{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__astronomy_astrophysics","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"astronomy_astrophysics","decision":"CANDIDATE","problem_id":"collective_multiplanet_orbital_instability_missed_by_elementwise_checks","causal_lever_id":"locally_valid_orbital_instability_mode_gate","proposal":{"problem":"Classifying the long-horizon stability of compact multiplanet systems is difficult because instability can arise from coupled combinations of orbital elements even when each planet and each pair appears acceptable under coordinate-level thresholds. A locally growing or transiently amplified collective perturbation can therefore be missed until an expensive integration reveals close encounters, ejection, or collision.","actors_substrate":["planetary-dynamics researchers","telescope-allocation and follow-up teams","scientific audiences relying on reported system architectures","observed or simulated compact multiplanet systems","orbital-state vectors, variational operators, and N-body trajectories"],"observable_state":"Across successive orbital epochs, correlated perturbations in eccentricities, inclinations, apsidal angles, and resonant variables persist, rotate, decay, or grow; elementwise summaries can remain benign while a collective perturbation gains amplitude.","consequence":"Systems may be labeled stable or physically plausible when they are not, or rejected unnecessarily, distorting population inference and consuming follow-up and simulation resources.","affected_objective":"Improve calibrated long-horizon stability screening and prioritize expensive N-body integration without treating a local modal approximation as proof of global stability.","structural_mapping":[{"archetype_element":"An explicit or locally approximated transformation acts on coupled variables.","domain_realization":"Linearize an N-body evolution map around a fitted orbital solution to obtain a finite-interval state-transition or variational operator.","claim_kind":"INFERENCE"},{"archetype_element":"Invariant directions reveal behavior hidden in named coordinates.","domain_realization":"Eigen- or singular directions represent collective orbital perturbations whose repeated growth, damping, rotation, or transient amplification is not attributable to one planet alone.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Decision relevance depends on response, not merely present amplitude.","domain_realization":"Rank modes by their effect on held-out instability outcomes under bounded perturbations, rather than by eigenvalue or observed variance alone.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Reduction is licensed by retained behavior and spectral separation.","domain_realization":"Keep a reduced modal model only when out-of-sample trajectory reconstruction, outcome-sensitive residuals, and the retained/dropped spectral gap meet preregistered tolerances.","claim_kind":"INFERENCE"},{"archetype_element":"Regime change invalidates a fixed basis.","domain_realization":"Recompute or retire the basis when orbital fits, resonance membership, modal directions, spectral gaps, or reconstruction errors drift beyond tolerance.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"Finite-time variational evolution about one fitted orbital solution and stated integration interval."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Scaled canonical orbital perturbations, with coordinate convention, units, uncertain parameters, and epoch fixed."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Eigenvectors of a well-conditioned local operator, supplemented by paired singular directions when non-normality matters."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalue growth or rotation rates and finite-time singular gains."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes exceeding preregistered outcome sensitivity, persistence, or reconstruction-consequence thresholds."},{"component":"Stable/Unstable Mode Partition","status":"adapted","domain_realization":"Classify locally decaying, growing, marginal, oscillatory, and transiently amplifying perturbations."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map bounded in-silico perturbations of fitted elements and uncertainties into modal coordinates; it is not a physical intervention on planets."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Compare reduced and full trajectories on withheld intervals, including structured errors in resonance and encounter-relevant variables."},{"component":"Mode Drift Monitor","status":"adapted","domain_realization":"Track basis rotation, gain changes, mode swaps, and residual growth across epochs and posterior orbital samples."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"State that findings are local, model-conditional screening evidence and not proof of global orbital stability."},{"component":"Mode-Coupling Register","status":"adapted","domain_realization":"Record near-degenerate modes, non-normal cross-talk, nonlinear resonances, and perturbations that activate other modes."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Bound perturbation size, orbital epoch range, and time horizon over which the variational approximation passes residual tests."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Require a preregistered retained/dropped separation and basis-stability tolerance before using modal reduction."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicit local variational operator when it has a numerically usable eigenbasis.","counterfactual_removal":"The proposal loses its invariant directions and repeated-growth classification."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb modal coordinates within orbital-fit uncertainty and rank effects on encounter or ejection labels while logging cross-effects.","counterfactual_removal":"Spectral prominence could be mistaken for outcome leverage, breaking the selection rule."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify growth only within each validated finite-time linearization window.","counterfactual_removal":"Modes would be descriptive directions without an instability-screening interpretation."},{"slug":"mode_shape_testing","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Real planetary systems cannot be deliberately excited and spatially instrumented; passive observations cannot guarantee excitation or observability of every mode.","counterfactual_removal":"No change; validation instead uses full simulations and posterior observational samples."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Planet importance scores do not answer whether a collective phase-space perturbation grows.","counterfactual_removal":"No change to the causal chain."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only estimate is unsafe where near-degenerate, oscillatory, or non-normal modes matter.","counterfactual_removal":"No change; the bounded test requires a broader spectrum."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"High observational variance is not a dynamical stability criterion.","counterfactual_removal":"No change; covariance modes are not used as instability evidence."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Run a small modal surrogate only inside the validated window to triage full integrations.","counterfactual_removal":"The diagnosis remains possible, but computational triage loses much of its speed advantage."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Test withheld full trajectories and outcome-relevant residual structure across retained-mode counts.","counterfactual_removal":"There is no defensible bound on discarded dynamics or reduction order."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Use finite-time singular directions to detect transient amplification or ill-conditioned eigen interpretations in non-normal operators.","counterfactual_removal":"Eigenvalue stability could conceal consequential transient growth."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document mode meanings, couplings, residuals, numerical conditioning, and prohibited global interpretations.","counterfactual_removal":"Results become easier to overstate or reuse outside their validated regime."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Monitor retained/dropped separation and basis rotation across epochs and orbital posterior samples.","counterfactual_removal":"A stale or non-identifiable reduced basis could continue governing classifications."}],"causal_chain":["Define a scaled orbital perturbation state and finite-time variational transformation around each fitted system.","Extract eigenmodes and gains; use singular directions to flag non-normal transient amplification.","Classify local modal behavior and perturb modes within stated uncertainties to estimate outcome leverage and coupling.","Retain only outcome-relevant modes that satisfy spectral-gap and withheld reconstruction criteria.","Use the bounded reduced model to triage systems for full N-body integration, while the full integration remains the adjudicator.","Halt modal use when residual, conditioning, gap, or drift limits fail; recompute or revert to full ensembles."],"baseline":"Ordinary screening uses per-planet or pairwise orbital thresholds followed by selected full N-body integrations, without an explicit collective-mode gate.","nearest_rival":"Ensemble full N-body stability classification augmented by established chaos or resonance diagnostics; it is more globally faithful but computationally heavier and remains the adjudicating comparator.","authority_safety":{"affected_parties":["researchers whose systems are classified","observing teams whose follow-up may be prioritized","scientific audiences receiving stability claims"],"decision_authority":"The planetary-dynamics study lead may authorize an internal computational pilot; observing or publication decisions remain with their existing review authorities.","authorized_first_step":"Run a preregistered retrospective test on 100 simulated compact systems with withheld long-horizon N-body labels, comparing baseline thresholds, the nearest rival, and the modal gate on discrimination, calibration, lead time, and compute cost.","excluded_actions":["No physical manipulation of celestial systems","No claim that local modal stability proves global stability","No cancellation of observations or public reclassification based solely on the pilot","No use outside validated perturbation and time windows"],"halt_rollback":"Stop modal triage and revert all pending cases to full N-body ensembles if residual, calibration, numerical-conditioning, spectral-gap, or mode-drift tolerances fail; retain the prior classifications and audit affected cases."}},"negative_tests":{"strongest_counterevidence":"The modal gate would add no value if nonlinear resonance crossing and chaotic transport dominate before any reproducible local mode emerges, or if full N-body and chaos diagnostics achieve equal or better accuracy and compute efficiency.","analogy_break":"Orbital dynamics are nonlinear and often Hamiltonian; local eigenvalue decay does not establish confinement to a global stability basin, while resonances and close encounters can abruptly invalidate the linearized operator.","failure_condition":"Modes rotate or swap across posterior samples, the operator is ill-conditioned, retained-mode residuals remain structured, or no stable spectral separation exists at useful horizons.","problem_falsifier":"Across representative compact systems, long-horizon failures are explained equally well by one directly observable element or pairwise threshold, with no reproducible coupled perturbation direction preceding them.","intervention_falsifier":"Coupled hidden directions exist, but adding the preregistered modal gate fails to improve held-out calibration, discrimination, lead time, or compute-normalized utility over the nearest rival.","risks":["False reassurance from locally stable modes","False alarms from transient numerical amplification","Coordinate or scaling dependence","Missed low-amplitude resonant dynamics","Mode identity swaps near degeneracy","Publication or observing bias introduced by an unvalidated triage score"]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_COMPOSITION","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":0.78,"generator_notes":"Closed-book structural transfer. The candidate is deliberately limited to computational screening because the target system cannot be physically controlled; empirical superiority and useful spectral separation remain untested hypotheses."}