{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__nanotechnology","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"nanotechnology","decision":"CANDIDATE","problem_id":"universal_self_assembly_outcome_verification","causal_lever_id":"restrict_and_label_self_assembly_verification_scope","proposal":{"problem":"A nanotechnology project seeks an always-terminating, exact verifier that accepts any programmable self-assembly design and decides whether every permitted assembly trajectory terminates only in the intended nanostructure, without first bounding the design language, material population, trajectory length, or environmental model. Repeated timeouts are liable to be reported as unsafe or impossible, while bounded successes are liable to be generalized to all designs. Whether the unrestricted class is undecidable is a HYPOTHESIS requiring a valid encoding and proof, not an assumed fact.","actors_substrate":["Designers of DNA-origami, molecular-machine, or other programmable self-assembly systems","Verification-tool developers and independent proof reviewers","Laboratory safety and research-governance authorities","Digital design descriptions, interaction rules, kinetic/environmental assumptions, and possible assembly trajectories","Laboratory personnel, downstream users, and communities or environments exposed to fabricated structures"],"observable_state":"The verifier's documentation promises a Boolean answer for an open-ended design class, but input scope and computation model are implicit; timeouts or incomplete searches are collapsed into NO; and results from finite molecule counts or bounded trajectory depth are presented as unrestricted guarantees.","consequence":"The team may spend resources pursuing an impossible universal verifier, reject viable designs on non-evidence, or approve designs using guarantees that do not cover unbounded trajectories, off-target assemblies, or changed environmental assumptions.","affected_objective":"Deliver trustworthy, terminating, scope-explicit verification of programmable nanoscale self-assembly while preventing UNKNOWN, timeout, and out-of-scope results from being interpreted as safe or unsafe.","structural_mapping":[{"archetype_element":"Unrestricted universal decision requirement","domain_realization":"Decide the terminal behavior of every permitted trajectory for every design in an open-ended self-assembly language.","claim_kind":"INFERENCE"},{"archetype_element":"Explicit instance and computation model","domain_realization":"Fix the design grammar, molecule-count semantics, transition rules, stochastic treatment, environmental inputs, and allowed external measurements.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Parallel constructive and impossibility evidence","domain_realization":"Seek a total verifier for restricted classes while testing whether the unrestricted formal model can simulate a known undecidable source through a property-preserving encoding.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Honest weaker fallback","domain_realization":"Route enforceably restricted designs to exact verification, finite regimes to exhaustive checking, and remaining designs to sound one-sided or UNKNOWN-producing analysis.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Formal class of self-assembly designs and the terminal-outcome property."},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Grammar for components, bonds, initial conditions, and environments."},{"component":"Computation Model Contract","status":"adapted","domain_realization":"Declared transition semantics, precision, randomness, and external-information access."},{"component":"Solvability Guarantee Profile","status":"direct","domain_realization":"Exact-total, one-sided, bounded, or unresolved status per class."},{"component":"Quantifier and Scope Map","status":"direct","domain_realization":"Separate every design/every trajectory claims from individual-design claims."},{"component":"Computability Status Lattice","status":"direct","domain_realization":"Classify fragments as decidable, recognizable, relative, undecidable, or unresolved."},{"component":"Constructive Procedure Witness","status":"direct","domain_realization":"Algorithm plus correctness and termination proof where available."},{"component":"Reduction Preservation Contract","status":"adapted","domain_realization":"Require a computable encoding preserving the target assembly property."},{"component":"Computability Impossibility Certificate","status":"direct","domain_realization":"Checked reduction or diagonal proof for the exact unrestricted model."},{"component":"Assumption Register","status":"adapted","domain_realization":"Record physical and formal assumptions, including finiteness and precision."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"Enforceable design fragments and finite regimes with total procedures."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Define which outcome can be confirmed by a finite witness."},{"component":"Unknown and Nontermination Policy","status":"direct","domain_realization":"Keep UNKNOWN, timeout, out-of-scope, and NO distinct."},{"component":"Fallback Solution Contract","status":"direct","domain_realization":"Label exact, bounded, and sound-approximate outputs by their actual guarantees."},{"component":"Computability Guarantee Record","status":"direct","domain_realization":"Versioned statement linking scope, model, evidence, and guarantee."},{"component":"Recheck Trigger","status":"adapted","domain_realization":"Reclassify after grammar, semantics, environment, or external capability changes."},{"component":"Termination Condition","status":"direct","domain_realization":"Declared finite bounds for operational analyses."},{"component":"Scope Boundary","status":"direct","domain_realization":"Machine-enforced fragment membership or conservative rejection."},{"component":"Decision Record","status":"direct","domain_realization":"Auditable choice of shipped verifier and fallback modes."},{"component":"Uncertainty Residue","status":"direct","domain_realization":"Open proof obligations and model-to-physical-system gaps."},{"component":"Independent Proof Review","status":"direct","domain_realization":"Separate review of reductions, algorithms, and formalization fidelity."},{"component":"Complexity Follow-On Gate","status":"direct","domain_realization":"After decidability, assess state explosion and practical resource cost."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use a finite over-approximation only if its soundness direction for assembly hazards is proved.","counterfactual_removal":"Without it, unrestricted cases lack a sound terminating fallback beyond abstention."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Enumerate all states only within explicit molecule, depth, and environment bounds.","counterfactual_removal":"Finite regimes would lose their complete within-bound verdict."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Version-link model, evidence, guarantee, and recheck triggers.","counterfactual_removal":"Guarantees could drift silently when the design language changes."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Measure feasibility only after a class is shown decidable.","counterfactual_removal":"Computable but infeasible fragments could be mistaken for operational solutions."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Required to establish exact total verification for any claimed fragment.","counterfactual_removal":"Positive decidability claims would rest on examples rather than a total witness."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"No self-referential construction is supplied; do not assume one transfers to physical assembly.","counterfactual_removal":"No change; the pilot tests a reduction route first."},{"slug":"enumeration_and_dovetailing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A relevant enumerable witness space has not been established.","counterfactual_removal":"No change to the bounded first test."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Dispatch by enforced scope and attach exact guarantee labels.","counterfactual_removal":"Weaker results could again be laundered into universal Boolean claims."},{"slug":"halting_problem_reduction","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Attempt only after fixing formal assembly semantics and the preserved outcome property.","counterfactual_removal":"The central undecidability hypothesis would lack a decisive test."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Define a syntactically enforceable self-assembly design fragment admitting a total verifier.","counterfactual_removal":"There would be no enforceable route from the universal claim to exact decidable coverage."},{"slug":"many_one_reduction_proof","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use as the required total, computable, answer-preserving form of any hardness transfer.","counterfactual_removal":"A halting analogy could be accepted without a valid preservation contract."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unenforced physical promises permit authoritative behavior outside the guarantee; prefer checkable syntax or conservative rejection.","counterfactual_removal":"No change because fragment membership supplies the restriction."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use an in-scope design to refute any overbroad totality or soundness claim.","counterfactual_removal":"Universal marketing claims would be harder to falsify cheaply."},{"slug":"proof_checking","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently check the exact formal theorem and expose premises.","counterfactual_removal":"An invalid boundary proof could authorize unsafe guarantee labels."},{"slug":"reduction_direction_checklist","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate any reduction on source-to-target direction, totality, and preservation.","counterfactual_removal":"A reversed or incomplete reduction could be mistaken for impossibility evidence."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"At a declared resource bound, return witnessed YES or UNKNOWN, never infer NO.","counterfactual_removal":"Timeouts could continue to become fabricated negative verdicts."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Proof automation is optional and cannot repair an unfaithful assembly formalization.","counterfactual_removal":"Manual independent checking still tests the boundary."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Relative oracle degrees do not answer the immediate total-verifier and one-sided-guarantee question.","counterfactual_removal":"No change to the proposed classification."}],"causal_chain":["Specify the self-assembly language, encoded instances, outcome property, quantifiers, and computation model.","Seek a total constructive verifier and a valid impossibility reduction in parallel.","Partition only on checked evidence into enforceable decidable fragments, bounded finite regimes, and unresolved remainder.","Route each instance to exact, bounded, or sound one-sided analysis and preserve UNKNOWN and out-of-scope states.","Record the scope-linked guarantee and recheck it when semantics or physical assumptions change."],"baseline":"Continue universal verifier development; test selected designs; impose timeouts; and emit Boolean safe/unsafe results without a proven class-wide termination or soundness contract.","nearest_rival":"Treat the problem solely as state-space explosion and optimize simulation, pruning, or hardware while retaining the unrestricted exact-total claim.","authority_safety":{"affected_parties":["Laboratory personnel","Nanostructure designers and verification users","Downstream product users","Communities and environments potentially exposed to fabricated structures"],"decision_authority":"The laboratory or product verification owner may authorize analysis changes; fabrication or release remains with the applicable research-safety and institutional authorities.","authorized_first_step":"On a non-released benchmark corpus, formalize one design grammar and outcome property; independently attempt a total verifier and a source-to-target reduction; then compare exact bounded checking, sound abstraction, and explicit-UNKNOWN routing. No physical fabrication is required.","excluded_actions":["Fabricating, deploying, or releasing a nanostructure based only on the pilot","Treating UNKNOWN, timeout, or out-of-scope as safe or unsafe","Claiming undecidability without a checked model-matching proof","Generalizing a bounded result beyond its declared bound"],"halt_rollback":"Stop the pilot if the formal property does not faithfully represent the physical safety claim, an abstraction is shown unsound, or output labels are collapsed downstream. Withdraw affected guarantee records and revert to explicit human review with no automated safety verdict."}},"negative_tests":{"strongest_counterevidence":"If every operational instance necessarily has a fixed finite molecule population, finite precision, and effectively enumerable state space, a total exhaustive procedure exists in principle; the problem is then complexity and model fidelity, not computability.","analogy_break":"A chemical assembly process is not automatically an arbitrary program. A reduction fails if its encoded transitions cannot be physically or formally realized, if stochastic/continuous dynamics change the preserved property, or if the verifier's actual scope is already finite.","failure_condition":"The proposal fails if enforceable fragments cover too little real work, abstractions cannot establish the promised soundness direction, or downstream systems cannot preserve UNKNOWN and scope labels.","problem_falsifier":"A proved total correct procedure for the full declared design class under the same representation and computation model, or proof that the declared class is necessarily finite and effectively enumerable, falsifies the alleged computability-boundary problem.","intervention_falsifier":"Even if the unrestricted boundary is real, the intervention is falsified if the routed system produces no greater correctly resolved coverage than baseline, misroutes in-scope instances, emits any false guaranteed verdict, or users continue interpreting UNKNOWN as Boolean.","risks":["An unfaithful formal model can yield a correct theorem about the wrong physical system.","A coarse abstraction can produce unusable false alarms; an unsound abstraction can produce false assurance.","Bounds or fragments may exclude the designs that matter while appearing comprehensive.","Complexity may make a decidable fragment operationally useless.","A boundary record can institutionalize an erroneous or stale conclusion."]},"null_rationale":null,"classification":{"candidate_kind":"TESTABLE_CONJECTURE","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":"Candidate depends on testing whether the chosen open-ended self-assembly formalism supports a faithful undecidability reduction. No claim of domain novelty or established undecidability is made."}