{"schema_version":1,"assessment_id":"eoa_inverse_innovation_exp03_opportunity320_20260801","source_experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"negative_space_design__mathematics","archetype_slug":"negative_space_design","domain_slug":"mathematics","title":"Recoverable goal isolation for crowded formal-proof displays","opportunity_summary":"Test whether reversible context collapse, protected spacing around the active goal, and explicit state labels improve identification of current proof obligations and relevant dependencies compared with a dense baseline and a highlight-only rival, without impairing correctness, context recovery, or accessibility.","adopter_authorizer":"Maintainers of interactive theorem-prover interfaces may authorize an optional experimental view; consenting proof authors, students, and instructors control its activation and immediate rollback.","scores":{"meaningful_impact":{"score":3,"rationale":"The proposal targets accurate and timely comprehension of proof obligations and could reduce irrelevant tactic attempts, but the sealed candidate provides no evidence about problem prevalence, effect magnitude, or downstream improvement in proof construction."},"stakeholder_pull":{"score":2,"rationale":"Affected users and an authorizing maintainer are identified, but the packet contains no expressed demand, adoption requests, observed urgency, or evidence that interface crowding is a priority for them."},"incremental_advantage":{"score":3,"rationale":"Reversible omission and dependency grouping offer a testable difference from both the dense baseline and highlight-only styling, but the nearest rival may deliver the same benefit without requiring context-recovery actions."},"distinctiveness_plausibility":{"score":3,"rationale":"The combination of protected separation, recoverable context, explicit empty-state meaning, and accessibility guardrails is internally differentiated from the stated rival, but prior art is explicitly unsearched and world distinctiveness is unmeasured."},"technical_implementability":{"score":4,"rationale":"The intervention is confined to presentation, preserves proof objects and tactic semantics, and supports instant rollback. Production implementation still depends on the unspecified prover architecture, asynchronous state handling, small-screen behavior, and accessible structural encoding."},"adoption_authority_feasibility":{"score":4,"rationale":"The interface maintainer has a plausible authority boundary, users retain activation control, and the first test uses consenting participants and archived tasks. Feasibility across shared or institutionally managed interfaces is not established."},"evidence_readiness":{"score":4,"rationale":"The candidate specifies a reversible 12–20-person crossover test, concrete outcomes, two relevant comparisons, falsifiers, exclusions, and halt conditions. It does not specify task sampling, decision thresholds, instrumentation readiness, or subgroup analysis feasibility."},"safety_net_benefit":{"score":3,"rationale":"Recoverable context, explicit labels, preserved proof records, and rollback provide safeguards against mistaken omission, and accessible structure could benefit screen-reader and keyboard-only users. The same design could instead conceal dependencies or make navigation worse, so net protective benefit remains untested."},"scalability":{"score":3,"rationale":"A presentation-only feature could plausibly be distributed through an interface once implemented, but portability across provers, proof-state models, display sizes, accessibility systems, and expert workflows is unknown."}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"10K_TO_50K","scope":"Design a research prototype and three test conditions, prepare archived proof tasks, recruit and compensate 12–20 participants, instrument accuracy, latency, reveal actions, completion-state errors, and accessibility failures, then analyze the bounded crossover study.","confidence":"MODERATE","assumptions":["An existing prover interface can be modified or simulated without rebuilding its proof engine.","Archived non-production tasks and suitable participants are available without costly licensing or institutional coordination.","The study is exploratory and does not require a large powered trial.","Accessibility review covers the prototype and study flows rather than full production certification."]},"initial_deployment_startup":{"band_2026_usd":"50K_TO_250K","scope":"Create a production-ready optional implementation for one prover interface, including state synchronization, reveal and rollback controls, persistent preferences, accessible semantics, small-screen behavior, automated tests, and maintainer review.","confidence":"LOW","assumptions":["Deployment targets one established interface and does not require changes to proof semantics or tactic execution.","The codebase exposes structured goals, dependencies, errors, loading states, and traces to the presentation layer.","No major interface-framework migration is required.","Existing maintainers can review and integrate the feature."]},"operational_launch":{"band_2026_usd":"10K_TO_50K","scope":"Conduct a limited opt-in release for one interface with documentation, user communication, accessibility regression testing, issue triage, monitoring of recovery and misinterpretation errors, and a supported rollback path.","confidence":"LOW","assumptions":["The production implementation has already passed functional review.","Launch remains optional and limited rather than mandatory or ecosystem-wide.","Existing release, support, and telemetry processes can be reused.","No regulated compliance program is triggered."]},"annual_recurring":{"band_2026_usd":"10K_TO_50K","scope":"Maintain compatibility with evolving proof-state and interface APIs, run accessibility and regression tests, triage user reports, update documentation, and periodically review error and opt-out signals.","confidence":"LOW","assumptions":["One prover interface is maintained.","The feature does not require dedicated full-time support.","Telemetry, if used, relies on existing consent and privacy infrastructure.","Major redesigns or expansion to additional provers are excluded."]}},"research_burden":"MODERATE","earliest_credible_horizon":"0_TO_3_MONTHS","pipeline_gates":{"recognizable_externally_supportable_problem":{"status":"UNCERTAIN","reason":"The packet defines concrete observable behaviors and consequences, but supplies no external or empirical evidence that representative users experience them with meaningful frequency or that display competition rather than mathematical-knowledge gaps is causal."},"identifiable_adopter_or_authorizer":{"status":"YES","reason":"Interactive theorem-prover interface maintainers can offer the experimental view, while consenting users control activation and rollback."},"distinct_testable_incremental_claim":{"status":"YES","reason":"The proposal claims that recoverable context removal and protected goal separation improve obligation and dependency identification beyond both the dense baseline and a highlight-only view, with specified benefit and harm measures."},"bounded_next_evidence_step":{"status":"YES","reason":"A reversible crossover study on archived non-production tasks with 12–20 consenting users is bounded, preserves proof semantics, names comparisons, and includes explicit intervention and problem falsifiers."},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"The maintainer and participant authority boundaries are stated; deletion, semantic changes, mandatory deployment, and hiding correctness-critical obligations are excluded; immediate rollback and accessibility-related halt conditions are specified."},"implementation_cost_scope_and_range":{"status":"UNCERTAIN","reason":"A one-interface implementation can be scoped and assigned broad resource bands, but the packet does not identify a prover, codebase architecture, accessibility framework, release process, or integration constraints needed to validate those ranges."}},"blocking_evidence":["Evidence that representative users actually have material active-goal or dependency-identification difficulty under the dense baseline.","Comparative results against both the dense baseline and highlight-only presentation, including accuracy, latency, context-recovery actions, completion-state errors, and accessibility failures.","Evidence separating display-competition effects from mathematical-knowledge gaps and reporting whether effects differ for experts, students, screen-reader users, and keyboard-only users.","Feasibility evidence from a named prover interface, including asynchronous loading states, accessible structure, small displays, and guaranteed access to all obligations.","Prior-art research on existing theorem-prover interfaces and literature; distinctiveness cannot be established from the sealed packet.","Adopter and user inquiry establishing whether maintainers and affected users consider the problem important enough to justify integration and maintenance."],"next_evidence_step":"Run a counterbalanced, reversible within-participant study with 12–20 consenting users on archived non-production proof tasks, comparing the dense baseline, highlight-only rival, and recoverable goal-isolation view. Predefine decision thresholds for active-goal and dependency-identification accuracy and latency, while recording reveal actions, completion-state mistakes, inaccessible obligations, and keyboard or screen-reader failures. Falsify the problem diagnosis if baseline identification is already accurate and prompt or errors track knowledge gaps; falsify the intervention if it does not outperform both comparisons on the primary measures or increases any specified recovery, correctness, or accessibility harm.","research_questions":["How frequent and consequential are active-goal and dependency-identification errors under the dense baseline for representative users?","Do errors arise from visual competition after controlling for task difficulty and mathematical knowledge?","Does recoverable goal isolation outperform highlight-only emphasis on accuracy or latency without increasing reveal actions or context loss?","Do outcomes differ among experts, students, keyboard-only users, and screen-reader users?","Can the interface encode grouping, hidden-content status, completion status, errors, and asynchronous loading accessibly and without ambiguity?","Which existing prover interfaces or studies already implement collapsible context, goal isolation, structured accessibility, or explicit empty-state semantics?","Would maintainers and users adopt and maintain an optional view if the bounded study meets its decision thresholds?"] ,"recommendation":"VALIDATE_PROBLEM_FIRST","uncertainty_constraints":["This is a closed-book assessment with no external sources.","Problem prevalence, stakeholder demand, effect magnitude, market or user population size, realized impact, and exact costs are unmeasured.","Prior art is explicitly unsearched, so novelty and world-level distinctiveness cannot be inferred.","All attention, latency, accuracy, accessibility, and workflow benefits remain prospective hypotheses.","Cost bands are resource-equivalent planning ranges based on an assumed single-interface scope, not quotations or point estimates.","The earliest horizon applies to the bounded non-production evidence study, not production deployment."],"closed_book_prior_art_boundary":"The sealed candidate distinguishes its mechanism from a stated highlight-only rival, but prior-art status is UNSEARCHED. This assessment therefore makes no claim that collapsible proof context, isolated goals, structured accessibility, protected spacing, or explicit empty-state semantics are novel, rare, or absent from existing theorem-prover interfaces or research."}