{"id":"2b99f375-23b9-4e0f-b078-829c8f7441f2","arxiv_id":"2512.11919","paper_version":3,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Event-level binary indicators and quantitative measures of causal effects are introduced in causal spaces, with standard treatment effect measures recovered as special cases.","lead":"The paper defines causal effects at the level of events rather than variables inside the causal spaces framework. This targets domains like images and text where raw data points lack clear semantic structure for traditional causal questions.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest assumption correctly isolates the two substantive prerequisites: (i) that the causal-spaces axioms are rich enough to support event-level questions, and (ii) that the intervention measures employed match those of interest in applications. Because the abstract asserts that the recovery of standard quantities is shown explicitly, and no counter-example or hidden assumption is detectable, the load-bearing concern remains exactly the one already flagged by the reader. No stronger or different objection emerges.","tokens_in":1770,"tokens_out":310,"duration_ms":19531,"concrete_test":"Take the quantitative measure defined in the paper for an event A and intervention measure P^do; instantiate the events as A = {Y > y} for a continuous outcome Y and the do-intervention on a binary treatment; verify algebraically that the measure reduces exactly to the usual average treatment effect (or risk difference) without extra assumptions beyond the causal-space axioms.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that binary presence/absence definitions for event-level causal effects can be introduced inside the causal-spaces axiomatization, that these definitions satisfy natural links to independence under the intervention measure, and that the accompanying quantitative measures recover standard treatment-effect functionals (e.g., ATE, ATT) as special cases when events are chosen appropriately. The abstract states that the required properties are proved; no internal contradiction, circularity, or unsupported step is visible from the given description.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper introduces binary definitions for the presence or absence of causal effects at the level of events (rather than variables) inside the recently proposed measure-theoretic causal-spaces framework. It proves properties that link these definitions to (in)dependence under an intervention measure, develops quantitative measures of effect strength and nature, and shows that standard treatment-effect functionals (ATE, ATT, etc.) arise as special cases when events are chosen appropriately.","tokens_in":1822,"tokens_out":306,"duration_ms":14417,"significance":"If the derivations hold, the work supplies a coherent event-level extension of causality that is continuous with classical variable-level measures. The explicit recovery of ATE/ATT as special cases and the measure-theoretic grounding are strengths that could support finer-grained causal questions in domains where variables lack semantic structure (images, text).","major_comments":[],"minor_comments":[{"comment":"The abstract states that properties are proved and that standard measures are recovered, but the main text should include explicit statements of the intervention-measure construction (e.g., the precise sigma-algebra and measure used for each binary definition) so that readers can verify the independence claims without external reference.","section":null},{"comment":"Notation for events and intervention measures should be introduced once in a dedicated preliminary section and then used consistently; several ad-hoc symbols appear in the quantifying-measure definitions that are not cross-referenced to the binary definitions.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive summary of our manuscript and the recommendation for minor revision. We are pleased that the event-level definitions, their links to intervention-based independence, the quantitative measures, and the recovery of ATE/ATT as special cases are viewed as coherent extensions within the causal-spaces framework. No specific major comments were raised in the report.","responses":[],"tokens_in":1171,"tokens_out":90,"duration_ms":28914,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core contribution is a shift to event-level causal effects within the causal spaces framework. They introduce binary definitions for whether a causal effect holds between events, prove links to independence under an intervention measure, and supply quantitative strength measures. Standard treatment effect functionals appear as special cases when events are chosen appropriately. This follows the probability-theory pattern of starting with events before variables, which fits the motivation for high-dimensional data where pixels or tokens lack semantic structure for variable-level questions. The work builds directly on the recent causal spaces axiomatization without circular definitions or data-dependent fitting, which keeps the claims clean. The recovery of classical measures is a useful bridge to existing results. The main limitation is that the abstract states the properties are proved and the intervention measures are constructed appropriately, but the actual derivations and explicit constructions are not visible in the provided material. Without those details it is hard to judge how tight the links are or whether the measures align with interventions of practical interest in vision or language settings. The framework itself may also prove too abstract for immediate application until concrete event definitions are worked out. This is for readers already comfortable with measure-theoretic causality who want a finer language for complex data domains. A serious referee should see it because the claims are specific and checkable, even if revisions will likely be needed on the proof details and operationalization.","headline":"This paper defines causal effects at the event level inside causal spaces, with binary presence checks and strength measures that recover ATE and similar quantities as special cases.","tokens_in":2321,"tokens_out":341,"would_cite":false,"duration_ms":20311,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"Causal effects on events via kernels in product spaces; no RS cost/φ/periodicity machinery","alignment":"orthogonal","rationale":"The paper's core definitions (active causal effect via K_U(ω,A)=P(A), conditional variants, mean/max effect scores with scale functions f, recovery of ATE via difference-in-means D_F) operate entirely within the causal-space axiomatization of Park et al. (2023). These structures have no isomorphism to the RS forcing chain (reality_from_one_distinction, J-cost uniqueness, φ-ladder constants, 8-tick periodicity, Alexander-duality D=3). No shared primitives, no parameter-free derivation of constants, and no contradiction with any RS theorem. Domain is purely statistical/causal-inference; RS has no opinion.","tokens_in":59635,"confidence":"high","tokens_out":185,"duration_ms":14444,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Causal effects can be defined and quantified directly on events rather than variables inside the causal spaces framework.","keywords":["causal effects","events","causal spaces","intervention measures","treatment effect","measure theory","event-level causality"],"falsifier":"A concrete example or data set in which the new event-level presence test or strength measure yields a different conclusion from the standard variable-level treatment effect under the same intervention measure.","tokens_in":2629,"feed_emoji":"","tokens_out":617,"duration_ms":19683,"temperature":0.7,"pith_summary":"The paper moves causal inquiry down to the level of individual events, following the pattern in probability theory where independence is first defined for events before random variables appear. Within causal spaces it supplies binary tests that say whether one event causally affects another, then proves these tests are equivalent to forms of independence under an intervention measure. It next introduces numerical measures of effect strength and shows that familiar treatment-effect quantities arise exactly when the events are chosen in the usual way. The shift matters in settings such as images or text where the raw data points have no natural variable-level semantics for causal questions.","feed_headline":"Causal effects defined on events recover standard treatment measures","feed_subtitle":"Binary tests and strength measures at event level in causal spaces include common treatment-effect quantities as special cases.","key_machinery":"Binary definitions of causal-effect presence on events, together with associated quantifying measures that connect effect strength to independence under intervention measures.","core_discovery":"Within the measure-theoretic framework of causal spaces, several binary definitions are introduced to determine the presence of causal effects on events, together with properties that link those definitions to (in)dependence under an intervention measure. Quantifying measures are then supplied that capture the strength and nature of causal effects on events, and common measures of treatment effect are recovered as special cases of these new quantities.","pith_inferences":["The same machinery could be used to pose causal questions about specific pixel patterns or token sequences without first inventing intermediate variables.","Event-level definitions might allow causal analysis inside trained models where only the raw input tokens or activations are observable.","The link to intervention-based independence could be used to import existing tools from measure-theoretic probability directly into causal estimation pipelines."],"forward_implications":["Binary tests decide whether a causal effect is present on a given event.","These tests are equivalent to independence statements under the intervention measure.","Numerical measures quantify both the strength and the directional nature of the effect.","Standard average treatment effect and related quantities appear as special cases when events are chosen to match the usual variable formulation."],"fun_headline_variants":["Event causal effects recover treatment measures","Binary tests link causal effects to independence","Quantifying measures for event causal effects","Event definitions yield treatment effect measures","Causal spaces ground effects at event level"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The causal-spaces axiomatization gives a rich enough setting for event-level causal questions and the intervention measures used in the proofs match the interventions that matter in the target domains.","fun_headline_variants_meta":{"raw":{"variants":["Event causal effects recover treatment measures","Binary tests link causal effects to independence","Quantifying measures for event causal effects","Event definitions yield treatment effect measures","Causal spaces ground effects at event level"]},"model":"grok-4.3","cost_usd":0.006881,"raw_usage":{"total_tokens":3179,"prompt_tokens":638,"num_sources_used":0,"completion_tokens":58,"cost_in_usd_ticks":68812000,"prompt_tokens_details":{"text_tokens":638,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2483,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":638,"tokens_out":58,"duration_ms":21036,"temperature":1.0,"reasoning_tokens":2483,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-16T22:51:58.237137+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A concrete example or data set in which the new event-level presence test or strength measure yields a different conclusion from the standard variable-level treatment effect under the same intervention measure.","supporting_citations":[],"review_version":1}