{"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__A","search_lanes":{"direct_problem":{"queries":["philosophical argument platform automated entailment unknown undecidable argument formalization","argumentation software formal logic proof search unknown outcome timeout entailment","philosophical argument platform theorem prover entailment checker software","argument mapping platform automatic validity checker philosophy logic"],"source_ids":["SRC6","SRC7","SRC8"],"no_result_note":"No retained source documents an actual philosophical-argument platform that promises a terminating ENTAILED/NOT_ENTAILED verdict for every input in an unrestricted formal language. The retained platforms establish nearby use cases, not the asserted universal binary requirement."},"closest_prior_art":{"queries":["TPTP SZS ontology theorem countersatisfiable gave up timeout official","SMT-LIB standard unknown response solver timeout incomplete","decidable fragments first order logic language restriction theorem prover routing unknown","philosophy logic teaching platform automated proof checker Carnap software formal logic"],"source_ids":["SRC3","SRC4","SRC5","SRC6","SRC7"],"no_result_note":null},"historical_terminology":{"queries":["Church 1936 unsolvable problem elementary number theory PDF undecidability entailment","Entscheidungsproblem Prädikatenlogik semi-entscheidbar unbekannt Timeout Beweisassistent","site:fr logique du premier ordre indécidable semi-décidable démonstrateur automatique inconnu"],"source_ids":["SRC1","SRC2"],"no_result_note":null},"products_practices_standards":{"queries":["site:tptp.org UserDocs SZS ontology status theorem countersatisfiable timeout gaveup","site:smt-lib.org SMT-LIB 2.7 reference manual check-sat unknown","Z3 guide unknown incomplete quantifiers official documentation","Carneades argument evaluation software proof standard of proof burden philosophy"],"source_ids":["SRC3","SRC4","SRC5","SRC6","SRC7"],"no_result_note":null},"non_english_regional":{"queries":["Entscheidungsproblem Prädikatenlogik semi-entscheidbar unbekannt Timeout Beweisassistent","site:fr logique du premier ordre indécidable semi-décidable démonstrateur automatique inconnu","制約 ソルバー unknown タイムアウト 証明 判定不能 論理"],"source_ids":["SRC2"],"no_result_note":"The French university source directly confirmed the terminology and result. German and Japanese searches produced corroborating or product-local material but no stronger source was retained within the eight-source limit."},"composition_subproblems":{"queries":["automated theorem prover proof certificate checker timeout unknown result standard","decidable fragments first order logic language restriction theorem prover routing unknown","formalizing philosophical arguments limitations logical validity soundness paper","logic course platform checks derivations formal arguments Carnap first order logic"],"source_ids":["SRC2","SRC3","SRC4","SRC5","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; copy hosted by the University of Pennsylvania","date_or_year":"1936","source_type":"PRIMARY_RESEARCH","language":"English","claims_supported":["Church proves that a relevant property of well-formed formulas is not recursive.","The paper distinguishes an effectively enumerable positive class from a complement that is not effectively enumerable, supporting the one-sided-recognition boundary.","The result supplies historical primary evidence against assuming that every expressive formal classification problem has a total binary procedure."]},{"source_id":"SRC2","title":"Automatiser les démonstrations","url":"https://www.lri.fr/~paulin/Logique/html/cours006.html","publisher":"Laboratoire de Recherche en Informatique, Université Paris-Sud/Paris-Saclay","date_or_year":"Undated course material, accessed 2026-08-04","source_type":"OFFICIAL_GUIDANCE","language":"French","claims_supported":["First-order validity and unsatisfiability are semi-decidable.","First-order validity and satisfiability are undecidable.","The page explains the boundary by reduction from an undecidable problem such as Turing-machine halting or Post correspondence.","First-order proof search cannot in general be bounded in advance."]},{"source_id":"SRC3","title":"SZS Ontology","url":"https://tptp.org/UserDocs/SZSOntology/","publisher":"TPTP World","date_or_year":"Undated living documentation, accessed 2026-08-04","source_type":"FIRST_PARTY_PRODUCT","language":"English","claims_supported":["Automated-theorem-proving practice distinguishes semantic successes from Timeout, GaveUp, and Error.","The standard associates successful statuses with proofs, refutations, or models.","The status vocabulary avoids converting resource exhaustion or incompleteness into a negative logical verdict."]},{"source_id":"SRC4","title":"The SMT-LIB Standard, Version 2.7","url":"https://smt-lib.org/papers/smt-lib-reference-v2.7-r2025-07-07.pdf","publisher":"SMT-LIB Initiative","date_or_year":"2025-07-07","source_type":"OFFICIAL_STANDARD","language":"English","claims_supported":["The standard permits sat, unsat, and unknown rather than requiring a binary result.","Unknown denotes inconclusive search caused by resource limits, solver incompleteness, or other reasons.","The reason-unknown facility can report memory exhaustion or known incompleteness for the submitted formula class.","Proof retrieval is associated with an established unsat result, supporting certificate-sensitive result handling."]},{"source_id":"SRC5","title":"Quantifiers | Online Z3 Guide","url":"https://microsoft.github.io/z3guide/docs/logic/Quantifiers/","publisher":"Microsoft Z3 project","date_or_year":"Undated living documentation, accessed 2026-08-04","source_type":"FIRST_PARTY_PRODUCT","language":"English","claims_supported":["Z3 is a decision procedure for supported quantifier-free theory combinations but not for quantified formulas in general.","Its principal quantified-formula procedure is inherently incomplete.","Z3 nevertheless implements decision procedures for recognizable fragments, including the effectively propositional and stratified-sorts fragments.","This is a deployed example of separating decidable fragments from broader best-effort reasoning."]},{"source_id":"SRC6","title":"Carneades Argumentation System","url":"https://carneades.github.io/","publisher":"Carneades Project / Thomas F. Gordon","date_or_year":"2014-2017 project releases","source_type":"FIRST_PARTY_PRODUCT","language":"English","claims_supported":["A real argumentation platform provides argument reconstruction, evaluation, mapping, and interchange.","Carneades implements argument and scheme validation and checks syntactic and semantic errors in knowledge bases.","The platform uses configurable argument-evaluation structures and inference mechanisms rather than advertising unrestricted universal logical entailment adjudication.","The project identifies a concrete developer and platform-maintainer context for possible adoption."]},{"source_id":"SRC7","title":"Carnap - About","url":"https://carnap.io/about","publisher":"Carnap Project / Open Tower","date_or_year":"Copyright 2015-2024; accessed 2026-08-04","source_type":"FIRST_PARTY_PRODUCT","language":"English","claims_supported":["Carnap is an operational framework for defining formal languages, logics, and semantics and checking proofs in specified systems.","It serves educators, students, and researchers and is used at dozens of universities.","Its declarative inference rules and typed language construction demonstrate enforceable representation and logic contracts.","It identifies developers, instructors, and institutional users who could authorize or adopt a bounded evaluation change.","Its existing proof checking is narrower than universally deciding whether arbitrary premise-conclusion pairs are entailed."]},{"source_id":"SRC8","title":"Logical Consequence","url":"https://plato.stanford.edu/archives/fall2019/entries/logical-consequence/index.html","publisher":"Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University","date_or_year":"Fall 2019 archived edition","source_type":"SECONDARY_RESEARCH","language":"English","claims_supported":["Logical consequence has multiple proof-theoretic and model-theoretic explications and many competing formal systems.","Validity is distinct from broader questions about content, truth, context, and inductive support.","A model-theoretic negative requires a counterexample, while a proof-theoretic positive requires a proof under specified rules.","Soundness is indispensable, whereas completeness cannot always be expected.","The source supports warning users that formal derivability is not an unqualified verdict of philosophical truth."]}],"problem_evidence":{"status":"PARTLY_SUPPORTED","finding":"The computability mechanism is well supported conditionally: if the admitted language contains unrestricted first-order logic or a comparably expressive class, a total correct binary validity/entailment decider cannot be assumed, while positive proof search may remain semi-decisive. Operational standards already treat timeout and incompleteness as non-negative outcomes. However, the search did not establish the proposal's crucial factual premise that a real philosophical-argument platform both admits such a language and requires universal terminating binary verdicts.","source_ids":["SRC1","SRC2","SRC3","SRC4","SRC5","SRC6","SRC7"],"uncertainty":"The actual grammar, semantics, admission policy, current result vocabulary, and error logs of the target platform are unspecified. The language could instead be finite or an enforceable decidable fragment, and observed failures could be dominated by ambiguous formalization rather than computability."},"adopter_evidence":{"status":"SUPPORTED","finding":"Concrete adopter and authorizer classes are identifiable. Carnap names its developers, supports instructor-controlled formal systems, and is used by dozens of universities; Carneades identifies a platform developer and implements argument evaluation. A platform developer/formal-logic maintainer together with an instructor or philosophy-content owner could authorize a read-only shadow evaluation.","source_ids":["SRC6","SRC7"],"uncertainty":"No evidence identifies which particular organization has the alleged universal-binary defect or confirms that its maintainers want this intervention."},"implementation_evidence":{"status":"PARTLY_SUPPORTED","finding":"Most technical elements are implementable and already demonstrated separately: syntax- and logic-specific checking, decidable-fragment procedures, proof-backed successes, countermodel-backed negatives, and explicit unknown/timeout/incomplete statuses. What remains unvalidated is the integrated domain intervention: automatic fragment classification and guarantee-labeled routing over real philosophical arguments, with a versioned boundary record and evidence that users understand the labels.","source_ids":["SRC2","SRC3","SRC4","SRC5","SRC7","SRC8"],"uncertainty":"No retained source reports the proposed 120-argument shadow test, coverage on philosophical corpora, classification accuracy, user comprehension, or comparative forced-binary error rates."},"prior_art":{"disposition":"ADJACENT_PRIOR_ART","closest_analogues":[{"name":"SMT-LIB result contract plus Z3 fragment-sensitive solving","source_ids":["SRC4","SRC5"],"same_problem":true,"same_causal_lever":true,"overlap":"The standard/product combination separates conclusive results from UNKNOWN, records incompleteness reasons, and distinguishes general quantified reasoning from implemented decidable fragments.","remaining_difference":"It is a solver interface and implementation practice, not a governance-and-routing package evaluated on philosophical argument representations; it does not supply the proposed platform-specific decision record, recheck workflow, or corpus evidence."},{"name":"TPTP SZS status and evidence ontology","source_ids":["SRC3"],"same_problem":true,"same_causal_lever":true,"overlap":"It provides machine-readable distinctions among theorem, counter-satisfiable, timeout, gave-up, error, proof, and model outcomes, directly opposing forced binary treatment of failed search.","remaining_difference":"It standardizes reporting for automated theorem proving but does not itself classify inputs into decidable fragments, prove an unrestricted-language boundary, or address philosophical formalization and user interpretation."},{"name":"Carnap formal-language and proof-checking platform","source_ids":["SRC7"],"same_problem":false,"same_causal_lever":false,"overlap":"It is a philosophy/logic-facing platform with declared languages, semantics, inference rules, proof checking, institutional users, and identifiable maintainers.","remaining_difference":"Carnap checks submitted derivations and bounded exercise types; the retained page does not promise or implement universal binary entailment adjudication, explicit UNKNOWN routing, or a computability-boundary record."},{"name":"Carneades structured argument evaluation system","source_ids":["SRC6"],"same_problem":false,"same_causal_lever":false,"overlap":"It is a deployed structured-argument platform with validation, semantic checks, configurable evaluation functions, and automated inference.","remaining_difference":"Its evaluation model concerns schemes, burdens, and structured argument acceptability rather than unrestricted formal entailment with fragment-specific totality guarantees."}],"contrastive_claim_remaining":"For a named philosophical-argument platform whose logs first confirm that expressive or unsupported inputs are currently coerced into binary entailment verdicts, mechanically enforced fragment routing—total decisions only inside proved fragments, certificate-backed YES outside them, countermodel-backed negatives where justified, and otherwise explicit UNKNOWN—will reduce unsound definitive verdicts relative to the existing baseline while retaining a predeclared usable coverage level on archived arguments.","contrastive_claim_falsifier":"The claim is falsified if the target language is already an enforceable decidable fragment; if no forced-binary errors are found; if the router accepts any invalid certificate or emits any unsound definitive verdict; if UNKNOWN is operationally treated as rejection; or if definitive-error reduction is absent at the predeclared coverage threshold.","confidence":"HIGH","search_limitations":"This was a bounded public-web search, not an exhaustive literature, source-code, patent, procurement, or incident-log review. No proprietary platform specifications or logs were available. Direct phrase misses were not treated as novelty evidence. The search cannot establish world novelty, patentability, freedom to operate, market size, routine use across all sectors, or realized impact."},"researchability_gates":{"externally_supported_problem":{"status":"INDETERMINATE","rationale":"Undecidability, semi-decision, and honest non-success statuses are externally supported, but the exact applied problem is not: no retained source shows a real philosophical platform combining an unrestricted expressive language with a universal terminating binary-verdict requirement.","source_ids":["SRC1","SRC2","SRC3","SRC4","SRC5","SRC6","SRC7"]},"identifiable_adopter_or_authorizer":{"status":"PASS","rationale":"Carnap and Carneades establish concrete platform developers, instructors, institutional users, and formal-logic content owners who can authorize a read-only shadow test and later approve result-contract changes.","source_ids":["SRC6","SRC7"]},"distinct_testable_incremental_claim":{"status":"PASS","rationale":"Despite close automated-reasoning practice, a distinct domain claim remains: applying fragment enforcement and guarantee-labeled routing to a confirmed forced-binary philosophical platform should reduce unsound definitive verdicts while preserving a specified coverage level.","source_ids":["SRC3","SRC4","SRC5","SRC7","SRC8"]},"bounded_next_evidence_step":{"status":"PASS","rationale":"The next step is bounded and reversible: select one named platform, inspect its published grammar and result contract, then replay 120 archived supported, unrestricted, malformed, and adversarial cases in read-only shadow mode with predeclared soundness, error-reduction, coverage, and label-comprehension measures.","source_ids":["SRC3","SRC4","SRC5","SRC7"]},"no_unresolved_safety_or_authority_stop":{"status":"PASS","rationale":"A shadow test need not publish verdicts, alter grading, replace peer review, or represent derivability as philosophical truth. Named maintainers and instructors provide an authorization path, and the principal epistemic hazards can be controlled by retaining UNKNOWN and explicit semantics/guarantee labels.","source_ids":["SRC7","SRC8"]},"adequate_search_evidence":{"status":"PASS","rationale":"All six required lanes were searched adversarially, including historical Entscheidungsproblem terminology, standards/products, French/German/Japanese terminology, and combinations of proof certificates, timeouts, decidable fragments, and philosophical formalization. Exactly eight opened sources from multiple independent publishers were retained, including primary research, an official standard, official guidance, and several first-party products.","source_ids":["SRC1","SRC2","SRC3","SRC4","SRC5","SRC6","SRC7","SRC8"]}},"strict_success":false,"screen_survival":false,"remaining_research_value":"MODERATE","recommended_next_step":"Before building the 120-case router pilot, identify one actual platform and perform a short specification-and-log audit: verify its admitted grammar and semantics, whether that class is decidable, whether it promises universal termination, and whether timeouts or unsupported inputs become negative verdicts. Proceed to the read-only stratified shadow test only if that audit confirms the applied problem; otherwise reframe the work around formalization ambiguity or ordinary result-contract quality.","world_novelty_boundary":"The bounded search found established adjacent mechanisms and products but no opened source containing the full philosophy-specific problem–intervention package. This leaves only a conditional, falsifiable domain-transfer claim; it does not establish world novelty, patentability, freedom to operate, market size, or realized impact."}