{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__information_theory","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"information_theory","decision":"CANDIDATE","problem_id":"finite_rate_remote_estimation_hidden_unstable_modes","causal_lever_id":"modal_growth_weighted_rate_allocation","proposal":{"problem":"A finite-rate encoder sends updates about a coupled dynamical source to a remote estimator or controller. Coordinate-wise or variance-weighted compression can keep aggregate distortion acceptable while estimation error grows along a coupled unstable direction, exhausting the channel budget or causing delayed loss of estimation or control.","actors_substrate":["coupled dynamical source or controlled process","sensor and encoder","finite-capacity noisy channel","decoder and remote estimator or controller","system operator and safety owner"],"observable_state":"Timestamped source states, encoded bit counts, channel errors, reconstructed states, aggregate distortion, consequence-weighted per-mode estimation error, estimated modal gains, reconstruction residuals, spectral gaps, and mode drift within a declared operating regime.","consequence":"A hidden error direction can grow between updates even when named-coordinate errors or average distortion look benign, producing late alarms, decoder saturation, or control failure.","affected_objective":"Maintain bounded, consequence-weighted reconstruction or estimation error at a fixed communication rate and latency.","structural_mapping":[{"archetype_element":"Coupled transformation rather than isolated coordinates","domain_realization":"A sampled local state transition jointly transforms the source state before its next encoded update; the encoder-channel-decoder loop constrains how accurately that transformed state can be reconstructed.","claim_kind":"INFERENCE"},{"archetype_element":"Invariant directions with scalar response","domain_realization":"Well-conditioned eigenvectors of the declared transition operator define candidate source modes, and eigenvalue magnitudes represent per-sample decay or amplification inside the validity window.","claim_kind":"INFERENCE"},{"archetype_element":"Finite information conduit","domain_realization":"The channel has bounded capacity and a noise profile, so additional precision assigned to one mode consumes resources unavailable to others.","claim_kind":"CORPUS"},{"archetype_element":"Action-relevant modal ranking","domain_realization":"Modes are ranked by estimated error amplification, outcome sensitivity, and reconstruction consequence rather than present variance alone.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Modal intervention","domain_realization":"Quantizer precision, update frequency, redundancy, and estimator attention are allocated by mode under the same total rate and latency budget.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual and drift visibility","domain_realization":"Out-of-sample reconstruction residuals, changing gains, rotating directions, and narrowing spectral gaps determine whether the modal codec remains authorized.","claim_kind":"INFERENCE"},{"archetype_element":"Bounded interpretation","domain_realization":"The decomposition is treated as a local engineering model, not proof that real source modes are globally independent or semantically meaningful.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"direct","domain_realization":"One sampling interval of the local source transition plus the encoder-channel-decoder boundary."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Scaled source-state deviations required by the estimator or controller, with missing and latent quantities declared."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"A complete, well-conditioned eigenbasis of the local transition operator; otherwise the proposed test is halted or revised."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues interpreted as decay, persistence, oscillation, or amplification per sampling interval."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain or prioritize modes whose growth, consequence sensitivity, or residual contribution exceeds preregistered thresholds."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Discrete-time modes are classified as decaying, marginal, or growing within the stated local regime."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map mode coordinates to bit allocation, quantizer resolution, update cadence, redundancy, and estimator gains."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Compare original and reconstructed held-out trajectories, including residual structure and worst consequence-weighted error."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Periodically compare modal directions and gains with the authorized basis."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"State operating range, sampling interval, scaling, linearity assumptions, and prohibited extrapolations."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record non-normality, near-degeneracy, nonlinear coupling, saturation, and perturbations that move multiple modes."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Bound state, disturbance, topology, and channel regimes in which the transition model is tested."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Require sufficient separation for stable mode identity and trigger review when the retained/discarded boundary narrows."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicit local state-transition operator only after conditioning and diagonalizability checks.","counterfactual_removal":"Without modes and gains, growth-aware rate allocation cannot be defined."},{"slug":"modal_sensitivity_sweep","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Perturb modal reconstruction error or allocated rate in bounded replay to rank outcome leverage and expose cross-effects.","counterfactual_removal":"The codec remains modal but lacks evidence that its rate ranking tracks the affected objective."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify modes by repeated sampled evolution within the declared local window.","counterfactual_removal":"The proposal loses the distinction between harmless reconstruction error and error that amplifies between updates."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation is unnecessary for the bounded first test because an explicit transition model and recorded trajectories are available; replay validation covers fit.","counterfactual_removal":"No causal or safety step changes."},{"slug":"network_spectral_centrality_analysis","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Node-importance ranking does not identify temporal state-growth modes or allocate communication rate.","counterfactual_removal":"No change."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only estimate may miss several unstable or consequence-critical modes, especially with a small gap.","counterfactual_removal":"No change; the complete decomposition supplies the required set."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions need not be invariant under source dynamics, and low-variance modes may still amplify.","counterfactual_removal":"No change."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The first test reallocates a fixed communication budget without requiring a reduced dynamical surrogate.","counterfactual_removal":"No change."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Use held-out trajectories, structured residual inspection, and consequence-weighted tolerances to gate mode deletion.","counterfactual_removal":"Discarded dynamics could remain invisible, so deployment would fail its fidelity gate."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Paired input-output singular directions measure one-step amplification but do not by themselves supply invariant temporal modes; use them only in a replacement design if eigenvectors are ill-conditioned.","counterfactual_removal":"No change to the candidate under its conditioning gate."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Record mode meanings, prohibited causal readings, coupling, residuals, thresholds, and the authorized regime.","counterfactual_removal":"Technical results could be acted on outside their tested scope, weakening governance viability."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Track retained/discarded separation and direction drift on scheduled model updates.","counterfactual_removal":"A fixed rate map could persist after mode identity becomes unstable."}],"causal_chain":["Coupled source dynamics amplify some combinations of state error more than named coordinates reveal.","A coordinate-wise or variance-only codec spends finite bits without accounting for those amplification directions.","Modal decomposition exposes locally invariant directions and their gains.","Stability and sensitivity analyses identify which modal errors threaten the objective.","Reallocating the unchanged rate budget toward those modes reduces their quantization error or update delay.","Residual, coupling, gap, and drift gates constrain use to regimes where that explanation remains adequate."],"baseline":"Encode named state coordinates independently, allocate equal bits or bits proportional to observed variance, and monitor aggregate reconstruction error.","nearest_rival":"An end-to-end predictive vector quantizer or joint source-channel controller optimized directly on full-state loss, without an explicit modal basis; it may capture nonlinear dependencies but is less interpretable and may require more data and computation.","authority_safety":{"affected_parties":["operators relying on remote estimates","people or assets exposed to controller error","data subjects represented in source measurements","communications and safety teams"],"decision_authority":"The system owner may authorize analysis; the control or safety owner must approve any live encoder, channel-allocation, or estimator change.","authorized_first_step":"Run a fixed-horizon offline replay or sandbox simulation using existing authorized traces, identical total rate and latency, preregistered regimes, and no production actuation; compare baseline, nearest rival, and modal allocation.","excluded_actions":["changing production control commands","increasing total transmission power or rate","dropping modes solely because they have low variance","testing through unsafe source excitation","extrapolating beyond the declared state or channel regime"],"halt_rollback":"Halt if the eigenbasis is ill-conditioned, the gap falls below threshold, held-out residual or worst-mode error exceeds tolerance, cross-mode coupling invalidates isolated allocation, or any safety metric worsens; retain or restore the baseline codec and estimator."}},"negative_tests":{"strongest_counterevidence":"A full-state predictive codec may already keep every consequence-critical directional error bounded at the same rate, or non-normal transient growth may make eigenmode-wise independent allocation misleading despite apparently stable eigenvalues.","analogy_break":"Unlike a normal same-space operator, a real source may be nonlinear, non-normal, partially observed, or regime-changing; its eigenvectors may be incomplete or fragile, and channel coding errors can couple modes that the decomposition treats separately.","failure_condition":"The candidate is unsuitable if no explicit or locally valid transition operator exists, modes are not identifiable over a useful window, residuals remain structured above tolerance, or the problem is governed by one directly observable coordinate.","problem_falsifier":"At the fixed rate, baseline replay shows bounded held-out error in every consequence-critical direction across the authorized regimes, with no hidden growing or coupled error mode despite acceptable aggregate metrics.","intervention_falsifier":"At identical rate and latency, modal allocation does not improve preregistered worst consequence-weighted directional error, violation frequency, or recovery time over both the baseline and nearest rival, or improvements disappear out of sample.","risks":["Ill-conditioned eigenvectors can turn small estimation errors into large allocation changes.","Optimizing modal error can worsen fairness or service quality for affected subgroups hidden by aggregate objectives.","Frequent model updates can cause mode swapping and unstable codec behavior.","A local linear model may create false confidence under large disturbances.","Extra protection for selected modes can starve residual but safety-relevant information."]},"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":0.84,"generator_notes":"Closed-book structural inference from the supplied packet; target-domain effectiveness and comparative advantage remain untested."}