{"id":"35fbf08d-dbb4-4987-bbc3-c20b58b1791e","arxiv_id":"2606.00731","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Introduces and studies Q-filters on bounded lattices.","lead":"The paper introduces the notion of Q-filters in bounded lattices and studies their properties. A smart generalist might read it to learn about new algebraic structures in order theory that could connect to logic or computation.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's UNVERDICTED verdict with LOW confidence stems directly from the absence of the full text. My review reaches the same point: without the actual definition, examples, or results, no concrete technical objection to the argument can be formulated. The claim itself is modest and does not assert anything falsifiable from the abstract alone.","tokens_in":1449,"tokens_out":236,"duration_ms":18266,"concrete_test":"Obtain the full manuscript and check whether the definition of Q-filter yields at least one non-trivial theorem or example that is not immediate from the definition of a filter in a bounded lattice; if none appears, the 'study' claim is empty.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is the introduction and study of Q-filters on bounded lattices. No specific theorems, definitions, or asserted properties are supplied that could be checked for internal inconsistency, hidden assumptions, or failure of a required condition. The reader's weakest assumption (non-trivial theory exists) cannot be tested from the given material, so no load-bearing concern is identifiable.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript introduces and studies the notion of Q-filters in bounded lattices.","tokens_in":1483,"tokens_out":209,"duration_ms":11464,"significance":"A non-trivial theory of Q-filters on bounded lattices could potentially add to the literature on filters and ideals in order theory and lattice theory, but the provided text supplies no definitions, theorems, examples, or derivations with which to evaluate whether any such theory is developed or whether it is interesting.","major_comments":[{"comment":"Abstract: the sole content of the manuscript is the sentence 'In this paper, we introduce and study the notion of Q-filters in bounded lattices.' No definition of a Q-filter is supplied, no properties are stated or proved, and no examples or comparisons with existing filter notions (e.g., prime filters, ultrafilters) appear. Consequently the central claim cannot be assessed for correctness or novelty.","section":"Abstract"}],"minor_comments":[],"recommendation":"reject","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the report. We agree that the submitted manuscript is incomplete and consists solely of the stated sentence, with no definitions, theorems, examples, or comparisons provided. We will revise the paper to supply a complete development of the theory.","responses":[{"response":"The referee correctly observes that the current version contains only the introductory sentence and supplies none of the required mathematical content. This was an error in the submission. The revised manuscript will include an explicit definition of Q-filters on bounded lattices, statements and proofs of their properties, concrete examples, and direct comparisons to existing notions such as prime filters and ultrafilters.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the sole content of the manuscript is the sentence 'In this paper, we introduce and study the notion of Q-filters in bounded lattices.' No definition of a Q-filter is supplied, no properties are stated or proved, and no examples or comparisons with existing filter notions (e.g., prime filters, ultrafilters) appear. Consequently the central claim cannot be assessed for correctness or novelty."}],"tokens_in":953,"tokens_out":245,"duration_ms":13648,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The central point is that the authors define and study Q-filters in bounded lattices, presenting this as new work. From the abstract alone that is the entire contribution.\n\nWhat is new is the specific definition of a Q-filter, which the paper states has not appeared before. If the full text supplies a clean definition plus some basic properties that do not collapse into existing filter notions like prime or maximal filters, that would count as incremental progress in lattice theory.\n\nThe paper does nothing visibly well because the abstract contains no derivations, no examples, and no stated theorems. There is therefore nothing to credit beyond the act of naming the object.\n\nThe main soft spot is the total absence of evidence that the notion supports a non-trivial theory. The weakest assumption in the work is that a worthwhile body of results follows from the definition; nothing in the given material tests or supports that assumption. Without comparisons to prior filter concepts or concrete calculations on small lattices, it is impossible to judge whether the idea is distinct or useful.\n\nThis paper is aimed at a narrow group of lattice theorists who routinely examine variations on filters. Most readers outside that subfield will find little to use.\n\nI would not bring it to a reading group. I would not cite it. It could still go to peer review if the full manuscript contains explicit definitions, small examples, and at least one or two non-obvious properties; otherwise a desk reject seems reasonable.","headline":"The paper introduces Q-filters on bounded lattices as a new notion but the abstract supplies no definition, examples, or theorems, so its actual content and value remain unclear.","tokens_in":1945,"tokens_out":370,"would_cite":false,"duration_ms":21937,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Q-filters form a distinct class of filters that can be defined and investigated in any bounded lattice.","keywords":["Q-filters","bounded lattices","filters","lattice theory","order theory","ideals","algebraic structures"],"falsifier":"A proof that every Q-filter on a bounded lattice is already a standard filter (or that the collection of Q-filters is empty or trivial in every non-trivial bounded lattice) would remove the motivation for the new notion.","tokens_in":2337,"feed_emoji":"","tokens_out":567,"duration_ms":15781,"temperature":0.7,"pith_summary":"The paper introduces Q-filters as a new notion specifically for bounded lattices and begins to develop their basic theory. It defines the objects and examines how they behave under the lattice operations of meet and join. A sympathetic reader would care if this definition yields properties that standard filters do not capture in the bounded case, because bounded lattices appear throughout order theory and algebra yet lack a tailored filter calculus. If the claim holds, the work supplies a concrete starting point for classifying filters without assuming extra structure such as distributivity.","feed_headline":"Q-filters defined and studied in bounded lattices","feed_subtitle":"The new notion supplies a filter calculus that works uniformly for lattices with only top and bottom elements.","key_machinery":"The Q-filter, the central new object defined on bounded lattices that carries the subsequent study of closure and related properties.","core_discovery":"The paper defines Q-filters on bounded lattices and studies their properties, establishing that this class is well-defined and admits an initial set of results that distinguish it within the broader theory of filters on lattices.","pith_inferences":["If Q-filters prove useful, analogous definitions could be attempted for other classes of posets or algebras that are not bounded.","The existence of a Q-filter calculus might simplify arguments that currently rely on embedding bounded lattices into larger structures.","Concrete examples of bounded lattices where Q-filters differ markedly from classical filters would make the definition immediately testable."],"forward_implications":["Q-filters exist and can be described explicitly in every bounded lattice.","The collection of all Q-filters on a given bounded lattice satisfies closure properties under the lattice operations.","Q-filters stand in a definable relation to other standard constructions such as ideals or congruences within the same lattice.","Results proved for Q-filters apply uniformly to all bounded lattices without further restrictions on the order."],"fun_headline_variants":["Q-filters defined in bounded lattices","Q-filters studied in bounded lattices","Defining Q-filters for bounded lattices","Q-filters analyzed in bounded lattices"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"A non-trivial and interesting theory of filters can be developed specifically for the class of bounded lattices using the proposed definition.","fun_headline_variants_meta":{"raw":{"variants":["Q-filters defined in bounded lattices","Q-filters studied in bounded lattices","Defining Q-filters for bounded lattices","Q-filters analyzed in bounded lattices"]},"model":"grok-4.3","cost_usd":0.005951,"raw_usage":{"total_tokens":2683,"prompt_tokens":390,"num_sources_used":0,"completion_tokens":38,"cost_in_usd_ticks":59512000,"prompt_tokens_details":{"text_tokens":390,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2255,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":390,"tokens_out":38,"duration_ms":17473,"temperature":1.0,"reasoning_tokens":2255,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T17:54:47.690282+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A proof that every Q-filter on a bounded lattice is already a standard filter (or that the collection of Q-filters is empty or trivial in every non-trivial bounded lattice) would remove the motivation for the new notion.","supporting_citations":[],"review_version":1}