{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp09_archetype_breadth150_20260804","cell_id":"computability_boundary_mapping__chemistry_materials","arm":"BREADTH_PROBE_ONE_SHOT","candidate_id":"computability_boundary_mapping__chemistry_materials__P1","proposal_index":1,"version":0,"title":"Computability Boundary for Universal Hazard Reachability in Generative Reaction Networks","problem":"A materials-design platform is asked to accept any finitely specified generative reaction network and always terminate with an exact yes-or-no answer to whether any permitted reaction sequence can produce a designated hazardous species or structure. The proposed input language permits integer-valued species populations, repeated rules, conditional reactions, polymer growth, and open feed streams, but its representation, execution semantics, quantifiers, and termination guarantee are implicit. Successful simulations and timeouts are consequently at risk of being presented as class-wide safety decisions even though the full problem's computability status has not been established.","actors":["computational chemists defining reaction rules","materials scientists screening candidate processes","process-safety engineers consuming hazard judgments","platform engineers implementing the analyzer","an independent formal-methods reviewer","laboratory or plant decision owners"],"observable_state":"For the same machine-readable reaction-network language, bounded simulations sometimes find a hazardous trajectory, while other runs exhaust their resource budgets without a witness. The interface nevertheless expects a Boolean SAFE or HAZARDOUS result and does not distinguish exhaustive non-reachability, timeout, malformed input, unsupported expressiveness, or unresolved reachability.","consequence":"A timeout or incomplete search can be converted into an unsupported safety judgment, while attempts to satisfy an unexamined universal exact-termination requirement can consume engineering effort without clarifying whether the obstacle is logical impossibility, computational complexity, or implementation quality.","affected_objective":"Maintain truthful, terminating, and auditable hazard-screening semantics without discarding useful exact analysis for enforceable finite reaction-network subclasses.","intervention":"Create a versioned Reaction-Network Reachability Boundary Record. It fixes the problem class, finite encoding, transition semantics, permitted feed and interaction, and the requested soundness, completeness, and termination guarantees. It then seeks both a constructive total procedure and a checked impossibility transfer for the unrestricted language. Until one is established, it classifies that language as unresolved and replaces forced Boolean output with WITNESS_FOUND, UNKNOWN_RESOURCE_LIMIT, UNKNOWN_BOUNDARY_STATUS, OUT_OF_SCOPE, and INVALID_MODEL. In parallel, it defines an enforceable closed, atom-bounded, finite-species fragment; applies bounded-domain exhaustive search there; and permits REACHABLE or UNREACHABLE only after the finite state space is exhaustively covered. Any language, feed, precision, or guarantee change triggers reclassification.","structural_mapping":[{"archetype_element":"Problem-Class Specification","domain_realization":"Decide whether at least one execution of any valid encoded reaction network reaches a state containing a designated hazardous species or substructure."},{"archetype_element":"Instance Representation Contract","domain_realization":"Encode finite species and reaction-rule descriptions, integer populations, initial conditions, feed rules, hazardous predicates, and execution semantics without implicit infinite-precision quantities or unstated chemical oracles."},{"archetype_element":"Computation Model Contract","domain_realization":"Declare a discrete transition-system analyzer with no laboratory oracle; any external database, expert judgment, or experimental measurement is a separately classified assisted capability."},{"archetype_element":"Solvability Guarantee Profile","domain_realization":"Separate sound witness detection, complete non-reachability, total termination, and uniform coverage of every valid network instead of bundling them into one Boolean promise."},{"archetype_element":"Quantifier and Scope Map","domain_realization":"Distinguish one modeled process, all networks within explicit atom and species bounds, and every network expressible in the unrestricted generative language."},{"archetype_element":"Computability Status Lattice","domain_realization":"Record the unrestricted language as unresolved pending proof; record positive witness search separately from total decision; classify only proven finite fragments as decidable."},{"archetype_element":"Decidable Subclass Map","domain_realization":"Identify closed networks with enforceable finite species, atom-count, population, and rule bounds whose reachable state graph is finite and effectively enumerable."},{"archetype_element":"Unknown and Nontermination Policy","domain_realization":"Preserve timeout, cancellation, unsupported model, unresolved status, and failure as distinct outcomes; none means that the hazardous state is unreachable."},{"archetype_element":"Fallback Solution Contract","domain_realization":"Route finite-fragment inputs to exhaustive decision, unrestricted inputs to bounded witness search with explicit unknown, and high-consequence unknowns to authorized safety review."},{"archetype_element":"Recheck Trigger","domain_realization":"Reopen the classification when unbounded feed, new recursion-like rule composition, continuous exact values, external solvers, or stronger public guarantees are introduced."}],"mechanism_mapping":[{"mechanism_slug":"halting_problem_reduction","role":"Attempt a property-preserving encoding from arbitrary program execution into reaction-network hazard reachability to test whether a total unrestricted decider would decide halting; accept the conclusion only if the encoding and semantics match.","counterfactual_removal":"Without this or another sound impossibility proof, repeated timeouts could not justify classifying the unrestricted problem as undecidable."},{"mechanism_slug":"bounded_domain_exhaustive_search","role":"Enumerate the complete reachable state graph for the enforceable closed, finite fragment and terminate with REACHABLE or UNREACHABLE.","counterfactual_removal":"The intervention would expose uncertainty but would not recover exact total decisions for a useful restricted class."},{"mechanism_slug":"semi_decision_with_explicit_unknown","role":"Return a checkable reaction trajectory when hazard reachability is witnessed, while reporting unresolved or resource-limited status rather than false when search ends without exhaustive coverage.","counterfactual_removal":"Operational deadlines would again pressure the interface to collapse incomplete search into an unsupported non-hazard conclusion."},{"mechanism_slug":"proof_checking","role":"Have an independent reviewer verify any constructive termination argument, reduction direction, semantic preservation claim, and finite-state bound before the public classification changes.","counterfactual_removal":"A model mismatch or reversed reduction could silently produce an invalid computability or safety claim."}],"causal_chain":["The unrestricted rule language permits open-ended state generation and repeated conditional transformations.","The product requirement quantifies over every valid encoded network and demands an exact answer with guaranteed termination.","Simulation success on selected instances establishes neither a total procedure nor exhaustive non-reachability; timeout establishes neither safety nor undecidability.","The boundary record makes representation, computation model, quantifiers, and guarantee explicit and tests constructive and impossibility evidence against the same specification.","An enforceable finite fragment yields a finite reachable-state graph that can be exhaustively searched, while the unrestricted class retains witness-search and explicit-unknown semantics until classified.","Downstream users receive conclusions whose meanings match the evidence and can route unknown or out-of-scope cases without treating them as safe."],"baseline":"The comparison baseline is bounded trajectory simulation followed by a forced Boolean classification: a found hazardous trajectory is labeled HAZARDOUS, while failure to find one before a cutoff is treated as SAFE or manually interpreted without a formal distinction among exhaustive absence, timeout, and unsupported input.","nearest_rivals":["Longer or more parallel reaction-trajectory simulation, which may find additional witnesses but does not establish totality or complete non-reachability for the declared class.","Conservative chemical hazard heuristics, which can screen structures or rules but operate under an error or abstention contract rather than deciding exact reachability.","Finite-state model checking applied without an enforceable scope contract, which is exact for the finite model received but does not automatically cover networks with unbounded feeds, populations, or generated species.","Manual expert review, which may support a process decision but is an assisted capability with competence, latency, refusal, and accountability conditions rather than an autonomous total algorithm."],"remaining_contrastive_claim":"The candidate's distinctive claim is not that a faster simulator or better chemical heuristic will improve predictions; it is that exact universal hazard reachability must first be classified relative to a precise reaction-rule language and computation model, after which exact decisions are confined to proven enforceable fragments and all weaker searches retain explicit unknown semantics.","authority_safety":{"decision_authority":"The process-safety owner retains authority over laboratory or plant disposition; the formal-methods reviewer may approve the computability classification and finite-fragment proof but may not declare a material or process safe.","authorized_first_step":"A computational chemist and formal-methods reviewer may formalize a non-production subset of the existing rule language, construct synthetic test networks, and evaluate proof obligations without changing safety labels or operating conditions.","excluded_actions":["Declaring an unrestricted network safe because search timed out or found no witness","Changing production, laboratory, or materials-release decisions on the basis of the boundary exercise alone","Claiming undecidability before a checked reduction or matching impossibility proof exists","Extending a finite-fragment guarantee to inputs whose fragment membership is not enforceably verified","Treating an expert, database, or experimental measurement as an unstated infallible oracle"],"halt_rollback":"Halt if formalization changes the chemical meaning of the screening question, fragment membership cannot be conservatively enforced, or a reviewer finds a representation or reduction mismatch. Roll back to the prior non-Boolean research output, preserve all prior safety controls, and mark every affected classification UNRESOLVED pending correction."},"negative_tests":{"strongest_counterevidence":"A checked uniform algorithm that exactly decides hazard reachability and terminates for every network admitted by the unrestricted representation would defeat the suspected boundary; alternatively, proof that the supposedly unrestricted language always induces a finite effectively enumerable state space would collapse it into the bounded case.","problem_falsifier":"If the operational requirement concerns only individually declared finite networks with verified bounds and makes no class-wide claim, then the central issue is complexity or model validity rather than computability-boundary confusion.","intervention_falsifier":"The intervention fails if its finite fragment cannot be recognized before analysis, if exhaustive enumeration does not terminate under the stated bounds, if the restriction removes the chemistry needed for the safety question, or if users still interpret UNKNOWN as SAFE.","risks":["A formal discrete model may omit kinetic, thermodynamic, spatial, or measurement conditions that determine real chemical hazard.","The finite fragment may exclude legitimate polymerization, feed, or surface-growth cases and shift review burden unevenly.","State-space exhaustion may be computable yet operationally intractable, requiring a separate complexity assessment.","A candidate impossibility reduction may exploit rule features absent from the deployed language and overstate the boundary.","Positive reachability in the symbolic model may describe a chemically infeasible trajectory unless model validity is reviewed separately.","Explicit unknown outcomes may delay decisions or encourage unsafe off-system workarounds."]},"next_evidence_step":"In a time-boxed, non-production review, write a minimal formal grammar and transition semantics for the actual reaction-rule inputs; select five synthetic networks spanning closed finite, bounded polymerizing, and open-feed cases; prove and independently check finiteness plus exhaustive termination for the closed fragment; and attempt one explicit halting-problem reduction into only the unrestricted grammar's permitted constructs. Record any failed proof obligation as unresolved, with no change to operational safety decisions.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Runtime isolation precludes comparison with other proposals; this candidate is independently anchored in exact hazard reachability for open-ended generative reaction networks rather than in property prediction, molecular optimization, or reaction-rate estimation.","revision_record":{"parent_version":null,"progress_targets_addressed":["Initial one-shot candidate only"],"conceptual_changes":[],"operational_changes":[],"evidence_changes":[],"claim_changes":[]}}