{"schema_version":1,"assessment_id":"eoa_inverse_innovation_exp03_opportunity320_20260801","source_experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"computability_boundary_mapping__mathematics","archetype_slug":"computability_boundary_mapping","domain_slug":"mathematics","title":"Guarantee-Labeled Routing for Theoremhood Results","opportunity_summary":"Assess whether a hypothesized mathematical reasoning service can replace timeout-as-NO behavior with certified fragment-relative decisions, witness-bearing YES results, and explicit UNKNOWN outputs. The candidate could prevent authoritative misclassification, but the target behavior, formal boundary proof, fragment deciders, and practical coverage are not yet established.","adopter_authorizer":"The mathematical reasoning service owner, contingent on independent formal-methods and mathematical-logic review.","scores":{"meaningful_impact":{"score":3,"rationale":"If the hypothesized timeout-as-NO behavior exists, the proposal could prevent rejection of valid conjectures and misuse of unresolved statements; however, the packet supplies no evidence that the behavior occurs or affects a material volume of decisions."},"stakeholder_pull":{"score":2,"rationale":"Mathematicians, database maintainers, reviewers, and downstream users are identified, but no actor is shown requesting the change, reporting the failure, or accepting frequent UNKNOWN results."},"incremental_advantage":{"score":4,"rationale":"Guarantee-labeled routing directly improves on the stated baseline and longer-timeout rival by separating certified decisions from bounded UNKNOWN rather than treating search failure as falsehood; the advantage still depends on valid scope proofs and useful fragment coverage."},"distinctiveness_plausibility":{"score":3,"rationale":"The combination of certified fragment routing, explicit abstention, versioned guarantees, and withdrawal rules is coherent and testable, but prior art is unsearched and world distinctiveness cannot be inferred closed-book."},"technical_implementability":{"score":3,"rationale":"Requirements auditing, routing, certificates, shadow evaluation, and rollback are concretely described, while the exact reduction, total fragment algorithms, trusted-checker reliability, and adequate representation of intended mathematics remain unresolved proof and engineering obligations."},"adoption_authority_feasibility":{"score":4,"rationale":"The service owner is an identifiable authority, independent review is required, and shadow mode avoids immediate production authority; feasibility is reduced by the need to change published label semantics and maintain formally certified scopes."},"evidence_readiness":{"score":2,"rationale":"A 60-input shadow test and explicit falsifiers are available, but the packet lacks evidence of the diagnosed service behavior, reference-label provenance, a checked boundary reduction, constructive fragment proofs, and a defined decision-utility measure."},"safety_net_benefit":{"score":5,"rationale":"Explicit UNKNOWN, prohibition of unqualified NO, certificate checks, scope controls, review gating, halt triggers, label withdrawal, and rollback directly limit authoritative mathematical misclassification."},"scalability":{"score":3,"rationale":"Versioned guarantees and reusable routing policies could extend across submissions, but scaling depends on how much routine mathematics falls within certified fragments and on continuing checker, proof, and scope maintenance."}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Audit one service's versioned requirements, interface semantics, routing configuration, and a bounded sample of timeout or failure labels; document whether the problem falsifier is met and specify the shadow-test oracle.","confidence":"LOW","assumptions":["The service owner grants timely access to requirements, interfaces, configurations, and relevant logs.","The audit is limited to one deployed or proposed service and does not include production changes.","Independent mathematical-logic review is included but no new general theorem prover is built."]},"initial_deployment_startup":{"band_2026_usd":"250K_TO_1M","scope":"Specify the formal language and computation model, complete and independently check the boundary and fragment proof obligations, implement certified routing and certificate validation, and integrate versioned YES/NO/UNKNOWN labels in a nonproduction environment.","confidence":"LOW","assumptions":["Several enforceable fragments can be supported without inventing fundamentally new decision procedures.","Existing service components can be modified rather than replaced wholesale.","The trusted checking base and required formalization remain bounded enough for independent review."]},"operational_launch":{"band_2026_usd":"50K_TO_250K","scope":"Conduct reproducible shadow evaluation, security and checker validation, workflow training, documentation, production-readiness review, and a controlled release with monitoring and rollback.","confidence":"LOW","assumptions":["The shadow test shows no unsound labels or scope escapes and demonstrates acceptable decision utility.","Launch covers one service and a limited initial set of certified fragments.","No major compliance regime or specialized hardware is required."]},"annual_recurring":{"band_2026_usd":"50K_TO_250K","scope":"Maintain fragment definitions, proofs, routing rules, checker dependencies, versioned guarantees, monitoring, incident review, and label-withdrawal capability.","confidence":"LOW","assumptions":["The supported language and fragment portfolio change gradually.","Independent review is periodic rather than continuous.","Submission volume does not require a large dedicated operations team."]}},"research_burden":"HIGH","earliest_credible_horizon":"12_TO_36_MONTHS","pipeline_gates":{"recognizable_externally_supportable_problem":{"status":"UNCERTAIN","reason":"The failure mode is coherent and falsifiable, but both the universal binary requirement and timeout-as-NO behavior are explicitly hypotheses with no independent evidence."},"identifiable_adopter_or_authorizer":{"status":"YES","reason":"The service owner is identified as the routing-policy authority, subject to independent formal-methods and mathematical-logic review."},"distinct_testable_incremental_claim":{"status":"YES","reason":"The candidate claims that certified fragment routing with explicit UNKNOWN avoids the baseline's timeout-as-NO errors, and the requirements audit plus shadow-test error, scope, and abstention thresholds can falsify that claim."},"bounded_next_evidence_step":{"status":"YES","reason":"A bounded audit of one service can compare documented and observed label semantics with the claimed baseline and terminate the inquiry if the stated problem falsifier is met, without live deployment."},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"The next step can remain read-only or shadow-mode; production authority is review-gated, unsafe NO and automatic rejection are excluded, and explicit halt and rollback conditions are supplied."},"implementation_cost_scope_and_range":{"status":"UNCERTAIN","reason":"The candidate identifies the main formal, software, review, evaluation, and maintenance work, but supplies no staffing, system complexity, data-access, fragment-count, or integration evidence sufficient to validate a resource range."}},"blocking_evidence":["Evidence that a specific service promises a terminating exact binary answer over an unrestricted class or displays timeout or search exhaustion as mathematical NO.","A precise specification of the accepted language, encoding, semantics, computation model, quantifiers, and enforced submission class.","An independently checked source-to-target reduction certificate supporting the unrestricted boundary claim.","Constructive totality, soundness, and scope proofs for every fragment authorized to emit binary labels.","A reproducible oracle for the 60-input shadow test, including provenance of preclassified cases and certificate-validation procedures.","Evidence that certified fragment coverage and the resulting UNKNOWN rate provide useful decisions without encouraging unsafe manual relabeling.","Reliability evidence and a defined trust boundary for the certificate checker."],"next_evidence_step":"Audit one identified service's versioned requirements, user interface, routing configuration, and a bounded sample of timeout or failure records; compare their promised and displayed semantics with the claimed universal-binary baseline, and stop if the audit finds no universal terminating claim, no UNKNOWN-to-NO behavior, and a constructive total decider for the entire enforced class.","research_questions":["Does any identified service actually promise terminating exact YES or NO for every formula and finitely presented first-order axiom system in its enforced input class?","Are timeout, search exhaustion, countermodel findings, and proof failures displayed distinctly, or is any of them represented as mathematical NO?","What exact formal reduction and answer-preservation proof support the claimed unrestricted computability boundary?","Which fragments have independently checked total decision procedures, and how precisely are fixed or bounded model domains distinguished from unrestricted finite-model semantics?","What proportion of representative work routes to certified decisions rather than UNKNOWN, and what decision-utility rule makes that coverage acceptable?","Can every emitted certificate be checked by an independently validated trusted base, with scope escape detected before publication?","Do maintainers and downstream users accept UNKNOWN and label withdrawal without informal coercion to binary answers?"],"recommendation":"VALIDATE_PROBLEM_FIRST","uncertainty_constraints":["The existence and behavior of the target service are hypothetical.","Problem prevalence, affected decision volume, stakeholder demand, and realized impact are unmeasured.","Prior art is unsearched, so distinctiveness and comparative prevalence cannot be established.","The packet does not contain the exact undecidability reduction or fragment-decidability proofs.","The representational adequacy of the proposed formal language is unknown.","Fragment coverage, UNKNOWN frequency, decision utility, integration complexity, and checker reliability are unknown.","All cost bands are resource-equivalent planning ranges based only on the stated scope, not observed implementation data."],"closed_book_prior_art_boundary":"No external prior-art, prevalence, market, implementation, or cost evidence was consulted. The packet marks prior art as UNSEARCHED; therefore the assessment treats world novelty, existing comparable systems, stakeholder demand, realized impact, and exact costs as unknown."}