{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__mathematics","trajectory_id":"R","attempt_index":0,"candidate_sha256":"cd0df02bfaa3033051ced9dfb69254a978f536108a9c5561f22074e1af253b5b","gates":{"G1":{"status":"PASS","reason":"The candidate identifies an independently recognizable mathematical problem: asymptotic misclassification of coupled recurrences under coordinate-wise or finite-horizon analysis."},"G2":{"status":"PASS","reason":"The recurrence operator, generalized invariant subspaces, spectral responses, dominance rules, reconstruction checks, drift across parameter families, and interpretation limits correspond directly to the archetype without forcing empirical or network analogies."},"G3":{"status":"PASS","reason":"Separating the initial state into invariant or generalized modal components changes what can be proved about growth, decay, oscillation, cancellation, and exceptional initial-condition subspaces."},"G4":{"status":"PASS","reason":"Every archetype component receives a mathematically coherent realization, defective and non-normal cases are preserved, and unsuitable supplied mechanisms are explicitly rejected with valid counterfactual explanations."},"G5":{"status":"PASS","reason":"Formal inferences are distinguished from hypotheses, numerical evidence is denied proof authority, novelty is explicitly unsearched, and no citations or empirical performance claims are fabricated."},"G6":{"status":"PASS","reason":"The problem falsifier tests whether coupled modal ambiguity exists, while the intervention falsifier separately tests whether the workflow corrects classifications, simplifies proofs, and detects planted edge cases."},"G7":{"status":"PASS","reason":"Proof and review authority are separated, the first test is bounded, prohibited extrapolations are explicit, and halt conditions revert analysis to exact invariant-subspace, Jordan, or generating-function methods."}},"scores":{"structural_fit":{"score":4,"reason":"The proposal instantiates the full transformation-to-modes-to-classification-to-residual structure, including ties, defective cases, drift, and scope limits."},"domain_fidelity":{"score":4,"reason":"Definitions, proof obligations, exact-versus-numerical distinctions, generalized eigenspaces, multiplicities, and parameter-boundary qualifications are native to finite-dimensional recurrence analysis."},"causal_plausibility":{"score":4,"reason":"Modal separation exposes the initial-condition directions and polynomial factors that determine admissible asymptotic behavior, directly addressing the stated classification errors."},"component_translation":{"score":4,"reason":"All named components are translated with explicit domain realizations, and adaptations preserve their functional roles rather than merely renaming them."},"adversarial_survival":{"score":4,"reason":"The candidate directly handles absent eigenbases, tied roots, eigenvalue crossings, exceptional initial conditions, non-normal transients, ill-conditioning, and the limits of finite-horizon checks."},"reframing_gain":{"score":3,"reason":"The modal workflow makes exceptional subspaces, robustness, and proof scope more systematic, although a complete generating-function or characteristic-root analysis can recover much of the same mathematics."},"practicality_testability":{"score":4,"reason":"The bounded recurrence corpus, exact reconstruction comparison, symbolic asymptotics, planted edge cases, and explicit halt criteria support a concrete evaluation."},"expected_value_risk":{"score":4,"reason":"The proposed trial is bounded and reversible, while safeguards sharply limit the risk of converting unstable numerical eigenstructure into an invalid theorem."},"novelty_evidence":{"score":0,"reason":"Prior art is explicitly unsearched, so no comparative novelty claim is supported by the closed-book packet."}},"weighted_total":92.5,"disposition":"DEEP_RESEARCH","fabrication_findings":[],"weak_dimensions":["novelty_evidence"],"actionable_critique":[{"priority":"MEDIUM","issue":"The packet establishes structural value but supplies no evidence that the composed workflow is novel relative to established recurrence, Jordan-form, invariant-subspace, and perturbation-analysis practice.","repair":"Conduct a bounded prior-art comparison and state which claimed contribution is established, recombined, or unsupported.","evidence_boundary":"This closed-book evaluation can judge internal mathematical coherence but cannot establish novelty or historical precedence."}],"repairs":[],"improvement_attribution":{"kind":"NONE","reason":"This is the original attempt, with unchanged problem and causal-lever identifiers and no registered prior repairs."},"trajectory_replacement":false,"arm_guess":"MECHANISM_PACKET","recommendation":"SUCCESS","tester_summary":"The candidate is an unusually complete and domain-faithful translation of invariant-mode decomposition into coupled-recurrence analysis. Its formal causal lever, edge-case handling, falsifiers, bounded test, and authority controls survive the supplied adversarial cases; only novelty remains unevidenced."}