{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp05_complete_proposal_portfolio20_20260803","cell_id":"computability_boundary_mapping__film_media_production","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"cbm_fmp_canon_entailment_boundary_05","proposal_index":5,"version":0,"title":"Proof-and-Countermodel Boundary for Serialized-Canon Queries","problem":"A serialized-production continuity service accepts a formal story bible containing characters, identities, locations, temporal relations, event rules, and recursively derived consequences. It is asked to terminate on every bible and decide exactly whether a proposed script fact is required by canon, forbidden by canon, or left open. The unrestricted rule language permits unbounded time points and recursive derivation, but the service exposes a definitive three-way result even when proof search reaches a resource limit. Missing proofs, bounded countermodels, database absence, and actual non-entailment are consequently at risk of being collapsed.","actors":["showrunner","screenwriter","script coordinator","continuity editor","story-bible modeler","episodic producer","standards or franchise reviewer"],"observable_state":"A canon query receives REQUIRED, FORBIDDEN, or OPEN without a linked proof, complete finite model, rule-fragment classification, or search bound. Recursive queries sometimes consume the allotted budget, after which absence of a derivation is reported as OPEN or permitted. The record does not state whether reasoning used open-world or closed-world semantics, which characters and time points were quantified, or whether executable and recursive rules were allowed.","consequence":"A script can be cleared because the checker failed to derive a contradiction in time, or blocked because an omitted fact was treated as false. Additional engineering may be directed toward a total exact reasoner for an unrestricted recursive language. A formally correct result can also be mistaken for narrative truth when the encoded bible omits a relevant event, identity distinction, or temporal assumption.","affected_objective":"Support auditable continuity decisions across an evolving serialized story world while distinguishing checked entailment, checked contradiction, exact finite-fragment openness, bounded countermodels, unresolved proof search, and defects in the formalization.","intervention":"Replace the definitive unrestricted canon classifier with a model-relative proof-and-countermodel service. First freeze the canon grammar, time and identity semantics, quantifier domains, open-world policy, rule evaluation model, and meanings of REQUIRED, FORBIDDEN, and OPEN. Test the unrestricted total-exact requirement with a reviewed reduction: encode an arbitrary program and input as an initial configuration plus recursive transition rules over successor time points, and ask whether a HALTED fact is derivable. The finite canon theory derives HALTED exactly when the encoded computation halts; therefore, a total exact entailment decider for this unrestricted rule class would decide halting. If the construction survives independent review, reserve exact three-way answers for an enforceable finite canon fragment with enumerated entities and time points, bounded relations, total predicates, and acyclic rules. Exhaustively model-check that fragment. Route recursive or otherwise unrestricted bibles to fair proof search for the query and its formal negation. Return REQUIRED-PROOF or FORBIDDEN-PROOF only with independently checkable derivations; at the operational bound return UNKNOWN. A finite countermodel may be reported as BOUNDED-COUNTERMODEL but cannot establish unrestricted non-entailment. Attach the formalization version, fragment, assumptions, proof or model, bounds, and recheck triggers to every result, while leaving canon interpretation and script approval with the designated creative authority.","structural_mapping":[{"archetype_element":"Problem-Class Specification","domain_realization":"Define the target as formal entailment of a canon proposition or its negation from an encoded story theory, not informal narrative plausibility or database lookup."},{"archetype_element":"Instance Representation Contract","domain_realization":"Version the syntax for characters, identity, locations, events, successor time, episode boundaries, relations, quantifiers, negation, recursive rules, and each queried proposition."},{"archetype_element":"Computation Model Contract","domain_realization":"State whether domains are finite or unbounded, rules are acyclic or recursive, predicates are total or executable, and external human judgments or databases act as additional information sources."},{"archetype_element":"Quantifier and Scope Map","domain_realization":"Separate facts about named episodes, conclusions over a finite enumerated canon, consequences of an unrestricted recursive theory, and statements about every possible future continuation."},{"archetype_element":"Computability Impossibility Certificate","domain_realization":"Construct a finite canon theory representing machine configurations and transitions and show that its HALTED proposition is derivable exactly when the source program halts."},{"archetype_element":"Reduction Preservation Contract","domain_realization":"Require proof that the source-to-canon translation is total and computable, produces well-formed rules, preserves each computation step, and introduces no unsupported HALTED derivation."},{"archetype_element":"Assumption Register","domain_realization":"Record successor-time semantics, rule inference semantics, treatment of negation, domain closure, consistency assumptions, and the distinction between derivability and truth in an intended story world."},{"archetype_element":"Decidable Subclass Map","domain_realization":"Define a mechanically recognizable fragment with finite named domains, bounded time, total relations, and acyclic rules for which exhaustive model checking terminates."},{"archetype_element":"Constructive Procedure Witness","domain_realization":"Provide the finite-fragment evaluator with a termination measure and correctness argument for REQUIRED, FORBIDDEN, and OPEN classifications."},{"archetype_element":"One-Sided Recognition Contract","domain_realization":"For recursive theories, permit fair derivation search to confirm a query or its negation when a finite proof exists without promising that failure to find either proves openness."},{"archetype_element":"Unknown and Nontermination Policy","domain_realization":"Keep UNKNOWN distinct from exact finite-fragment OPEN, REQUIRED-PROOF, FORBIDDEN-PROOF, BOUNDED-COUNTERMODEL, malformed theory, contradiction in the formalization, and tool failure."},{"archetype_element":"Uncertainty Residue","domain_realization":"Record unexpanded rules, unbounded domains, unresolved proof obligations, competing identity assumptions, and formalized narrative facts awaiting creative confirmation."},{"archetype_element":"Computability Guarantee Record","domain_realization":"Store theory and query hashes, semantics, fragment classification, proof or countermodel, checker version, search schedule, resource bound, and result label."},{"archetype_element":"Recheck Trigger","domain_realization":"Re-evaluate when an episode, retcon, identity assertion, temporal rule, domain boundary, negation policy, inference rule, or checker version changes."}],"mechanism_mapping":[{"mechanism_slug":"halting_problem_reduction","role":"Tests unrestricted total entailment by translating a program execution into recursive canon transitions whose HALTED fact is derivable exactly when the source computation halts.","counterfactual_removal":"Timeouts or failed implementations could be mistaken for proof of undecidability, or a total unrestricted classifier could be pursued without examining its solvability."},{"mechanism_slug":"many_one_reduction_proof","role":"Requires one total computable map from each program-input pair to a canon-theory query with preserved yes membership.","counterfactual_removal":"The boundary would rest on a resemblance between recursion and computation rather than a checkable target construction."},{"mechanism_slug":"reduction_direction_checklist","role":"Checks that the map runs from the known source into canon entailment and verifies configuration encoding, transition preservation, HALTED correspondence, and semantic assumptions.","counterfactual_removal":"A reversed reduction or extra derivation path could support an invalid impossibility conclusion."},{"mechanism_slug":"language_fragment_restriction","role":"Creates an enforceable finite canon language by bounding domains and time and excluding recursion, executable predicates, and unbounded quantification from exact mode.","counterfactual_removal":"The checker could issue exact three-way results for theories that do not satisfy its termination argument."},{"mechanism_slug":"abstract_interpretation_or_model_checking","role":"Exhaustively evaluates the finite canon model and all permitted valuations so exact fragment verdicts cover the declared domain rather than selected story examples.","counterfactual_removal":"Finite-fragment results could depend on sampled queries or manually traversed relation chains instead of complete evaluation."},{"mechanism_slug":"constructive_algorithm_and_correctness_proof","role":"Supplies the finite evaluator and proves termination, sound derivation, and completeness for the restricted three-way classification.","counterfactual_removal":"Calling the fragment decidable would not establish that the deployed evaluator actually decides it correctly."},{"mechanism_slug":"theorem_prover_guided_search","role":"Searches recursive theories for formal derivations of the query or its negation and retains successful certificates while exposing unresolved goals.","counterfactual_removal":"Unrestricted reasoning would either be abandoned entirely or presented through opaque answers without checkable support."},{"mechanism_slug":"enumeration_and_dovetailing","role":"Fairly interleaves proof branches for the proposition and its negation so one divergent branch cannot starve a finite derivation elsewhere.","counterfactual_removal":"Depth-first proof search could remain trapped on an infinite branch despite the existence of a short valid proof."},{"mechanism_slug":"proof_checking","role":"Independently re-verifies derivations, reduction arguments, and finite-model certificates under the frozen inference rules.","counterfactual_removal":"Canon decisions would depend on the proof searcher's authority rather than a small auditable checking procedure."},{"mechanism_slug":"semi_decision_with_explicit_unknown","role":"Terminates operational proof search at a declared bound and returns UNKNOWN rather than interpreting absence of a proof as OPEN or permitted.","counterfactual_removal":"Resource exhaustion would again become a false negative entailment verdict."},{"mechanism_slug":"fallback_mode_router","role":"Routes queries to exact finite model checking, proof search, bounded countermodel search, formalization repair, or human review and labels the earned guarantee.","counterfactual_removal":"Exact openness, proof-search failure, bounded countermodels, and malformed canon data could collapse into the same continuity decision."},{"mechanism_slug":"computability_boundary_decision_record","role":"Versions the adopted reasoning boundary, formal semantics, shipped result labels, supporting proof, and changes requiring reclassification.","counterfactual_removal":"Later increases in rule expressiveness or changes in canon semantics could silently invalidate the original guarantee."}],"causal_chain":["An unrestricted canon language with successor time and recursive rules can encode configurations and transitions of an arbitrary computation.","A finite theory can represent the source program's initial configuration and derive each subsequent configuration through its transition rules.","The canon proposition HALTED has a finite derivation exactly when the encoded program eventually reaches its halting state.","Conditional on a valid reviewed translation, an always-terminating exact entailment classifier for the unrestricted theory class would decide the halting problem.","Restricting the canon to finite enumerated domains and acyclic total rules removes the unbounded recursive derivation used by the reduction.","Exhaustive model checking can then decide the query, its negation, or genuine underdetermination within that enforced fragment.","For recursive theories, fair proof search can confirm propositions carrying finite derivations, but operational exhaustion remains UNKNOWN and bounded countermodels remain bounded.","Proof certificates, explicit labels, and versioned formalizations let continuity reviewers use machine reasoning without transferring its formal guarantee to unstated narrative meaning."],"baseline":"Store canon facts and rules in a searchable bible or rule engine, run derivation until a result or timeout, and translate absence of a retrieved fact or proof into OPEN, false, or permitted without recording whether the search was complete or the reasoning language was decidable.","nearest_rivals":["Manual continuity review: can interpret narrative intent and incomplete records but does not provide a uniform terminating entailment procedure for every formal recursive theory.","Graph-database reachability: can answer finite relationship queries under a fixed schema but does not justify unrestricted recursive logical entailment.","Closed-world rule evaluation: can make absence behave as false and terminate on some finite databases, but changes the semantics rather than deciding an open-world unrestricted query.","An unrestricted theorem prover with a Boolean wrapper: may find valid proofs, but timeout or failed proof search cannot support an unqualified negative answer.","Finite episode-by-episode model checking: can be exact for its declared characters, events, and time range but cannot silently generalize to unbounded future canon.","Language-model continuity answers: may provide useful review prompts but do not supply the totality, formal semantics, or checkable proof required by the declared exact classifier."],"remaining_contrastive_claim":"The proposal's remaining contrast is a canon-governance protocol that separates exact finite-model classification from one-sided proof discovery in recursive story theories and requires proof, bounded-countermodel, and UNKNOWN outputs to remain operationally distinct. This is a scoped design contrast, not a claim of novelty, prevalence, demand, or effect size.","authority_safety":{"decision_authority":"The showrunner or formally designated canon authority decides narrative canon and script acceptance. The script coordinator or story-bible modeler maintains the formal representation but cannot turn UNKNOWN into permission or rewrite canon through model configuration alone.","authorized_first_step":"Using synthetic story worlds only, the continuity tooling team may freeze a draft rule semantics, construct the computation-to-canon reduction for independent review, define a small finite fragment, and test proof, countermodel, and routing behavior. The pilot may not alter an active story bible or approve a production script.","excluded_actions":["Reject, approve, or rewrite a script solely because unrestricted proof search returns UNKNOWN.","Treat absence of a fact or proof as false unless the recorded finite-fragment semantics explicitly support that conclusion.","Report a BOUNDED-COUNTERMODEL as unrestricted proof of non-entailment.","Treat formal entailment as proof that the encoded premise set faithfully captures narrative intent.","Silently add or remove characters, identities, episodes, time points, rules, or negation assumptions after issuing a result.","Allow executable or recursive rules into exact finite mode through an unchecked escape hatch.","Represent the reduction-based boundary as established before its preservation obligations pass independent review."],"halt_rollback":"Halt the pilot if the proof checker accepts a seeded invalid derivation, finite mode misclassifies a fully enumerated synthetic theory, recursive syntax bypasses fragment enforcement, fair search starves a known finite proof, or downstream interfaces render UNKNOWN as OPEN or permitted. Disable machine-issued continuity classifications, preserve theories and traces, return decisions to human review, invalidate affected records, and require corrected semantics plus independent rechecking before resumption."},"negative_tests":{"strongest_counterevidence":"The strongest counterevidence would show that the actual canon language is an enforced finite acyclic rule system over explicitly enumerated characters, events, and time points, with a total correct evaluator for every permitted query. The task would then be decidable, leaving data quality, semantic fidelity, or computational cost rather than an unrestricted computability boundary.","problem_falsifier":"The problem is falsified if the service performs only finite database retrieval, never claims exact conclusions for recursive or unbounded theories, already distinguishes missing data and timeout from non-entailment, and leaves every unresolved query explicitly undecided.","intervention_falsifier":"The intervention fails if the reduction cannot encode valid canon theories, HALTED can be derived without corresponding source halting, fragment membership is unenforceable, the finite evaluator is incomplete, the proof checker is unsound, dovetailing is unfair, or result consumers collapse UNKNOWN or bounded countermodels into OPEN. Its operational premise is also defeated if canon stewards cannot formalize any synthetic query without losing the meaning they intend to test.","risks":["A checked proof can create false confidence when the formal story model omits or misstates narrative facts.","Finite-domain restrictions may exclude long-range identity, time-travel, alternate-world, or retcon structures needed by a production.","Open-world and closed-world interpretations may be confused by reviewers or downstream tools.","Recursive proof search can consume substantial resources while producing UNKNOWN.","A bounded countermodel may exploit unrealistic worlds allowed only because relevant canon constraints were omitted.","Formal tooling can displace rather than support the designated creative authority.","Contradictory canon premises may make both a proposition and its negation derivable unless inconsistency handling is explicit.","Story bibles, planned reveals, and proof traces may expose confidential plot information.","Frequent formalization changes may invalidate stored results faster than they are reviewed."]},"next_evidence_step":"Run one closed-book, non-production evaluation. Freeze a minimal temporal canon grammar and inference semantics. Have a reviewer who did not author the construction check the program-input-to-canon reduction for total translation, well-formed initial and transition rules, step correspondence, absence of spurious HALTED derivations, and the derivability biconditional. Implement a prototype finite evaluator, proof scheduler, certificate checker, and router against 20 synthetic micro-canons: five finite-fragment entailed queries, four finite-fragment negated queries, three genuinely open finite-fragment queries, three recursive theories with finite proofs behind divergent branches, three recursive theories with no proof found inside the operational bound, and two theories invalidated by changed identity or negation semantics. Record fragment classification, proof schedule, explored valuations, proof or countermodel, assumptions, output label, and reviewer judgment. Fail the evidence step if any invalid proof is accepted, a complete finite query is misclassified, a known finite recursive proof is starved, an exhausted search returns OPEN, or a semantic change preserves the prior result.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 governed universal termination and cleared-asset behavior of executable interactive packages through finite-state preflight and sound abstraction. Proposal 2 governed exact semantic equivalence of render-graph substitutions through proof-carrying rewrites and checked transformation certificates. Proposal 3 governed existence of a constraint-conforming edit through bounded exhaustive synthesis and open dovetailed witness search. Proposal 4 governed shortest exact procedural representations of media masters through a diagonal minimal-description boundary and finite-space minimum certificates. Proposal 5 instead governs logical entailment inside serialized story canon. Its causal path embeds computation as recursive temporal facts and distinguishes finite-model three-way decisions from one-sided proof discovery, bounded countermodels, and UNKNOWN. It is independently adoptable by a writers' room or continuity department without analyzing interactive playback, replacing render graphs, generating cuts, or optimizing archival package size.","revision_record":{"parent_version":null,"progress_targets_addressed":["Created one complete candidate at proposal index 5.","Selected a serialized-canon entailment problem distinct from the four earlier production, rendering, editorial-synthesis, and preservation problems.","Specified a recursive-derivation reduction, finite model-checking fragment, proof protocol, authority controls, falsifiers, and bounded first evidence.","Explained diversity from every earlier sealed proposal."],"conceptual_changes":["Initial version; applied computability-boundary mapping to exact entailment and non-entailment claims over recursive serialized-story theories."],"operational_changes":["Initial version; introduced proof-backed REQUIRED and FORBIDDEN labels, exact finite-fragment OPEN, BOUNDED-COUNTERMODEL, explicit UNKNOWN, and canon-authority safeguards."],"evidence_changes":["Initial version; prior art remains unsearched and first evidence is limited to independent reduction review and 20 synthetic micro-canons."],"claim_changes":["Initial version; makes no novelty, prevalence, demand, or effect-size claim and conditions the unrestricted impossibility conclusion on a valid independently checked reduction."]}}