{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__music_musicology","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"music_musicology","decision":"CANDIDATE","problem_id":"recurrent_coupled_ensemble_rehearsal_deviations","causal_lever_id":"target_persistent_rehearsal_transition_modes","proposal":{"problem":"Ensemble rehearsals often correct isolated tempo, balance, articulation, intonation, or synchronization errors, yet coordinated deviations recur or migrate across sections and passages. The recognizable problem is inefficient rehearsal and an interpretation that remains unstable despite repeated local corrections.","actors_substrate":["conductor or rehearsal director","performing musicians and sections","repeated performances of the same scored passages","rehearsal audio and timing/dynamics/intonation measurements"],"observable_state":"For each rendition, a passage-level vector of section-specific tempo deviation, dynamic balance, onset dispersion, articulation duration, and intonation relative to the ensemble's agreed interpretation.","consequence":"Local corrections may suppress one visible error while leaving intact, or amplifying, a coupled pattern that reappears in later renditions.","affected_objective":"Achieve a stable, coherent ensemble interpretation with less rehearsal time and without degrading musician agency, expressiveness, or hearing safety.","structural_mapping":[{"archetype_element":"Transformation acting on coupled variables","domain_realization":"A locally fitted operator maps one rendition's deviation vector to the next after the ensemble's ordinary rehearsal response.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Invariant directions with scalar response","domain_realization":"Combinations such as tempo acceleration plus thinning articulation across several sections may recur as approximate modes with measurable persistence or gain.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Action relevance differs from surface magnitude","domain_realization":"A modest coordinated deviation may be more persistent and rehearsal-sensitive than the largest single-section error.","claim_kind":"INFERENCE"},{"archetype_element":"Residual and drift limits","domain_realization":"Score changes, learning, fatigue, personnel, venue, and conductor strategy can invalidate a fixed modal account.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"One ensemble, fixed passages, and consecutive renditions under a specified rehearsal protocol."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Standardized passage-by-section performance deviations plus documented measurement uncertainty."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Eigenvectors of the fitted rehearsal-to-rehearsal transition operator."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues estimating decay, persistence, oscillation, or growth per rendition."},{"component":"Dominant Mode Selection Rule","status":"direct","domain_realization":"Retain modes only when persistence, outcome sensitivity, and out-of-sample residual improvement pass thresholds."},{"component":"Stable/Unstable Mode Partition","status":"adapted","domain_realization":"Classify modes by eigenvalue magnitude, with uncertainty intervals and marginal cases left undecided."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map conductor-approved cue bundles or sectional exercises to targeted modal coordinates."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Reconstruct held-out rendition changes and inspect both error magnitude and structured leftovers."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Re-estimate mode angles and ordering across rehearsals."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Treat modes as local descriptive rehearsal dynamics, not fixed traits of musicians or works."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degenerate, non-orthogonal, or intervention-coupled modes."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"Same ensemble, conductor, repertoire segment, venue configuration, and nearby rehearsal stage."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Require uncertainty-adjusted separation between retained and omitted modes before simplification."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicitly fitted local transition matrix; use conditioning diagnostics for non-normal cases.","counterfactual_removal":"No invariant rehearsal directions or gains would be identified."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Test small, conductor-approved cue perturbations and measure musical outcome and cross-mode effects.","counterfactual_removal":"Modes could be described but not ranked by actionable leverage."},{"slug":"modal_stability_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Classify persistence only within the stated rehearsal window.","counterfactual_removal":"Monitoring would not distinguish self-decaying deviations from persistent or growing ones."},{"slug":"mode_shape_testing","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Adapt excitation to consensual, musically plausible cue variations rather than physical forcing.","counterfactual_removal":"The fitted modes would lack a prospective response check."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Section importance is not the target; centrality would substitute a social or score network for rendition dynamics.","counterfactual_removal":"No change to the causal chain."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The state is bounded enough for a full spectrum, and near-tied modes are substantively important.","counterfactual_removal":"No change to the causal chain."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions need not describe rehearsal-to-rehearsal persistence; retained as the nearest rival.","counterfactual_removal":"No change to the proposed intervention."},{"slug":"reduced_order_model","disposition":"unused","contribution_type":"NONE","adaptation_or_rejection":"A runnable surrogate is unnecessary for the bounded first test.","counterfactual_removal":"The pilot can still estimate and test modal cues."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use held-out renditions and musically weighted residual tolerances.","counterfactual_removal":"Mode count and omitted musical structure would lack a falsifiable fidelity gate."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Useful for conditioning or reconstruction, but singular vectors are not invariant transition directions.","counterfactual_removal":"No change unless the fitted operator proves too ill-conditioned for eigen-analysis."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document uncertainty, musical interpretation limits, couplings, and prohibited personnel-level readings.","counterfactual_removal":"Technically tentative modes could be misrepresented as musician traits or causal facts."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track uncertainty-adjusted gap and mode-angle drift between rehearsal blocks.","counterfactual_removal":"A once-valid reduced basis could continue being used after it loses separation or identity."}],"causal_chain":["Repeated renditions provide coupled deviation states.","A local transition model estimates which combinations persist, decay, oscillate, or grow.","Residual, conditioning, and spectral-gap gates determine whether modal interpretation is usable.","Sensitivity tests identify cue bundles that selectively reduce persistent outcome-relevant modes.","Conductor-authorized modal cues replace selected symptom-by-symptom corrections.","Held-out recurrence, musical outcomes, residuals, and drift determine continuation or rollback."],"baseline":"The conductor listens for conspicuous errors and corrects passages, sections, or musical dimensions one at a time using ordinary rehearsal judgment.","nearest_rival":"PCA-based performance profiling that finds high-variance combinations but does not model how deviations propagate between renditions.","authority_safety":{"affected_parties":["performing musicians","conductor or rehearsal director","audio and performance-data subjects"],"decision_authority":"The conductor controls rehearsal choices; participating musicians collectively authorize recording and analytical use under ensemble governance.","authorized_first_step":"Using consented recordings, fit on prior renditions, then test ordinary correction versus modal cue bundles on matched passages across at most four rehearsals; report only passage- or section-level results.","excluded_actions":["individual musician scoring or discipline","public attribution of modes to named performers","automated rehearsal commands","changes outside normal rehearsal intensity or safe sound exposure","claims that a mode is an intrinsic property of a musician, work, or culture"],"halt_rollback":"Stop modal cueing and return to ordinary rehearsal if consent is withdrawn, residual or drift thresholds fail twice, mode estimates are ill-conditioned, hearing or workload concerns arise, or musical outcomes worsen on two matched comparisons."}},"negative_tests":{"strongest_counterevidence":"Rehearsal evolution may be dominated by deliberate conductor choices, score-specific learning, fatigue, and changing attention rather than a stationary transition; apparent modes may also be shared measurement or score-form artifacts.","analogy_break":"Unlike a fixed physical operator, an ensemble learns strategically and may change its own response when analyzed or cued; linear modes can therefore be local descriptions without independent or causal reality.","failure_condition":"No well-conditioned, reproducible modal basis with acceptable held-out reconstruction and spectral separation exists inside a useful rehearsal window.","problem_falsifier":"After accounting for measurement error and passage context, deviations do not recur as coupled cross-variable patterns, and coordinate-level correction predicts subsequent renditions equally well.","intervention_falsifier":"Reproducible modes exist, but modal cue bundles do not reduce held-out recurrence, rehearsal time, or blinded musical-quality measures more than ordinary local correction.","risks":["overfitting a small number of renditions","confusing descriptive modes with musical causes","suppressing intentional variation or expressiveness","turning section-level analysis into personnel surveillance","mode swapping or instability near a small spectral gap","extra recording, cognitive load, or rehearsal disruption"]},"null_rationale":null,"classification":{"candidate_kind":"DOMAIN_TRANSFER","prior_art_status":"UNSEARCHED","evidence_maturity":"HYPOTHESIS"},"revision_change_log":{"revision_kind":"ORIGINAL","prior_problem_id":null,"prior_causal_lever_id":null,"problem_changed":false,"causal_lever_changed":false,"conceptual_changes":[],"operational_changes":[],"repairs_addressed":[]},"confidence":0.74,"generator_notes":"Closed-book structural transfer. Target-domain dynamics, reproducibility, and treatment effects are hypotheses; no claim of novelty or prior-art absence is made."}