{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__astronomy_astrophysics","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"astronomy_astrophysics","decision":"CANDIDATE","problem_id":"unrestricted_astrophysical_eventual_outcome_classification","causal_lever_id":"guarantee_tiered_astrophysical_reachability_routing","proposal":{"problem":"An astrophysical simulation service is asked to return an exact, terminating YES/NO answer for every admitted dynamical model and initial condition to questions such as whether a collision, escape, instability, or threshold event will ever occur. Model language, time horizon, numerical representation, and external evidence are not bounded, while timeouts are liable to be reported as negative outcomes. HYPOTHESIS: sufficiently expressive executable model classes may make this universal reachability requirement undecidable; the packet supplies no domain-specific proof.","actors_substrate":["astrophysicists submitting dynamical models","simulation-platform maintainers","reviewers and downstream catalog users","encoded initial conditions and evolution laws","compute infrastructure and certificate checkers"],"observable_state":"The interface promises Boolean eventual-outcome classifications across an open-ended model class, yet some runs time out or remain inconclusive and the system does not distinguish NO, UNKNOWN, out-of-scope, and numerical failure.","consequence":"Unresolved trajectories can be mislabeled as impossible events, while engineering effort is spent pursuing a total classifier without first establishing whether its declared class admits one.","affected_objective":"Scientifically defensible classification of long-term astrophysical outcomes without false certainty or unbounded commitment to impossible automation.","structural_mapping":[{"archetype_element":"unrestricted total-exact automation demand","domain_realization":"Exact terminating eventual-event classification for every admitted astrophysical model and initial condition.","claim_kind":"HYPOTHESIS"},{"archetype_element":"implicit representation and computation model","domain_realization":"Continuous versus finite-precision states, executable evolution laws, event predicates, horizon, and permitted certificates are unspecified.","claim_kind":"INFERENCE"},{"archetype_element":"boundary mapping and weaker fallback","domain_realization":"Classify enforceable fragments, bounded horizons, certified witnesses, and unresolved cases, then route each query to the strongest justified guarantee.","claim_kind":"INFERENCE"},{"archetype_element":"status honesty","domain_realization":"Keep proven NO distinct from unobserved event, timeout, numerical failure, out-of-scope, and UNKNOWN.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Define model families, initial conditions, event predicates, and eventual-reachability question."},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Specify finite encodings, numerical semantics, units, tolerances, and malformed-input handling."},{"component":"Computation Model Contract","status":"adapted","domain_realization":"Declare arithmetic, simulation semantics, certificate access, and any human or observational oracle."},{"component":"Solvability Guarantee Profile","status":"adapted","domain_realization":"Separate exact decision, certified YES, bounded non-occurrence, approximation, and UNKNOWN."},{"component":"Quantifier and Scope Map","status":"direct","domain_realization":"Record whether claims cover every model, a fragment, a bounded horizon, or one instance."},{"component":"Computability Status Lattice","status":"direct","domain_realization":"Track decidable, recognizable, partial, relative, unresolved, and any proved-undecidable classes."},{"component":"Constructive Procedure Witness","status":"adapted","domain_realization":"Retain algorithms plus correctness and termination arguments for supported fragments."},{"component":"Reduction Preservation Contract","status":"adapted","domain_realization":"Require any source-to-astrophysical-model encoding to preserve the event answer in the claimed direction."},{"component":"Computability Impossibility Certificate","status":"adapted","domain_realization":"Accept undecidability only after a domain-matched reduction or direct proof."},{"component":"Assumption Register","status":"direct","domain_realization":"Version arithmetic, model expressiveness, promises, horizon, and event semantics."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"Map enforceable finite-state, bounded-time, or syntactically restricted model classes."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Return certified YES when a checkable event witness is found without implying eventual NO."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Expose UNKNOWN, timeout, numerical failure, and out-of-scope separately."},{"component":"Fallback Solution Contract","status":"direct","domain_realization":"Label bounded, approximate, witness-only, and human-reviewed outputs with their actual guarantees."},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Publish a versioned, falsifiable guarantee for each supported mode."},{"component":"Recheck Trigger","status":"direct","domain_realization":"Reassess after model-language, arithmetic, event-predicate, oracle, or scope changes."},{"component":"Termination Condition","status":"adapted","domain_realization":"Set explicit step, horizon, precision, or search bounds for total fallback modes."},{"component":"Scope Boundary","status":"direct","domain_realization":"Mechanically reject or quarantine unsupported models and predicates."},{"component":"Decision Record","status":"direct","domain_realization":"Record selected modes, evidence, assumptions, and rejected universal claims."},{"component":"Uncertainty Residue","status":"adapted","domain_realization":"List unproved totality, abstraction error, unresolved instances, and model-to-reality mismatch."},{"component":"Independent Proof Review","status":"direct","domain_realization":"Have an independent reviewer check formal claims and their physical interpretation."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"Send proved-decidable fragments to scaling and numerical-feasibility analysis."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No sound finite over-approximation for the proposed physical semantics is supplied.","counterfactual_removal":"No change; bounded and restricted modes remain available."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Exhaust finite encodings within declared horizon and precision bounds.","counterfactual_removal":"The proposal loses its complete terminating bounded mode."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version the boundary, guarantees, assumptions, and triggers.","counterfactual_removal":"Guarantees could drift without traceability."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Assess cost only after decidability is established.","counterfactual_removal":"Decidable but infeasible fragments may be deployed prematurely."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Require totality and correctness evidence for exact fragment solvers.","counterfactual_removal":"Exact-mode claims would lack constructive support."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No self-referential astronomical construction is supplied.","counterfactual_removal":"No effect on the unresolved general-class status."},{"slug":"enumeration_and_dovetailing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Candidate enumeration and certified physical witnesses are not yet defined.","counterfactual_removal":"The bounded explicit-UNKNOWN protocol remains intact."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Route queries among exact-fragment, bounded, certified-YES, approximate, and escalation modes.","counterfactual_removal":"Weaker results could be presented under the universal guarantee."},{"slug":"halting_problem_reduction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"It becomes relevant only if a total computable answer-preserving embedding is constructed.","counterfactual_removal":"The proposal still avoids claiming undecidability."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Enforce a syntactic model fragment with a proved terminating procedure.","counterfactual_removal":"There is no enforceable exact-answer region."},{"slug":"many_one_reduction_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No target-specific mapping is available in the packet.","counterfactual_removal":"Impossibility remains unresolved rather than weakened."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unenforced physical promises could yield authoritative-looking errors; prefer checkable fragments.","counterfactual_removal":"The enforceable restriction remains."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use one in-scope timeout-misclassified or solver-failing instance to refute an existing universal implementation claim.","counterfactual_removal":"Universal overclaim detection becomes less decisive."},{"slug":"proof_checking","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently verify termination, correctness, and any impossibility certificate.","counterfactual_removal":"Boundary claims depend excessively on author authority."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate any later undecidability reduction and expose 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 certified YES or bounded UNKNOWN, never infer NO from exhaustion.","counterfactual_removal":"Timeouts can again masquerade as negative scientific conclusions."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Formal goals and semantics do not yet exist; proof checking suffices for the first test.","counterfactual_removal":"No change to initial viability."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No oracle-relative scientific requirement is present.","counterfactual_removal":"No change to the flat operational boundary needed here."}],"causal_chain":["Make the model class, encoding, quantifiers, and guarantee explicit.","Prevent unsupported transfer from timeout or chaos to undecidability.","Identify enforceable exact fragments and bounded complete regimes.","Route remaining queries to certified-YES, approximation, or explicit UNKNOWN.","Version evidence and recheck when expressiveness or assumptions change."],"baseline":"Run numerical simulations until an event occurs or resources expire, then report event/no-event through a Boolean interface, sometimes supplementing with expert judgment.","nearest_rival":"Numerical sensitivity, uncertainty-quantification, and scaling analysis; these address error and cost for specified computations but do not determine whether a total exact classifier exists for the declared class.","authority_safety":{"affected_parties":["researchers whose models are classified","downstream users of stability or event catalogs","platform operators","scientific reviewers"],"decision_authority":"The simulation platform's scientific owner may approve interface labels and the pilot; any computability verdict requires independent formal review plus domain review.","authorized_first_step":"Audit one model language and one event predicate; formalize their encoding and guarantees, then replay a bounded set of previously timed-out cases using outputs YES_WITH_CERTIFICATE, UNKNOWN_BOUND, OUT_OF_SCOPE, and NUMERICAL_FAILURE.","excluded_actions":["Claiming the unrestricted class undecidable without a valid proof","Reporting timeout as NO","Generalizing bounded results beyond their fence","Silently excluding difficult models","Treating mathematical-model certification as confirmation of physical reality"],"halt_rollback":"Halt the pilot if output labels are collapsed downstream, fragment membership cannot be enforced, or formal semantics diverge from the scientific task; revert to non-decisional simulation outputs and preserve all audit records."}},"negative_tests":{"strongest_counterevidence":"Operational astrophysical workflows may already use finite-precision states, fixed horizons, and finitely encoded integrators. If so, exhaustive evaluation is decidable in principle and the real problem is state-space growth or numerical validity, an anti-signature for this archetype.","analogy_break":"Astrophysical chaos, sensitivity to initial conditions, continuum mathematics, and long runtimes do not themselves imply undecidability; moreover, a proof about an encoded model does not automatically describe the physical universe.","failure_condition":"The mapping fails if no reusable universal exact guarantee is being claimed, or if every admitted instance is enforceably finite and bounded and only practical cost or approximation error causes failures.","problem_falsifier":"Show from the current specification and interface that inputs, horizons, and representations are enforceably bounded and that timeout/UNKNOWN is already distinct from NO, with no class-wide total-exact claim.","intervention_falsifier":"After formalization and pilot routing, unsupported Boolean conclusions persist at the same rate, or the restricted exact mode cannot preserve the scientifically intended event semantics and provides no useful coverage.","risks":["A formal restriction may exclude scientifically important models.","Users may treat UNKNOWN as evidence for stability.","Finite-precision certificates may not transfer to continuous physical dynamics.","Complexity may make a decidable bounded mode unusable.","An official decision record may enshrine an incorrect boundary."]},"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":0.78,"generator_notes":"The candidate is conditional on an actually unrestricted, reusable total-exact requirement. No astronomy-specific undecidability result is asserted; the first objective is classification of the requirement and evidence boundary."}