{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__gender_studies","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"gender_studies","decision":"CANDIDATE","problem_id":"universal_gender_equity_policy_outcome_decision","causal_lever_id":"restrict_and_label_policy_analysis_guarantees","proposal":{"problem":"Institutions may claim that an automated audit can determine, correctly and with guaranteed termination, whether any executable policy or workflow will ever produce a formally specified gender-disparate outcome. For open-ended policies with unbounded state, this universal guarantee may be unsupported, while timeouts, abstractions, and sampled simulations are liable to be reported as definitive compliance findings.","actors_substrate":["gender-equity researchers and auditors","policy owners","software and workflow designers","workers, students, and service users affected by policies","institutional review and governance bodies"],"observable_state":"An audit accepts unrestricted executable policies, promises a binary compliant/noncompliant result, and collapses timeout, abstraction uncertainty, out-of-scope input, and no detected disparity into the same output.","consequence":"A policy may receive false assurance, or useful auditing may be abandoned after repeated analyzer failures are mistaken for proof of undecidability.","affected_objective":"Produce trustworthy, interpretable gender-equity assessments without overstating what automated policy analysis can decide.","structural_mapping":[{"archetype_element":"open-ended problem class","domain_realization":"All executable institutional policies and unbounded workflows, rather than a fixed corpus or finite set of cases.","claim_kind":"HYPOTHESIS"},{"archetype_element":"universal exact terminating answer","domain_realization":"A binary verdict about whether a policy can ever yield a specified gender-disparate outcome.","claim_kind":"HYPOTHESIS"},{"archetype_element":"decidable restriction","domain_realization":"A mechanically enforceable finite-state policy language with bounded actors, attributes, transitions, and horizon.","claim_kind":"INFERENCE"},{"archetype_element":"weaker honest fallback","domain_realization":"Sound over-approximation, bounded exploration, or human escalation labeled with UNKNOWN and scope metadata.","claim_kind":"INFERENCE"},{"archetype_element":"semantic fidelity invariant","domain_realization":"The formal disparity predicate and policy model must remain traceable to the equity question affected parties recognize.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Define policies, outcome predicates, and whether the claim concerns all executions."},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Publish the policy grammar, state variables, identity categories, and encoding limits."},{"component":"Computation Model Contract","status":"adapted","domain_realization":"Declare finite-state exploration, abstraction, resource bounds, and any human input."},{"component":"Solvability Guarantee Profile","status":"adapted","domain_realization":"Distinguish exact, sound-one-sided, bounded, and unresolved verdicts."},{"component":"Quantifier and Scope Map","status":"adapted","domain_realization":"Separate every policy/every execution claims from individual-policy findings."},{"component":"Computability Status Lattice","status":"adapted","domain_realization":"Classify fragments as decidable, recognizable, relative, or unresolved."},{"component":"Constructive Procedure Witness","status":"adapted","domain_realization":"Require an algorithm plus correctness and termination arguments for exact fragments."},{"component":"Reduction Preservation Contract","status":"adapted","domain_realization":"Require any impossibility transfer to preserve the policy outcome predicate."},{"component":"Computability Impossibility Certificate","status":"adapted","domain_realization":"Require a matching proof before calling the unrestricted audit undecidable."},{"component":"Assumption Register","status":"direct","domain_realization":"Record finiteness, observability, semantics, and abstraction assumptions."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"List enforceable policy fragments supporting total analysis."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Specify which violations can be confirmed by witnesses without guaranteeing clearance."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Keep UNKNOWN, timeout, out-of-scope, false, and tool failure distinct."},{"component":"Fallback Solution Contract","status":"adapted","domain_realization":"Label each bounded or approximate result with its actual guarantee."},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Version the shipped audit claim and supporting evidence."},{"component":"Recheck Trigger","status":"adapted","domain_realization":"Reassess after grammar, disparity predicate, state, or external-input changes."},{"component":"Termination Condition","status":"direct","domain_realization":"Set explicit state, depth, time, or step bounds."},{"component":"Scope Boundary","status":"direct","domain_realization":"Mechanically reject or quarantine policies outside the supported fragment."},{"component":"Decision Record","status":"direct","domain_realization":"Record why each analysis mode and public claim was authorized."},{"component":"Uncertainty Residue","status":"direct","domain_realization":"Retain unproved obligations and abstraction-induced false-alarm risk."},{"component":"Independent Proof Review","status":"adapted","domain_realization":"Have an independent reviewer check formal claims and semantic correspondence."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"After decidability, evaluate whether the fragment is practically analyzable."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Over-approximate policy executions; a clearance is valid only if abstraction soundness is established.","counterfactual_removal":"No sound scalable fallback would cover policies beyond exhaustive finite exploration."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Exhaustively inspect a small finite policy fragment and horizon.","counterfactual_removal":"The first test would lack a total, checkable bounded reference result."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version scope, guarantees, evidence, and recheck triggers.","counterfactual_removal":"Guarantees could drift without provenance."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Gate fragments proved decidable for practical cost assessment.","counterfactual_removal":"Decidability could be mistaken for deployability."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Required evidence for an exact fragment.","counterfactual_removal":"Exactness would rest on tests rather than class-wide obligations."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No packet evidence supplies a valid self-referential construction for this policy class.","counterfactual_removal":"No causal change."},{"slug":"enumeration_and_dovetailing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A bounded explicit-UNKNOWN protocol is safer for the initial institutional use.","counterfactual_removal":"No causal change."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Route in-fragment, abstract, bounded, and escalation cases while preserving labels.","counterfactual_removal":"Weaker outputs could again be laundered into binary verdicts."},{"slug":"halting_problem_reduction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Undecidability is unresolved until a computable predicate-preserving embedding is exhibited.","counterfactual_removal":"No causal change."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use a syntactically enforceable finite-state policy language.","counterfactual_removal":"The exact terminating guarantee would lack a defensible scope."},{"slug":"many_one_reduction_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Retain as a future evidence standard, but no source-to-target map is supplied.","counterfactual_removal":"No current causal change."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"An unenforced promise permits authoritative behavior outside the guarantee; enforceable syntax is preferred.","counterfactual_removal":"No causal change."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use an in-scope policy missed or mislabeled by the baseline to refute its universal claim.","counterfactual_removal":"Overbroad baseline claims would be harder to falsify cheaply."},{"slug":"proof_checking","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently check termination, correctness, and declared premises.","counterfactual_removal":"Formal gaps could authorize a false boundary."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate any later impossibility claim and expose encoding assumptions.","counterfactual_removal":"A reversed or incomplete reduction could be accepted."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Return witnessed violation or UNKNOWN at the resource bound, never infer compliance.","counterfactual_removal":"Timeouts could again become false clearance."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unneeded for the bounded first test and unable to repair a semantically wrong model.","counterfactual_removal":"No causal change."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Relative oracle degrees do not answer the immediate shipped-guarantee question.","counterfactual_removal":"No causal change."}],"causal_chain":["Specify the policy class, execution semantics, disparity predicate, and universal quantifiers.","Enforce a finite decidable fragment and classify other inputs explicitly.","Run exact bounded analysis or a sound over-approximation under a labeled contract.","Route unconfirmed or unsupported cases to UNKNOWN or accountable human review.","Version the guarantee and recheck it when language or assumptions change.","Reduce false definitive clearances while preserving useful limited automation (HYPOTHESIS)."],"baseline":"Ordinary bias audits use samples, simulations, checklists, or unrestricted analyzers and may communicate 'no disparity found' without separating absence of evidence from a universal clearance.","nearest_rival":"A conventional mixed-method gender-impact assessment using sampled outcomes, qualitative review, and expert judgment, without a formal computability-boundary classification.","authority_safety":{"affected_parties":["people categorized or governed by audited policies","gender-minoritized groups","policy operators and reviewers"],"decision_authority":"An equity-governance body with affected-party representation authorizes scope and public claims; technical staff may not upgrade guarantees.","authorized_first_step":"Pilot on synthetic, non-deployed finite-state policies with seeded disparity witnesses; compare exhaustive truth, abstract results, UNKNOWN rates, and baseline labels.","excluded_actions":["inferring anyone's gender identity from proxy data","deploying automatic sanctions or eligibility decisions","reporting UNKNOWN or timeout as compliant","generalizing beyond the tested fragment","treating formal clearance as proof of substantive justice"],"halt_rollback":"Stop if the abstraction misses a seeded real violation, scope membership cannot be enforced, identity categories cause material semantic misrepresentation, or outputs are presented without labels; withdraw the affected guarantee record and revert to human review."}},"negative_tests":{"strongest_counterevidence":"If the operational policy language and state space are already finite, effectively enumerable, and covered by a proven total algorithm, the problem is decidable and the remaining issue is complexity or semantic validity, not a computability boundary.","analogy_break":"Gendered harm is contextual, intersectional, and reflexive; unlike program safety, it may not admit a stable formal predicate. Human deliberation also supplies situated judgment rather than a reliable computational oracle.","failure_condition":"The restricted fragment excludes the policies stakeholders most need assessed, or abstraction alarms and UNKNOWN outputs are so frequent that users bypass the system.","problem_falsifier":"No stakeholder or product actually claims an exact terminating class-wide verdict, or the equity predicate cannot be stabilized enough to define a decision problem; then the diagnosed computability problem is absent or premature.","intervention_falsifier":"In the bounded pilot, guarantee labels and routing do not reduce false definitive clearances or improve correct interpretation relative to the mixed-method rival, while maintaining useful coverage.","risks":["Formalization may erase nonbinary, intersectional, or changing identities.","A sound computational result may legitimize an unjust disparity definition.","Restricted coverage may be advertised as universal.","Human escalation may reproduce institutional power asymmetries.","False alarms may divert scrutiny from harms outside the model."]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_ADAPTATION","prior_art_status":"UNSEARCHED","evidence_maturity":"HYPOTHESIS"},"revision_change_log":{"revision_kind":"ORIGINAL","prior_problem_id":null,"prior_causal_lever_id":null,"problem_changed":false,"causal_lever_changed":false,"conceptual_changes":[],"operational_changes":[],"repairs_addressed":[]},"confidence":0.78,"generator_notes":"Closed-book structural transfer. The candidate is conditional on the audit operating over executable policy models with a stable formal outcome predicate; it does not claim that gender or justice itself is algorithmically decidable."}