{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp11_mechanism_context_external20_20260804","research_id":"eoa_inverse_innovation_exp11_external_scrutiny_20260804","cell_id":"computability_boundary_mapping__philosophy","opaque_id":"computability_boundary_mapping__philosophy__B","search_lanes":{"direct_problem":{"queries":["computational philosophy automated theorem proving consistency entailment timeout unknown","formal philosophy automated reasoning theorem prover consistency metaphysics","philosophical theory consistency automated theorem prover undecidable","computational metaphysics theorem prover consistency Isabelle Nitpick"],"source_ids":["SRC2","SRC3","SRC4"],"no_result_note":null},"closest_prior_art":{"queries":["theorem prover timeout does not mean false unknown proof countermodel","automatic theorem proving proof countermodel unknown interface decidable fragments","formal methods timeout false unsound solver unknown result policy","automated reasoning consistency model finder proof philosophical arguments limitations formalization"],"source_ids":["SRC5","SRC6","SRC7","SRC8"],"no_result_note":null},"historical_terminology":{"queries":["semidecision procedure theorem proving undecidable first-order logic proof search historical","Entscheidungsproblem automated theorem proving decision procedure","Alan Turing 1936 On Computable Numbers PDF Entscheidungsproblem original","Alonzo Church 1936 unsolvable problem elementary number theory PDF original"],"source_ids":["SRC1","SRC2"],"no_result_note":null},"products_practices_standards":{"queries":["SMT-LIB standard unknown result reason-unknown timeout official","TPTP SZS ontology timeout unknown theorem status official","Z3 guide unknown timeout incomplete theory official","automated theorem prover three-valued result proved disproved unknown timeout standard"],"source_ids":["SRC5","SRC6","SRC7","SRC8"],"no_result_note":null},"non_english_regional":{"queries":["Entscheidungsproblem automatisches Beweisen unentscheidbar Timeout unbekannt Theorie Konsistenz","procédure de décision logique indécidable preuve automatique délai inconnu","decidibilidad demostración automática lógica desconocido tiempo agotado consistencia teoría","Entscheidungsproblem automatisches Beweisen entscheidbare Fragmente"],"source_ids":[],"no_result_note":"German, French, and Spanish searches reproduced the established Entscheidungsproblem, semidecision, and decidable-fragment vocabulary but yielded no stronger direct regional implementation evidence than the retained international standards and first-party documentation."},"composition_subproblems":{"queries":["automatic theorem proving proof countermodel unknown interface decidable fragments","theorem prover timeout does not mean false unknown proof countermodel","automated reasoning consistency model finder proof philosophical arguments limitations formalization","site:tptp.org SZS ontology Timeout GaveUp Unknown"],"source_ids":["SRC2","SRC4","SRC5","SRC6","SRC7","SRC8"],"no_result_note":null}},"sources":[{"source_id":"SRC1","title":"An Unsolvable Problem of Elementary Number Theory","url":"https://www.cis.upenn.edu/~cis5110/Church-UnsolvableProblemElementary-1936.pdf","publisher":"American Journal of Mathematics / Johns Hopkins University Press","date_or_year":"1936","source_type":"PRIMARY_RESEARCH","language":"English","claims_supported":["Church formalizes effective calculability and proves that not every problem in the relevant class is solvable.","The historical decision-problem terminology predates modern theorem-prover interfaces by decades.","More computation cannot turn every unrestricted formal decision problem into a correct total procedure."]},{"source_id":"SRC2","title":"Automated Reasoning","url":"https://plato.stanford.edu/entries/reasoning-automated/","publisher":"Stanford Encyclopedia of Philosophy","date_or_year":"2001; substantive revision 2024","source_type":"SECONDARY_RESEARCH","language":"English","claims_supported":["Automated-reasoning design requires specifying the problem class, representation language, inference mechanism, and presentation of solutions.","Higher-order unification is undecidable, while interactive systems and human guidance are important fallbacks.","Computational metaphysics already uses provers and model finders to investigate consistency and entailment of formal philosophical theories.","Formal encodings do not automatically cover concepts absent from the prover language."]},{"source_id":"SRC3","title":"Computational Philosophy","url":"https://plato.stanford.edu/entries/computational-philosophy/","publisher":"Stanford Encyclopedia of Philosophy","date_or_year":"2020; substantive revision 2024","source_type":"SECONDARY_RESEARCH","language":"English","claims_supported":["Theorem provers are already applied to metaphysics, ethics, modal arguments, and philosophy of religion.","Named researchers and projects constitute an identifiable population of potential adopters.","Reported philosophical applications include discovered inconsistencies, proofs, countermodels, and formal consequences rather than unrestricted adjudication of philosophical truth."]},{"source_id":"SRC4","title":"Steps Toward a Computational Metaphysics","url":"https://mally.stanford.edu/abstracts/computational.html","publisher":"Branden Fitelson and Edward N. Zalta / Stanford University","date_or_year":"2007","source_type":"PRIMARY_RESEARCH","language":"English","claims_supported":["The authors implemented a fragment of axiomatic metaphysics in Prover9's first-order syntax.","The work demonstrates an actual philosophy-domain theory-and-thesis assessment workflow.","Only a fragment of the second-order theory was represented, supporting the importance of explicit scope boundaries."]},{"source_id":"SRC5","title":"The SMT-LIB Standard, Version 2.0","url":"https://smt-lib.org/papers/v2-ref-manual-draft.pdf","publisher":"SMT-LIB Initiative","date_or_year":"2010","source_type":"OFFICIAL_STANDARD","language":"English","claims_supported":["The standard fixes theories, logics, typed representations, commands, and solver responses.","The standard check result is sat, unsat, or unknown rather than an unconditional Boolean.","Reasons for unknown include timeout, memory exhaustion, and solver incompleteness; proof, model, and unsatisfiable-core queries are separately represented."]},{"source_id":"SRC6","title":"SZS Ontology","url":"https://tptp.org/UserDocs/SZSOntology/","publisher":"TPTP World","date_or_year":"Introduced 2004; current documentation accessed 2026-08-04","source_type":"OFFICIAL_STANDARD","language":"English","claims_supported":["The automated-theorem-proving standard distinguishes theorem, contradictory axioms, counter-satisfiable, satisfiable, and unsatisfiable outcomes.","Unknown, timeout, resource exhaustion, incompleteness, inappropriate input, and errors are distinct no-success states.","The ontology explicitly says lack of success is not the same as failure and defines proof, refutation, and model evidence forms."]},{"source_id":"SRC7","title":"Ivy: Decidability","url":"https://microsoft.github.io/ivy/decidability.html","publisher":"Microsoft Research","date_or_year":"Undated first-party documentation; accessed 2026-08-04","source_type":"FIRST_PARTY_PRODUCT","language":"English","claims_supported":["Ivy reduces automated obligations to a declared decidable fragment and explains formulas that fall outside it.","Inside the fragment the underlying solver has a decision guarantee; outside it, even small formulas may diverge or fail to produce reliable countermodels.","Ivy implements an especially close analogue by refusing out-of-fragment checks and returning actionable scope explanations."]},{"source_id":"SRC8","title":"SMTChecker and Formal Verification","url":"https://docs.solidity.org/en/latest/smtchecker.html","publisher":"Solidity Project","date_or_year":"Version 0.8.37-develop documentation; accessed 2026-08-04","source_type":"FIRST_PARTY_PRODUCT","language":"English","claims_supported":["A deployed verification interface distinguishes proved failure from a timeout where neither case was proved.","For a timeout, the tool reports an unknown-derived potential warning to preserve soundness rather than treating timeout as false.","The documentation limits claims to the formal specification and records unsupported constructs, abstractions, assumptions, counterexamples, and potential unsoundness."]}],"problem_evidence":{"status":"PARTLY_SUPPORTED","finding":"The core computability problem is well supported: unrestricted formal decision guarantees fail for sufficiently expressive classes, and actual computational-philosophy work uses expressive theorem provers and model finders. Standards and products explicitly distinguish unknown, timeout, incompleteness, and out-of-scope from logical falsity. However, no retained source establishes an existing philosophy platform that both promises universal terminating Boolean adjudication and currently converts timeouts into rejection.","source_ids":["SRC1","SRC2","SRC3","SRC4","SRC5","SRC6","SRC7","SRC8"],"uncertainty":"The theoretical failure mode is real, but the proposal's concrete Boolean-demanding platform and baseline error rate remain hypothetical."},"adopter_evidence":{"status":"PARTLY_SUPPORTED","finding":"Named computational-philosophy researchers and projects already submit formal metaphysical theories to Prover9, Mace, Isabelle, and related systems, making the user population identifiable. The retained evidence does not identify an actual platform editorial board or institution authorized to run the proposed adjudicative pilot.","source_ids":["SRC2","SRC3","SRC4"],"uncertainty":"Potential adopters are identifiable, but a committed operator or authorizer with control over a live interface is not."},"implementation_evidence":{"status":"PARTLY_SUPPORTED","finding":"Nearly every technical mechanism has working analogues: standard typed logic declarations, sat/unsat/unknown results, separate timeout and incompleteness states, proof and model evidence, decidable-fragment enforcement, out-of-scope refusal, and sound timeout handling. Evidence is absent for the complete philosophy-specific governance package, including versioned guarantee records, appeal rights, independent logical review, and the proposed 60-case evaluation.","source_ids":["SRC5","SRC6","SRC7","SRC8"],"uncertainty":"Technical feasibility is strong by transfer, while workflow feasibility and behavioral effects in philosophy have not been demonstrated."},"prior_art":{"disposition":"ADJACENT_PRIOR_ART","closest_analogues":[{"name":"SMT-LIB result and logic contracts","source_ids":["SRC5"],"same_problem":true,"same_causal_lever":true,"overlap":"Standardizes declared logics and theories, typed inputs, sat/unsat/unknown results, reasons for unknown, resource limits, proofs, models, and unsatisfiable cores.","remaining_difference":"It is a solver interchange standard, not a philosophy-facing adjudication policy with independent review, appeals, governance records, and measured effects on editorial interpretation."},{"name":"TPTP SZS outcome ontology","source_ids":["SRC6"],"same_problem":true,"same_causal_lever":true,"overlap":"Separates successful logical classifications from unknown, timeout, resource-out, incomplete, inappropriate, and error states and associates results with proofs, refutations, or models.","remaining_difference":"It standardizes ATP reporting but does not itself enforce decidable fragments or govern philosophy-platform decisions."},{"name":"Ivy decidable-fragment enforcement","source_ids":["SRC7"],"same_problem":true,"same_causal_lever":true,"overlap":"Maps a solver boundary, machine-checks fragment membership, refuses obligations outside the supported fragment, explains the scope violation, and uses countermodels inside the fragment.","remaining_difference":"It addresses program verification rather than arbitrary philosophical theories and lacks the proposed editorial, appeal, and independent-review workflow."},{"name":"Solidity SMTChecker unknown-on-timeout policy","source_ids":["SRC8"],"same_problem":true,"same_causal_lever":true,"overlap":"Treats inability to prove either side within a timeout as unknown and preserves soundness instead of rendering a negative verdict.","remaining_difference":"Its fallback is a conservative verification warning in software engineering, not a four-state philosophy interface or computability certificate."},{"name":"Computational metaphysics with Prover9 and model finders","source_ids":["SRC2","SRC3","SRC4"],"same_problem":true,"same_causal_lever":false,"overlap":"Uses proofs and models to investigate consistency and entailment of formally encoded philosophical theories and already restricts some richer theories to representable fragments.","remaining_difference":"The sources do not document a prior computability-boundary audit, enforced totality profile, distinct timeout policy, or governance record."}],"contrastive_claim_remaining":"For computational-philosophy workflows specifically, a machine-enforced fragment boundary plus proof/countermodel/unknown/out-of-scope interface and independently reviewed guarantee record will reduce timeout-to-false or timeout-to-rejection errors relative to the current interface, while preserving known-valid results and producing reproducible classifications.","contrastive_claim_falsifier":"The claim is falsified if an equivalent governed package is already routine in the target philosophy workflow, or if a preregistered comparison shows no reduction in timeout/false collapse, cannot conservatively enforce fragment membership, rejects a known-valid case, or produces unresolved reviewer disagreement.","confidence":"HIGH","search_limitations":"The bounded search used eight retained direct sources across theory, philosophy applications, standards, and first-party implementations. It found no public evidence for the specific proposed platform or its timeout-rejection baseline. It did not inspect proprietary systems, unpublished policies, all languages, or patent literature."},"researchability_gates":{"externally_supported_problem":{"status":"PASS","rationale":"Undecidability and semidecision boundaries are established, actual philosophy workloads use automated proof and model search, and standards document timeout and incompleteness as non-verdict states. The unverified part is prevalence in the hypothesized platform, not existence of the underlying failure mode.","source_ids":["SRC1","SRC2","SRC3","SRC4","SRC5","SRC6","SRC7"]},"identifiable_adopter_or_authorizer":{"status":"INDETERMINATE","rationale":"Named computational-metaphysics practitioners are identifiable potential adopters, but no retained source identifies a platform operator or editorial board with authority over the proposed deployment.","source_ids":["SRC2","SRC3","SRC4"]},"distinct_testable_incremental_claim":{"status":"PASS","rationale":"Although the technical lever is established in adjacent fields, its governed philosophy-domain transfer leaves a falsifiable incremental claim about reducing timeout-to-negative errors and improving independently reproducible classifications.","source_ids":["SRC4","SRC5","SRC6","SRC7","SRC8"]},"bounded_next_evidence_step":{"status":"PASS","rationale":"A frozen 60-pair, non-public comparison of the current interface against four distinct result states is bounded, measurable, reversible, and can test fragment enforcement, known-valid preservation, timeout rendering, and reviewer agreement.","source_ids":["SRC5","SRC6","SRC7","SRC8"]},"no_unresolved_safety_or_authority_stop":{"status":"PASS","rationale":"The proposed first step excludes automatic rejection and public classification, supplies explicit halt conditions, and can operate as trace-labeled research. Final deployment still requires a real board's authorization, but that does not create a safety stop for the non-adjudicative pilot.","source_ids":["SRC6","SRC8"]},"adequate_search_evidence":{"status":"PASS","rationale":"All six required lanes were searched adversarially using modern and historical terminology, standards and products, non-English queries, and component combinations. Eight opened direct sources include multiple independent publishers and six primary, official, standards, or first-party sources.","source_ids":["SRC1","SRC2","SRC3","SRC4","SRC5","SRC6","SRC7","SRC8"]}},"strict_success":false,"screen_survival":true,"remaining_research_value":"MODERATE","recommended_next_step":"Identify one willing computational-philosophy operator and accountable authorizer; audit its current output policy to verify that timeout-to-negative collapse occurs; then preregister the 60-pair non-public comparison with a frozen grammar, fragment checker, proof/countermodel/unknown/out-of-scope states, independent logician review, and the stated halt rules.","world_novelty_boundary":"The search establishes close adjacent prior art and a remaining context-specific empirical claim only. It cannot establish world novelty, patentability, freedom to operate, market size, realized impact, or the absence of equivalent unpublished or proprietary philosophy workflows."}