{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__performing_arts_theatre","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"performing_arts_theatre","decision":"CANDIDATE","problem_id":"coupled_ensemble_rehearsal_instability","causal_lever_id":"rehearsal_transition_modal_control","proposal":{"problem":"Live productions can retain recurring timing, spacing, delivery, and technical-cue breakdowns despite repeated notes because the failures arise from coupled ensemble patterns rather than isolated performer or crew errors.","actors_substrate":["performers and understudies","director and choreographer","stage manager and technical operators","repeated runs of a fixed scene and cue sequence"],"observable_state":"For each scene segment and run: entrance and line timing, tempo, performer spacing, movement transitions, vocal-energy measures, technical-cue latency, near-misses, and blinded observer ratings of coherence.","consequence":"Coordinate-level notes may shift symptoms without damping the coupled pattern, causing repeated missed cues, unsafe transitions, wasted rehearsal time, and inconsistent artistic delivery.","affected_objective":"Stabilize repeatable, safe ensemble execution while preserving intentional performance variation.","structural_mapping":[{"archetype_element":"Transformation","domain_realization":"INFERENCE: the locally fitted map from one execution of a fixed scene segment to the next under an unchanged cast, blocking, and cue plan.","claim_kind":"INFERENCE"},{"archetype_element":"Coupled state","domain_realization":"INFERENCE: performer, spatial, vocal, and technical-cue measurements jointly define execution state.","claim_kind":"INFERENCE"},{"archetype_element":"Invariant modes","domain_realization":"HYPOTHESIS: reproducible combinations such as tempo–entrance–cue-latency patterns persist or change approximately as directions across runs.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Scalar response","domain_realization":"INFERENCE: each fitted mode receives a run-to-run gain and an outcome-sensitivity score.","claim_kind":"INFERENCE"},{"archetype_element":"Stable versus unstable modes","domain_realization":"HYPOTHESIS: some coupled patterns decay with rehearsal while others persist or amplify.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Modal intervention","domain_realization":"HYPOTHESIS: changing a shared cue, transition constraint, or rehearsal prompt aimed at a mode will outperform disconnected individual notes.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual and drift governance","domain_realization":"INFERENCE: reconstruction error, mode rotation, and spectral-gap loss determine when the model must be revised or retired.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"Successive runs of the same scene segment with cast, blocking, and cue plan held fixed."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Standardized timing, spacing, movement, vocal, technical, safety, and coherence observations."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Eigenvectors of a fitted local run-to-run operator, checked against empirical rehearsal responses."},{"component":"Modal Gain Spectrum","status":"adapted","domain_realization":"Estimated persistence or amplification per coupled rehearsal mode."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes exceeding preregistered outcome sensitivity or safety relevance, subject to residual tolerance."},{"component":"Stable/Unstable Mode Partition","status":"adapted","domain_realization":"Classify modes as decaying, persistent, oscillatory, or growing within the rehearsal window."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map shared cues, pacing prompts, spacing constraints, and transition drills to affected modes."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Reconstruct held-out run states and inspect both error magnitude and structured leftovers."},{"component":"Mode Drift Monitor","status":"adapted","domain_realization":"Re-estimate after cast, staging, venue, cue-plan, or artistic-direction changes."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Treat modes as local descriptive control aids, not performer traits or universal artistic laws."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degenerate, non-orthogonal, and intervention-linked modes."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"Only the fixed scene, staging configuration, personnel, and bounded rehearsal period used for fitting."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Predeclare the minimum retained-versus-discarded separation required for simplified decisions."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicitly fitted local transition matrix, reporting conditioning and incomplete-basis failures.","counterfactual_removal":"No transformation-based invariant directions or gains would support the proposed lever."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb rehearsal controls one at a time in closed runs and rank mode and outcome responses.","counterfactual_removal":"Modes could be described but not connected to actionable leverage."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify run-to-run gains only inside the fixed-scene window.","counterfactual_removal":"Persistent or growing coordination patterns would not be distinguished from self-correcting ones."},{"slug":"mode_shape_testing","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use safe cue or pacing perturbations and ambient rehearsal variation to validate fitted mode shapes.","counterfactual_removal":"The operator-derived modes would have weaker empirical validation, though estimation could proceed."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The target is coupled execution dynamics, not ranking people as network nodes.","counterfactual_removal":"No causal or viability change."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A full small fitted spectrum is needed; dominant-only recovery would hide relevant secondary or near-degenerate modes.","counterfactual_removal":"No loss because full decomposition supplies the needed spectrum."},{"slug":"principal_component_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Use only to inspect scaling, collinearity, and low-dimensional structure; variance components are not treated as dynamical modes.","counterfactual_removal":"Preprocessing diagnostics weaken, but the causal chain remains intact."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable surrogate adds complexity unnecessary for the bounded rehearsal decision.","counterfactual_removal":"The fitted modal analysis and intervention test remain viable."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Set held-out prediction and structured-residual tolerances before using reduced modes.","counterfactual_removal":"Important omitted behavior could be hidden, making simplification unsafe."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Use for conditioning diagnostics and regularized fitting of the run-to-run mapping, not as proof of invariant dynamics.","counterfactual_removal":"Estimation becomes less robust to collinearity, while the conceptual chain survives."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document mode meanings, uncertainty, coupling, prohibited person-level interpretations, and validity window.","counterfactual_removal":"Decision-makers could mistake tentative local patterns for performer attributes or causal facts."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Track gap, mode rotation, residuals, and reorderings after each new rehearsal block.","counterfactual_removal":"There would be no hard gate for retiring a collapsing or drifting modal simplification."}],"causal_chain":["Repeated fixed-scene runs provide multivariate state transitions.","A local operator exposes coupled directions and their gains.","Stability and sensitivity distinguish consequential growing patterns from loud but harmless variation.","A shared rehearsal control is chosen to reduce the targeted mode.","Held-out residual, safety, outcome, gap, and drift checks determine whether the intervention and modal account remain usable."],"baseline":"Ordinary practice: directors and stage managers issue observation-led notes to individuals or departments, then judge improvement from subsequent full runs.","nearest_rival":"A cue-by-cue checklist and targeted sectional rehearsal based on the largest observed delays or errors, without estimating coupled modes.","authority_safety":{"affected_parties":["performers and understudies","stage management and technical crew","creative leadership","eventual audiences"],"decision_authority":"The director and stage manager jointly authorize the pilot; performers and relevant safety leads may veto perturbations affecting movement, consent, workload, or technical safety.","authorized_first_step":"Run a consented pilot on one production and three fixed scene segments across 8–12 rehearsals; preregister measures and thresholds, estimate on early runs, then compare one mode-targeted rehearsal block with the nearest rival using held-out segments or counterbalanced runs.","excluded_actions":["public-performance experimentation","unsafe timing, spacing, rigging, fight, intimacy, or accessibility changes","automated personnel ranking or discipline","claims that modes diagnose talent, intent, or personality","extrapolation across casts, scenes, venues, or staging regimes"],"halt_rollback":"Stop and revert to the approved cue plan if any near-miss increases, consent is withdrawn, residual or drift tolerance is breached, the spectral gap falls below threshold, or the targeted block worsens preregistered outcomes."}},"negative_tests":{"strongest_counterevidence":"HYPOTHESIS: rehearsal failures may be primarily idiosyncratic, interpretive, or rapidly changing; the nearest rival may improve outcomes equally while requiring less data and imposing less measurement burden.","analogy_break":"Performers are adaptive agents who interpret observation and deliberately vary delivery; artistic revisions can change the transformation itself, so theatre modes are neither passive physical modes nor stable performer properties.","failure_condition":"The approach fails if the fixed-scene window cannot yield a reproducible, adequately conditioned transition model with acceptable held-out residuals and a usable spectral gap.","problem_falsifier":"Across repeated fixed-condition runs, coupled cross-variable patterns are no more stable or predictive than shuffled data, or a single observable cue/error variable explains the consequential breakdowns adequately.","intervention_falsifier":"Reproducible modes exist, but preregistered mode-targeted controls do not reduce the targeted modal amplitude, safety incidents, timing error, or blinded coherence loss more than the nearest rival.","risks":["measurement and observer effects may alter performance","subjective ratings may encode directorial bias","mode labels may stigmatize performers","small samples may create unstable or spurious modes","optimization may suppress artistically intentional variation","extra instrumentation may distract performers or expose sensitive recordings"]},"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. The fit depends on obtaining repeated, sufficiently stationary measurements of an unchanged scene; absent that condition, classify NO_FIT rather than treating generic rehearsal patterns as modes."}