","Upper bounds link stochastic Fisher info to pointwise mutual info","Bounds on pointwise mutual info from stochastic Fisher information"]},"model":"grok-4.3","cost_usd":0.009113,"raw_usage":{"total_tokens":3924,"prompt_tokens":504,"num_sources_used":0,"completion_tokens":60,"cost_in_usd_ticks":91128000,"prompt_tokens_details":{"text_tokens":504,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3360,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":504,"tokens_out":60,"duration_ms":48533,"temperature":1.0,"reasoning_tokens":3360,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-22T10:34:39.041427+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A numerical example or analytical counterexample in a simple probability distribution where pointwise mutual information exceeds the derived bound from stochastic Fisher information.","supporting_citations":[],"review_version":1}