{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__education_pedagogy","trajectory_id":"R","attempt_index":0,"archetype_slug":"computability_boundary_mapping","domain_slug":"education_pedagogy","decision":"CANDIDATE","problem_id":"universal_student_program_autograding_overclaim","causal_lever_id":"scope_and_verdict_contract_for_program_autograding","proposal":{"problem":"Programming courses deploy or procure autograders expected to return a correct, terminating pass/fail verdict for every well-formed student program, including whether arbitrary code terminates and satisfies behavioral requirements. Timeouts and unsupported cases may consequently be recorded as failures rather than distinguished from unknown.","actors_substrate":["students submitting programs","instructors and teaching assistants","course and curriculum leads","autograder developers or vendors","appeals and accessibility staff"],"observable_state":"The published grading contract quantifies over an open-ended programming language, while logs expose timeout, analyzer failure, or silent input restriction as ordinary incorrect verdicts.","consequence":"Students can receive unsupported grades, instructors inherit avoidable appeals, and institutions invest in an exact universal grader whose declared guarantee may be unattainable.","affected_objective":"Valid, explainable, timely, and equitable assessment of student programming competence.","structural_mapping":[{"archetype_element":"Unrestricted class-wide exact-and-terminating requirement","domain_realization":"One Boolean grade is required for every program expressible in the course language.","claim_kind":"INFERENCE"},{"archetype_element":"Implicit representation and computation model","domain_realization":"The contract does not fix language features, executable specification format, runtime environment, or permitted external assistance.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Timeout collapsed into false","domain_realization":"Resource exhaustion is reported as an incorrect solution rather than UNKNOWN or SYSTEM_FAILURE.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Decidable restricted region","domain_realization":"A mechanically enforced language fragment, finite test domain, or bounded execution regime can carry a narrower guarantee.","claim_kind":"INFERENCE"},{"archetype_element":"Weaker honest fallback","domain_realization":"Outside the exact region, the grader returns witnessed YES, bounded evidence, UNKNOWN, or human review with its guarantee label.","claim_kind":"INFERENCE"},{"archetype_element":"Reclassification on model change","domain_realization":"Adding recursion, concurrency, reflection, nondeterminism, or external services triggers renewed boundary review.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Problem-Class Specification","status":"adapted","domain_realization":"Define the exact program properties and submission class being graded."},{"component":"Instance Representation Contract","status":"adapted","domain_realization":"Version the source language, specification format, dependencies, and runtime image."},{"component":"Computation Model Contract","status":"adapted","domain_realization":"Declare machine resources, nondeterminism, network access, and human/oracle inputs."},{"component":"Solvability Guarantee Profile","status":"adapted","domain_realization":"Separate total exact, sound incomplete, bounded, and human-reviewed verdicts."},{"component":"Quantifier and Scope Map","status":"adapted","domain_realization":"Expose whether claims cover every program, a fragment, or only bounded instances."},{"component":"Computability Status Lattice","status":"direct","domain_realization":"Classify each grading property as decidable, recognizable, relative, undecidable, or unresolved."},{"component":"Constructive Procedure Witness","status":"adapted","domain_realization":"For an exact region, retain the grader and its correctness and termination argument."},{"component":"Reduction Preservation Contract","status":"direct","domain_realization":"Require a total property-preserving encoding before transferring impossibility."},{"component":"Computability Impossibility Certificate","status":"adapted","domain_realization":"Attach a checked reduction for any unrestricted grading property declared undecidable."},{"component":"Assumption Register","status":"adapted","domain_realization":"Record language, rubric formalization, sandbox, and input promises."},{"component":"Decidable Subclass Map","status":"adapted","domain_realization":"List enforceable language fragments and finite domains with exact grading."},{"component":"One-Sided Recognition Contract","status":"adapted","domain_realization":"Specify which witnessed successes can be confirmed without claiming complete rejection."},{"component":"Unknown and Nontermination Policy","status":"adapted","domain_realization":"Keep UNKNOWN, TIMEOUT, OUT_OF_SCOPE, and SYSTEM_FAILURE distinct from FAIL."},{"component":"Fallback Solution Contract","status":"adapted","domain_realization":"Route unsupported submissions to bounded evidence or authorized review."},{"component":"Computability Guarantee Record","status":"adapted","domain_realization":"Version the public grading guarantee and supporting evidence."},{"component":"Recheck Trigger","status":"adapted","domain_realization":"Reassess after language, rubric, runtime, or external-capability changes."},{"component":"Termination Condition","status":"adapted","domain_realization":"Set explicit resource bounds and return UNKNOWN when exhausted."},{"component":"Scope Boundary","status":"adapted","domain_realization":"Mechanically reject or quarantine submissions outside the guaranteed fragment."},{"component":"Decision Record","status":"direct","domain_realization":"Record the selected exact and fallback modes and rationale."},{"component":"Uncertainty Residue","status":"adapted","domain_realization":"List unproved properties, unsupported constructs, and unresolved formalization gaps."},{"component":"Independent Proof Review","status":"adapted","domain_realization":"Have a reviewer independent of grader authors check boundary arguments."},{"component":"Complexity Follow-On Gate","status":"adapted","domain_realization":"Evaluate runtime and capacity only after establishing in-principle solvability."}],"mechanism_dispositions":[{"slug":"abstract_interpretation_or_model_checking","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Use only for sound, explicitly one-directional checks on a finite abstraction.","counterfactual_removal":"Removes a useful sound fallback but leaves the boundary and routing chain intact."},{"slug":"bounded_domain_exhaustive_search","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Provide exact verdicts only over a precisely enumerated finite domain.","counterfactual_removal":"The bounded exact grading region loses its completeness basis."},{"slug":"computability_boundary_decision_record","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Version guarantees, evidence, and recheck triggers.","counterfactual_removal":"Guarantee drift becomes difficult to detect, though routing can still operate."},{"slug":"computational_complexity_analysis","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Estimate feasibility after decidability classification.","counterfactual_removal":"A valid method might still be operationally unusable."},{"slug":"constructive_algorithm_and_correctness_proof","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Certify totality and correctness for each exact fragment.","counterfactual_removal":"Exact-fragment claims would rest on testing rather than class-wide evidence."},{"slug":"diagonalization_impossibility_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Redundant because a domain-specific reduction is easier to audit.","counterfactual_removal":"No change."},{"slug":"enumeration_and_dovetailing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Unbounded nontermination is unsuitable for grade release; use bounded semi-decision.","counterfactual_removal":"No change."},{"slug":"fallback_mode_router","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Dispatch exact, sound, bounded, and human-review paths with labels.","counterfactual_removal":"Weaker outputs could be presented as ordinary pass/fail grades."},{"slug":"halting_problem_reduction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use a checked reduction only for grading properties that subsume arbitrary termination.","counterfactual_removal":"The proposed unrestricted impossibility boundary lacks decisive evidence."},{"slug":"language_fragment_restriction","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Enforce a syntactic fragment admitting a total grader.","counterfactual_removal":"The exact guarantee again ranges over unrestricted programs."},{"slug":"many_one_reduction_proof","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Its obligations are incorporated in the selected halting reduction; a second reduction adds no causal work.","counterfactual_removal":"No change."},{"slug":"promise_problem_restriction","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"An unenforced promise permits authoritative outputs on violating submissions; prefer checked syntax.","counterfactual_removal":"No change."},{"slug":"proof_by_counterexample","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use one in-scope failure to refute an existing universal product claim.","counterfactual_removal":"The pilot loses a cheap overclaim test but not its positive classification method."},{"slug":"proof_checking","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Independently check the exact theorem, assumptions, and reduction.","counterfactual_removal":"A subtle proof or formalization gap could authorize invalid grading."},{"slug":"reduction_direction_checklist","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Independent proof checking already covers direction and stronger obligations.","counterfactual_removal":"No change."},{"slug":"semi_decision_with_explicit_unknown","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Bound one-sided search and return UNKNOWN, never FAIL, at exhaustion.","counterfactual_removal":"Timeout would again be liable to masquerade as evidence of incorrectness."},{"slug":"theorem_prover_guided_search","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Optional automation is unnecessary for the bounded first test and cannot replace semantic validation.","counterfactual_removal":"No change."},{"slug":"turing_reduction_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Relative computability degrees do not determine the required grading interface.","counterfactual_removal":"No change."}],"causal_chain":["Specify the graded property, program class, representation, quantifiers, and computation model.","Check constructive evidence and a property-preserving impossibility reduction under independent review.","Enforce an exact decidable fragment and finite bounds.","Route remaining submissions to sound, bounded, UNKNOWN, or human-review modes.","Expose labels to gradebook consumers and recheck the boundary after material changes.","This reduces unsupported fail verdicts while preserving usable automation (HYPOTHESIS)."],"baseline":"A test-suite-and-timeout autograder emits pass/fail, with exceptional cases handled through ad hoc appeals.","nearest_rival":"Improve test coverage, sandbox capacity, and timeout thresholds while retaining a universal Boolean grading contract.","authority_safety":{"affected_parties":["students whose grades or progression may change","instructors and teaching assistants","accessibility and appeals staff"],"decision_authority":"The course lead may authorize a shadow pilot; any grading-policy change requires the institution's normal faculty assessment and appeals authority.","authorized_first_step":"Run one assignment in shadow mode on archived or consented submissions: formalize one executable property, enforce one fragment, compare current verdicts with labeled exact/unknown/failure outputs, and independently review every disagreement; do not alter grades.","excluded_actions":["changing grades during the shadow test","treating UNKNOWN as FAIL","silently excluding language features","deploying an unchecked impossibility claim","sending identifiable student code outside approved systems"],"halt_rollback":"Halt if a supposedly exact verdict is refuted, fragment membership is misclassified, protected or accommodation-relevant groups show materially higher unresolved rates, or an UNKNOWN reaches the gradebook as FAIL; disable the new routing and preserve the prior appeals path."}},"negative_tests":{"strongest_counterevidence":"The actual grader may already accept only a finite, mechanically enforced language and finite instance set, distinguish all exceptional states, and make no unrestricted semantic claim; then this is complexity or capacity work, not a computability-boundary problem.","analogy_break":"Student competence is not identical to program semantics: even a perfect program-property decider cannot infer authorship, understanding, intent, or pedagogical mastery. Those constructs require separate assessment validity evidence.","failure_condition":"The mapping fails if the targeted rubric remains semantically ambiguous or primarily judges style, explanation, creativity, or understanding rather than a formal program property.","problem_falsifier":"Audit the specification, interface, and logs; falsify the problem if every accepted input lies in an enforced decidable class and timeout, unknown, out-of-scope, system failure, and incorrect are already kept distinct through grading and appeals.","intervention_falsifier":"Falsify the intervention if the shadow test's independently reviewed exact region produces any wrong verdict, or if labeled routing does not reduce unsupported fail classifications without unacceptable unresolved volume or subgroup disparity.","risks":["A narrow fragment may cease to assess the intended learning objective.","UNKNOWN may delay feedback or shift excessive work to instructors.","Formal proofs may certify the wrong rubric formalization.","Human escalation may be scarce, inconsistent, or biased.","Bounds may be reported beyond their tested scope.","Students may strategically target routing boundaries."]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_COMPOSITION","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":0.86,"generator_notes":"Closed-book structural transfer. The proposed prevalence, disparity, and outcome effects are hypotheses; no claim of novelty or existing educational deployment is made."}