{"schema_version":1,"assessment_id":"eoa_inverse_innovation_exp03_opportunity320_20260801","source_experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__mathematics","archetype_slug":"invariant_mode_decomposition_design","domain_slug":"mathematics","title":"Invariant-mode workflow for coupled linear recurrence classification","opportunity_summary":"Apply generalized invariant-mode decomposition, conditioning checks, reconstruction, and boundary-case tests to explicit finite-dimensional coupled linear recurrences so that growth, decay, persistence, oscillation, cancellations, and exceptional initial-condition subspaces are classified within a declared scope. The candidate is mathematically coherent, but its prevalence, realized advantage, and distinctiveness remain unverified.","adopter_authorizer":"The mathematician responsible for the proof adopts and applies the workflow; an independent reviewer accepts or rejects the resulting formal claim.","scores":{"meaningful_impact":{"score":4,"rationale":"Preventing omitted exceptional initial conditions, incorrect dominant growth classes, and invalid stability claims would materially improve theorem correctness and traceability, although the frequency of these failures is unsupported."},"stakeholder_pull":{"score":3,"rationale":"Authors, reviewers, students, and downstream theorem users have a plausible interest in reliable classifications, but the packet provides no adoption inquiry or evidence that these actors perceive the problem as sufficiently burdensome to change practice."},"incremental_advantage":{"score":3,"rationale":"The workflow offers structured treatment of generalized eigenspaces, modal coefficients, ties, conditioning, reconstruction, and parameter boundaries beyond coordinate-wise finite iteration; however, no bounded comparison yet shows corrections or reduced proof complexity relative to complete generating-function or characteristic-polynomial analysis."},"distinctiveness_plausibility":{"score":3,"rationale":"The intervention-oriented composition and explicit halt rules may be distinguishable as a workflow, but novelty relative to recurrence, Jordan-form, invariant-subspace, and perturbation-analysis practice is unsearched and unverified."},"technical_implementability":{"score":4,"rationale":"The authorized test is bounded to an explicit 5–20 dimensional linear recurrence and uses established formal objects such as generalized eigenspaces and direct-iterate reconstruction. Nearly defective, strongly non-normal, or unsuitable coefficient-field cases can still prevent reliable computation."},"adoption_authority_feasibility":{"score":5,"rationale":"Decision authority is explicit: the proof author controls the claim and an independent reviewer controls acceptance. The proposal requires no transfer of authority to an automated system and prohibits treating floating-point eigenpairs as proof."},"evidence_readiness":{"score":4,"rationale":"The packet specifies an exact bounded recurrence test, baseline comparisons, reconstruction checks, residual and conditioning criteria, edge cases, and an intervention falsifier. No test result or prepared comparison corpus is supplied."},"safety_net_benefit":{"score":4,"rationale":"Residual, conditioning, dominance-gap, perturbation, and reconstruction checks could expose tied, defective, or unstable classifications, with explicit halt and rollback to exact recurrence, invariant-subspace, Jordan, or generating-function analysis. Their detection performance remains untested."},"scalability":{"score":3,"rationale":"The workflow can plausibly be reused across explicit finite-dimensional recurrences and parameter families, but its stated scope excludes unknown operators and may become impractical when dimension, coefficient field, conditioning, or stable modal identity prevents usable decomposition."}},"score_confidence":"MODERATE","costs":{"first_evidence":{"band_2026_usd":"UNDER_10K","scope":"A non-live desk test on one exact 5–20 dimensional recurrence, including generalized spectral analysis, initial-condition subspace classification, comparison with direct iterates and a coordinate or generating-function solution, and documentation of the falsifier outcome.","confidence":"MODERATE","assumptions":["The recurrence and initial conditions are already specified.","Existing symbolic or numerical mathematics software is available.","The test is performed by one mathematically qualified investigator over a bounded period.","No proprietary data, hardware, or compliance review is required."]},"initial_deployment_startup":{"band_2026_usd":"10K_TO_50K","scope":"Create reusable analysis templates, proof-reporting conventions, conditioning and residual checks, edge-case examples, and reviewer guidance for use by a small mathematics team.","confidence":"LOW","assumptions":["Deployment remains within explicit finite-dimensional linear recurrences.","Startup includes specialist labor, software configuration, documentation, and internal validation.","No custom production-grade symbolic algebra platform is built.","The amount of training and integration with existing proof workflows is unknown."]},"operational_launch":{"band_2026_usd":"10K_TO_50K","scope":"Run a limited multi-user proof-review pilot, apply the workflow to a bounded recurrence corpus, compare classifications and proof complexity with current methods, and independently review outputs before accepting claims.","confidence":"LOW","assumptions":["Launch is a controlled scholarly workflow rather than automated theorem approval.","The corpus can be assembled without paid data access.","All conclusions receive qualified human review.","Difficult defective or non-normal examples may require additional specialist time."]},"annual_recurring":{"band_2026_usd":"UNDER_10K","scope":"Maintain templates and examples, update software-dependent checks, and periodically audit recurrence analyses for unsupported modal separation or scope expansion.","confidence":"LOW","assumptions":["Use remains limited to a small team and modest case volume.","Existing mathematics software licenses cover the work.","Recurring costs exclude major new software development and large-scale formal verification.","Case-specific proof labor is charged to the underlying research rather than central maintenance."]}},"research_burden":"MODERATE","earliest_credible_horizon":"0_TO_3_MONTHS","pipeline_gates":{"recognizable_externally_supportable_problem":{"status":"YES","reason":"The sealed candidate identifies a logically recognizable failure mode: coordinate-wise or finite-horizon analysis can miss excited growing, tied, defective, or exceptional initial-condition directions. Exact recurrence examples can support the existence of the problem, although its prevalence is unverified."},"identifiable_adopter_or_authorizer":{"status":"YES","reason":"The proof author is the identified adopter and claim authority, while an independent reviewer has explicit acceptance or rejection authority."},"distinct_testable_incremental_claim":{"status":"YES","reason":"The proposal claims that the structured modal workflow can correct classifications or reduce proof complexity relative to coordinate-wise iteration or complete root-based analysis, and it is falsified if neither benefit occurs or its checks miss included tied and defective cases."},"bounded_next_evidence_step":{"status":"YES","reason":"The packet authorizes a safe, non-live test on one exact 5–20 dimensional recurrence with fixed-horizon reconstruction and symbolic asymptotic comparison."},"no_unresolved_safety_or_authority_stop":{"status":"YES","reason":"Numerical evidence is denied proof authority, prohibited extrapolations are explicit, author and reviewer roles are separated, and failures trigger a halt and rollback to exact or alternative formal analysis."},"implementation_cost_scope_and_range":{"status":"YES","reason":"The explicit finite-dimensional scope and specified analytical tasks support broad resource-equivalent bands for a desk test and small-team pilot, although actual labor, software, and difficult-case requirements remain uncertain."}},"blocking_evidence":["No bounded result shows that the workflow corrects a classification or reduces proof complexity relative to coordinate-wise, generating-function, or full characteristic-root analysis.","Prior art is unsearched and unverified, so the distinctiveness of the composed workflow cannot be established.","No evidence establishes how often the stated misclassification problem occurs or whether authors and reviewers would adopt an additional formal workflow.","The reliability of the proposed checks on nearly defective and strongly non-normal cases has not been demonstrated."],"next_evidence_step":"Conduct the authorized non-live test on one exact 5–20 dimensional recurrence or parameterized family containing tied or defective behavior. Compare the proposed generalized-modal workflow with coordinate-wise finite iteration and a complete generating-function or characteristic-root solution, verify reconstructed against direct iterates over a fixed horizon, and classify all initial-condition subspaces symbolically. Falsify the incremental claim if it corrects no classification, does not reduce proof complexity under a declared rubric, or its residual, gap, and conditioning checks fail to flag the included edge case.","research_questions":["Does the workflow change any asymptotic classification or reveal an exceptional initial-condition subspace missed by the baseline?","Under a declared measure such as proof steps, unresolved cases, or reviewer corrections, does it reduce proof complexity relative to a complete generating-function or characteristic-root derivation?","Do the residual, spectral-gap, conditioning, and perturbation checks reliably halt on tied, defective, nearly defective, and strongly non-normal cases?","Which elements, if any, are distinct from established recurrence, Jordan-form, invariant-subspace, and perturbation-analysis workflows?","Do proof authors and reviewers regard the added traceability as valuable enough to justify its analytical overhead?"] ,"recommendation":"PRIOR_ART_RESEARCH","uncertainty_constraints":["Closed-book assessment provides no external evidence about problem prevalence, stakeholder demand, prior art, historical precedence, or realized impact.","The proposal applies only to explicit finite-dimensional linear recurrences and does not establish usefulness for unknown operators, unsuitable coefficient fields, or nonlinear systems outside a stated neighborhood.","Cost bands are resource-equivalent planning ranges, not observed prices, and depend strongly on specialist labor and case difficulty.","Nearly defective or strongly non-normal matrices may make modal coefficients unstable even when short-run reconstruction appears adequate.","A successful bounded example would not establish general effectiveness across recurrence families or all parameter boundaries."],"closed_book_prior_art_boundary":"Prior art is unsearched and unverified in this closed-book assessment; no conclusion is made about novelty, prevalence, historical precedence, market size, or whether equivalent recurrence-analysis workflows already exist."}