{"id":"330307ba-4828-495a-8ef3-f8233799dde1","arxiv_id":"2606.21010","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Introduces causal-constitutive loops to specify system boundaries such that self-determination is satisfied when constitutive relations involve two or more independent variables, implying dual-process organization.","lead":"The paper proposes defining boundaries of self-determining systems via closures of loops formed by causal and constitutive relations. This framework requires constitutive relations to involve at least two independent variables to ensure internal causes and avoid supervenience, resulting in a dual-process structure.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Constraint requiring constitutive relations to have ≥2 independent variables may presuppose system closure rather than derive internal causes from it.","rationale":"The reader's weakest_assumption already isolates the same circularity risk in the constraint step. Because the full text was not needed to locate this structural gap and the abstract states the 'necessarily includes' claim without further derivation, the concern remains the single most load-bearing one; no stronger internal inconsistency or external-consensus clash was evident.","tokens_in":1652,"tokens_out":326,"duration_ms":14799,"concrete_test":"Formalize the causal/constitutive distinction and loop-closure definition in a minimal logical system (e.g., first-order logic with two relation symbols); add only the 'at least two independent variables' axiom and attempt to derive existence of an internal cause; check whether the derivation succeeds or requires an extra premise about system identity or boundary.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The argument defines boundaries via causal-constitutive loop closures, then asserts that constraining constitutive relations to ≥2 independent variables forces internal causes (hence self-determination) and yields two interdependent loops. This step is load-bearing because identifying a relation as constitutive (asymmetric to causal) and counting its 'independent variables' appears to require an already-delineated system whose internal structure is not yet justified by the loop-closure definition. Without an explicit derivation showing how the two-variable rule alone generates an internal cause from the loop axioms, the move risks being a stipulation that encodes the desired self-determination rather than following from the minimal constraint.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper defines a self-determining system as one with internal causes and proposes that system boundaries are closures of causal-constitutive loops formed by two asymmetric relations. It claims that constraining constitutive relations to involve at least two independent variables forces the presence of internal causes (hence self-determination) while avoiding reduction to supervenience, and that this minimal constraint produces two interdependent loops implying a dual-process organization.","tokens_in":1824,"tokens_out":544,"duration_ms":19817,"significance":"If the argument can be made non-circular and supported by explicit derivation, the framework could provide a conceptual tool for distinguishing self-determination from standard causal or supervenience accounts in systems theory and AI. As written, however, the contribution remains definitional with no formal proofs, counter-example analysis, or empirical tests supplied.","major_comments":[{"comment":"Abstract: The central claim that 'by constraining constitutive relations, the resulting system necessarily includes internal causes' is presented as following from the two-independent-variable requirement, yet the boundary definition ('system boundaries can be defined as closures of loops formed by these relations') already encodes internal relations via the loop-closure operation; no derivation is given showing how the variable-count constraint alone generates an internal cause from the loop axioms without presupposing the closure.","section":"Abstract"},{"comment":"Abstract: The assertion that the two-variable constraint 'leads to two interdependent loops, which implies a dual-process organization' lacks any formal mapping from loop interdependence to the notion of 'process'; without an explicit definition or derivation of what counts as a process or how the loops are shown to be interdependent beyond the constitutive/causal distinction, this implication does not follow from the stated minimal requirement.","section":"Abstract"},{"comment":"Abstract: The requirement that constitutive relations 'must involve at least two independent variables' to prevent reduction to supervenience is introduced as a stipulation without an argument demonstrating why a single-variable constitutive relation would collapse into supervenience or how the two-variable case is independently justified rather than chosen to produce the desired internal-cause outcome.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract introduces technical terms such as 'causal-constitutive loops' and 'dual-process organization' without providing initial definitions or citations to related literature on closure or constitutive relations.","section":null}],"recommendation":"major_revision","confidential_remarks":"The manuscript's content is almost entirely conceptual and definitional with no algorithmic, computational, or empirical components, raising questions about fit for a cs.AI venue."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive feedback highlighting the need for more explicit derivations in our conceptual framework. We agree that the manuscript would benefit from additional formalization to strengthen the claims. We address each major comment below and will revise the paper accordingly.","responses":[{"response":"We recognize the potential circularity concern. The loop-closure is a general mechanism for boundary definition, but the two-variable constraint on constitutive relations is what ensures the presence of internal causes by requiring interdependence that cannot be fully externalized. We will add a dedicated subsection providing a step-by-step logical derivation from the axioms of causal and constitutive relations to demonstrate how the variable constraint produces internal causation independently of the closure assumption.","revision_made":"yes","referee_comment":"[Abstract] Abstract: The central claim that 'by constraining constitutive relations, the resulting system necessarily includes internal causes' is presented as following from the two-independent-variable requirement, yet the boundary definition ('system boundaries can be defined as closures of loops formed by these relations') already encodes internal relations via the loop-closure operation; no derivation is given showing how the variable-count constraint alone generates an internal cause from the loop axioms without presupposing the closure."},{"response":"We agree that 'process' requires explicit definition. In the revised manuscript, we will define a 'process' as a sequence of state changes driven by the causal relations within the loop. We will then derive the interdependence of the two loops (one causal, one constitutive) and show how this necessitates a dual-process structure. This will include a formal mapping.","revision_made":"yes","referee_comment":"[Abstract] Abstract: The assertion that the two-variable constraint 'leads to two interdependent loops, which implies a dual-process organization' lacks any formal mapping from loop interdependence to the notion of 'process'; without an explicit definition or derivation of what counts as a process or how the loops are shown to be interdependent beyond the constitutive/causal distinction, this implication does not follow from the stated minimal requirement."},{"response":"The justification is that a single-variable constitutive relation would allow all system properties to be determined by a single factor, effectively making the system supervenient on that factor without internal causation. With two or more independent variables, the constitutive relation requires mutual determination that introduces internal causes. We will expand the manuscript with this argument and a brief counter-example for the single-variable case to show the collapse.","revision_made":"yes","referee_comment":"[Abstract] Abstract: The requirement that constitutive relations 'must involve at least two independent variables' to prevent reduction to supervenience is introduced as a stipulation without an argument demonstrating why a single-variable constitutive relation would collapse into supervenience or how the two-variable case is independently justified rather than chosen to produce the desired internal-cause outcome."}],"tokens_in":1360,"tokens_out":607,"duration_ms":15934,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The central move is to define self-determining systems through closures of causal-constitutive loops and then add the requirement that constitutive relations involve two independent variables to block supervenience reduction. This is presented as yielding two interdependent loops and therefore a dual-process structure.\n\nWhat is new is the explicit two-variable constraint on constitutive relations together with the dual-process consequence. The paper does a clear job stating the difficulties that arise when boundaries are drawn from causal relations alone, such as external causes and circularity.\n\nThe soft spot is that the argument stays at the level of definitions. The stress-test concern holds up on the abstract: counting independent variables in a constitutive relation and labeling it as such appears to require an already-delineated system, so the constraint does not obviously generate internal causes from the loop axioms. No derivation, counter-example, or worked case is supplied, which leaves the central claim thin.\n\nThis is for people working on conceptual foundations of autonomy in AI or systems theory. A reader already thinking about closure arguments might pick up the distinction between the two relation types.\n\nIt is worth sending to peer review so the full manuscript can be checked for any supporting derivations or applications that would make the two-variable rule less ad hoc.","headline":"The paper claims that forcing constitutive relations to have at least two independent variables creates internal causes and dual-process organization, but this step looks like a stipulation that assumes the boundary it aims to derive.","tokens_in":2314,"tokens_out":335,"would_cite":false,"duration_ms":14867,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Constraining constitutive relations to at least two variables forces internal causes and two interdependent loops in self-determining systems.","keywords":["self-determining systems","causal relations","constitutive relations","system closure","causal-constitutive loops","dual-process organization","boundary specification","supervenience"],"falsifier":"A concrete system that achieves self-determination and closed boundaries while using only single-variable constitutive relations, or a demonstration that multi-variable constitutive relations can still reduce to supervenience.","tokens_in":2558,"feed_emoji":"🔄","tokens_out":559,"duration_ms":11908,"temperature":0.7,"pith_summary":"The paper defines a self-determining system as one where causes originating inside it affect the system. Pure causal definitions of boundaries run into problems with external inputs and circular causation. The authors separate causal relations from constitutive relations and close loops that combine both types to mark system boundaries. Requiring that constitutive relations depend on at least two independent variables guarantees the presence of internal causes, meets the self-determination condition, and blocks reduction to supervenience. The minimal case produces two linked loops, which the paper presents as the basis for a dual-process organization.","feed_headline":"Two interdependent loops close self-determining system boundaries","feed_subtitle":"Requiring constitutive relations to depend on at least two variables forces internal causes and blocks reduction to supervenience.","key_machinery":"causal-constitutive loops, formed by asymmetric causal and constitutive relations, which close to define system boundaries and enforce self-determination when constitutive relations require multiple variables","core_discovery":"A self-determining system is one in which causes originating within the system influence the system itself. System boundaries are defined as closures of loops formed by causal and constitutive relations. By constraining constitutive relations to involve at least two independent variables, the resulting system necessarily includes internal causes and thereby satisfies self-determination. This minimal requirement leads to two interdependent loops, which implies a dual-process organization.","pith_inferences":["The same constraint could be used to test whether artificial agents achieve autonomy without external supervisory loops.","The requirement for two variables might be checked directly in dynamical models by counting the independent inputs to each constitutive mapping.","If the two-loop structure holds, removing one loop should break self-determination in any implementation that follows the definition."],"forward_implications":["Self-determining systems must contain internal causes once constitutive relations are constrained to multiple variables.","Constitutive relations with only one variable collapse the account into supervenience.","Two interdependent loops are the direct structural consequence of the minimal constraint.","Boundaries are marked by combined causal-constitutive closure rather than causal closure alone.","The organization takes the form of dual-process structure."],"fun_headline_variants":["Causal-constitutive loops close self-determining boundaries","Two loops close self-determining boundaries via causal and constitutive relations","Constitutive relations with two variables close self-determining loops","Interdependent causal-constitutive loops define self-determining closure"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"Constitutive relations can be defined independently to require at least two variables without already assuming the self-determination or boundary closure the definition is meant to produce.","fun_headline_variants_meta":{"raw":{"variants":["Causal-constitutive loops close self-determining boundaries","Two loops close self-determining boundaries via causal and constitutive relations","Constitutive relations with two variables close self-determining loops","Interdependent causal-constitutive loops define self-determining closure"]},"model":"grok-4.3","cost_usd":0.006763,"raw_usage":{"total_tokens":3026,"prompt_tokens":588,"num_sources_used":0,"completion_tokens":68,"cost_in_usd_ticks":67628000,"prompt_tokens_details":{"text_tokens":588,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2370,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":588,"tokens_out":68,"duration_ms":21965,"temperature":1.0,"reasoning_tokens":2370,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T14:45:28.344177+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A concrete system that achieves self-determination and closed boundaries while using only single-variable constitutive relations, or a demonstration that multi-variable constitutive relations can still reduce to supervenience.","supporting_citations":[],"review_version":1}