{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__religious_studies_theology","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"religious_studies_theology","decision":"CANDIDATE","problem_id":"arbitrary_formal_theology_entailment_overclaim","causal_lever_id":"enforceable_decidable_fragment_with_labeled_unknown","proposal":{"problem":"A research platform is expected to return a terminating YES/NO answer about whether any query follows from, conflicts with, or is permitted by any user-supplied formalization of doctrines or ritual rules. The accepted rule language, quantifiers, and guarantee are not fixed, so timeouts or failed proof searches may be reported as non-entailment while decidable fragments and unrestricted inputs inherit the same claim. Whether an actual platform has this defect is HYPOTHESIS.","actors_substrate":["theologians and religious-studies researchers encoding rule systems","software and formal-methods researchers","participating religious communities whose positions are represented","students and downstream corpus users"],"observable_state":"The interface accepts formally encoded axioms, rules, and queries but emits an unqualified binary verdict despite timeout, unsupported syntax, or unfinished proof search.","consequence":"A computational limit or representation gap is presented as a substantive theological finding, creating false comparisons, exclusions, or claims of doctrinal inconsistency.","affected_objective":"Produce reproducible formal analysis without misrepresenting theological meaning, inferential status, or community authority.","structural_mapping":[{"archetype_element":"Unrestricted universal analyzer","domain_realization":"An entailment or consistency service advertised for arbitrary encoded doctrinal and ritual rule systems.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Implicit instance representation","domain_realization":"Unstated grammar and semantics for axioms, rules, modalities, quantifiers, and queries.","claim_kind":"INFERENCE"},{"archetype_element":"Total exact guarantee","domain_realization":"A correct terminating YES/NO theological-entailment verdict for every accepted formal system.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Decidable region","domain_realization":"A mechanically enforceable logical fragment paired with a proved terminating decision procedure.","claim_kind":"INFERENCE"},{"archetype_element":"One-sided fallback","domain_realization":"Proof search may certify entailment with a checkable derivation but returns UNKNOWN at its resource bound.","claim_kind":"INFERENCE"},{"archetype_element":"Boundary governance","domain_realization":"Versioned records connect syntax, semantics, proof obligations, output labels, and reclassification triggers.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Define formal entailment, inconsistency, and permission as separate classes."},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Publish machine grammar, semantics, and query encoding."},{"component":"Computation Model Contract","status":"adapted","domain_realization":"Fix proof calculus, machine, resources, and any human or prover assistance."},{"component":"Solvability Guarantee Profile","status":"adapted","domain_realization":"Distinguish total decision, proof recognition, and bounded analysis."},{"component":"Quantifier and Scope Map","status":"adapted","domain_realization":"State whether claims cover every system, one fragment, or named corpora."},{"component":"Computability Status Lattice","status":"adapted","domain_realization":"Record decidable, recognizable, partial, relative, or unresolved status."},{"component":"Constructive Procedure Witness","status":"adapted","domain_realization":"Supply the fragment decider with correctness and termination arguments."},{"component":"Reduction Preservation Contract","status":"adapted","domain_realization":"Require any impossibility transfer to preserve encoded instances and answers."},{"component":"Computability Impossibility Certificate","status":"adapted","domain_realization":"Leave unrestricted impossibility unresolved absent a checked reduction or direct proof."},{"component":"Assumption Register","status":"adapted","domain_realization":"List semantic, syntactic, finiteness, consistency, and oracle assumptions."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"Map enforceable logical fragments and their coverage loss."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"A checked derivation licenses YES; failure to find one does not license NO."},{"component":"Unknown and Nontermination Policy","status":"adapted","domain_realization":"Separate UNKNOWN, timeout, malformed, out-of-fragment, and false."},{"component":"Fallback Solution Contract","status":"adapted","domain_realization":"Route to exact fragment decision, bounded proof search, or abstention."},{"component":"Computability Guarantee Record","status":"adapted","domain_realization":"Version the procedure, fragment, proof, and public guarantee."},{"component":"Recheck Trigger","status":"adapted","domain_realization":"Reassess after grammar, semantics, prover, corpus, or guarantee changes."},{"component":"Termination Condition","status":"adapted","domain_realization":"Prove fragment termination and bound fallback search explicitly."},{"component":"Scope Boundary","status":"adapted","domain_realization":"Mechanically reject or quarantine inputs outside the supported fragment."},{"component":"Decision Record","status":"adapted","domain_realization":"Record why each shipped mode and label was authorized."},{"component":"Uncertainty Residue","status":"adapted","domain_realization":"Retain open proof obligations and unformalized theological content."},{"component":"Independent Proof Review","status":"adapted","domain_realization":"Have an independent reviewer check theorem, encoding, and proof."},{"component":"Complexity Follow-On Gate","status":"adapted","domain_realization":"Assess cost only after a total procedure is established."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Finite over-approximation could analyze transition models, but the proposed core task is logical entailment and one-directional safety lacks a defined analogue.","counterfactual_removal":"No change to the proposed causal chain."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Exhaustively test all formulas and rule sets within a tiny declared grammar and size bound.","counterfactual_removal":"The pilot loses a complete bounded check but the boundary intervention remains viable."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version the supported fragment, guarantees, assumptions, and recheck triggers.","counterfactual_removal":"Guarantees can drift silently after language or prover changes."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Evaluate scaling only for fragments shown decidable.","counterfactual_removal":"Decidability could be mistaken for deployable feasibility."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Require an exhibited fragment decider plus correctness and termination proofs.","counterfactual_removal":"The restricted exact mode would lack its total-decision warrant."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No self-referential construction for the theological encoding is supplied.","counterfactual_removal":"Unrestricted status remains honestly unresolved."},{"slug":"enumeration_and_dovetailing","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Fairly interleave derivation searches when the calculus permits enumerable proofs.","counterfactual_removal":"The proposal loses its principled complete-on-YES recognizer."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Route each query to exact, bounded-recognition, or out-of-scope modes with guarantee labels.","counterfactual_removal":"Weaker results can again be laundered as universal binary verdicts."},{"slug":"halting_problem_reduction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The packet supplies no computable embedding into this target problem.","counterfactual_removal":"No justified impossibility conclusion is lost."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Define a syntactically checkable fragment admitting the proved decider.","counterfactual_removal":"There is no enforceable boundary supporting the total exact guarantee."},{"slug":"many_one_reduction_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Retain as an evidentiary option, but no source-to-target map is available closed-book.","counterfactual_removal":"Current classification is unchanged."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"An enforceable syntax restriction is safer than unchecked semantic promises.","counterfactual_removal":"The selected fragment contract still polices scope."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use an in-scope case where timeout becomes NO to refute any universal-correctness claim.","counterfactual_removal":"The pilot loses a cheap overclaim test, not its constructive evidence."},{"slug":"proof_checking","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently check termination, correctness, and formalized theorem alignment.","counterfactual_removal":"A flawed proof or wrong formalization could authorize false certainty."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate any later hardness claim on source-to-target direction and explicit assumptions.","counterfactual_removal":"Later impossibility claims become more vulnerable to reversed reductions."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Bound proof search and return UNKNOWN, never NO, when unconfirmed.","counterfactual_removal":"Timeout can again masquerade as theological non-entailment."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Optional implementation aid; proof search is not itself a total decision guarantee.","counterfactual_removal":"The core protocol can use any checked recognizer."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No oracle-relative classification is needed for the bounded first test.","counterfactual_removal":"No operational or causal element changes."}],"causal_chain":["Mechanically classify each encoded query against the supported fragment.","Use a proved total decider only inside that fragment.","For eligible unrestricted proof search, accept checked witnesses but label resource exhaustion UNKNOWN.","Route malformed and out-of-scope inputs without a substantive verdict.","Version guarantees and reopen classification when language or assistance changes.","Therefore computational failure is less likely to be published as theological negation or inconsistency."],"baseline":"One general-purpose prover or rule engine accepts heterogeneous formalizations and emits YES/NO, with timeout or search failure treated as NO.","nearest_rival":"Improve prover heuristics and increase search resources while retaining the universal binary interface.","authority_safety":{"affected_parties":["represented religious communities","researchers and students relying on classifications","authors whose formalizations are compared"],"decision_authority":"The research-methods lead and formal-methods reviewer may authorize computational labels; participating scholars or community representatives govern representational adequacy. Neither can make the tool an authority on religious truth.","authorized_first_step":"On synthetic, non-sensitive examples, define one small fragment, prove its decider, exhaustively test all instances to a fixed size, and verify that injected timeout and out-of-fragment cases produce distinct labels.","excluded_actions":["issuing orthodoxy or truth judgments","ranking traditions","applying labels to people or communities","silently translating natural-language doctrine into the formal fragment","generalizing bounded results beyond the declared bound"],"halt_rollback":"Stop publication if an in-fragment counterexample breaks correctness or termination, if scope checks can be bypassed, or if UNKNOWN is rendered as NO. Disable binary export and revert to research-only labeled traces until repaired and independently reviewed."}},"negative_tests":{"strongest_counterevidence":"The packet provides no observation of such a platform, no proof that the intended unrestricted language can encode general computation, and no demonstrated timeout-to-NO error. Existing target formalisms may already be finite or decidable; thus deployment and undecidability claims are HYPOTHESIS.","analogy_break":"Formal derivability is not theological truth, lived meaning, orthodoxy, or communal legitimacy. Even a perfect decider answers only the encoded calculus, and computability analysis cannot repair an unfaithful formalization.","failure_condition":"The fragment excludes most research-relevant questions, scope membership cannot be enforced, UNKNOWN is operationally treated as negative, or proof review finds semantic mismatch.","problem_falsifier":"An audit shows the actual accepted class is finite or enforceably decidable, has a checked total procedure, and never converts timeout, malformed, or out-of-scope states into substantive verdicts; remaining difficulty is then complexity or interpretation.","intervention_falsifier":"Against the ordinary baseline, the bounded pilot does not reduce false binary verdicts or guarantee mislabeling, or the proposed fragment decider fails a legitimate in-fragment case or its termination proof.","risks":["A narrow formal fragment may erase concepts central to a tradition.","Official-looking labels may be mistaken for religious authority.","Communities with fewer formalization resources may be disproportionately marked UNKNOWN or out-of-scope.","A checked proof may certify the wrong semantic model.","Abstention pressure may recreate hidden binary coercion downstream."]},"null_rationale":null,"classification":{"candidate_kind":"DOMAIN_TRANSFER","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":0.76,"generator_notes":"Closed-book structural transfer. The candidate is conditional on a genuinely formal, sufficiently expressive input language; it does not claim that theology itself is algorithmically decidable or undecidable."}