{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__innovation_entrepreneurship","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"innovation_entrepreneurship","decision":"CANDIDATE","problem_id":"startup_coupled_metric_thrashing","causal_lever_id":"locally_stable_venture_state_modes","proposal":{"problem":"Early-stage ventures often react to isolated acquisition, activation, retention, margin, support, and burn metrics even though these variables change together. This can produce repeated budget and product-priority reversals, obscure a growing failure pattern, and consume runway without resolving the underlying constraint. [HYPOTHESIS]","actors_substrate":["founders and functional leads","growth and product teams","venture operating data","customer cohorts and acquisition channels","experiment budgets and runway"],"observable_state":"Weekly vectors containing acquisition cost, activation, retained use, referral, gross margin, support load, burn, and experiment-learning yield, restricted to a declared product, segment, pricing, and channel regime.","consequence":"Teams may fund locally attractive KPI movements that worsen retention, service load, or cash persistence, while overlooking combinations of changes that consistently improve or destabilize the venture. [HYPOTHESIS]","affected_objective":"Increase validated learning and sustainable cohort contribution per unit of runway while bounding customer harm and decision churn.","structural_mapping":[{"archetype_element":"coupled transformation","domain_realization":"A locally estimated week-to-week transition from one venture-state vector to the next.","claim_kind":"HYPOTHESIS"},{"archetype_element":"invariant directions","domain_realization":"Repeatable combinations of funnel, unit-economic, operational, and cash variables that approximately retain their direction across weekly transitions.","claim_kind":"HYPOTHESIS"},{"archetype_element":"scalar response","domain_realization":"Estimated growth, decay, or persistence of each combined venture-state pattern.","claim_kind":"INFERENCE"},{"archetype_element":"dominant or unstable modes","domain_realization":"Patterns prioritized because they predict the objective, persist, or amplify downside rather than merely having large current values.","claim_kind":"INFERENCE"},{"archetype_element":"modal intervention","domain_realization":"A small portfolio change chosen to move several contributing metrics in the combination indicated by sensitivity analysis.","claim_kind":"HYPOTHESIS"},{"archetype_element":"residual and drift governance","domain_realization":"Out-of-sample forecast error, structured residuals, mode rotation, and gap loss determine when recommendations must stop.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"One venture's weekly transition within a fixed product-segment-pricing-channel regime."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Preregistered funnel, economics, service-load, cash, and learning variables with fixed units."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Approximate eigenvectors of the fitted local transition operator."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues with bootstrap uncertainty."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes meeting preregistered persistence, objective-sensitivity, risk, and residual criteria."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify decaying, marginal, oscillatory, and growing modes inside the declared window."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map feasible budget or experiment changes to predicted mode and objective movement."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Out-of-sample next-state error plus inspection for structured omitted behavior."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Weekly comparison of mode direction, ordering, gain, and residual."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Modes are local descriptive decision aids, not venture laws or causal factors."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degeneracy, non-orthogonality, cross-effects, and shared controls."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"Only observations without major changes in offering, pricing, segment, channel, or accounting definitions."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Trust selection only when the kept/dropped separation exceeds bootstrap uncertainty and a preregistered validation threshold."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the small fitted weekly transition matrix; report conditioning and complex modes.","counterfactual_removal":"No invariant basis or gain spectrum remains, so the proposed lever disappears."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb feasible controls locally and rank objective response while logging cross-effects.","counterfactual_removal":"Modes could be described but not translated into an intervention."},{"slug":"modal_stability_analysis","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Classify gains only within the unchanged venture regime.","counterfactual_removal":"The team loses the growing-versus-decaying priority signal, materially weakening monitoring."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor placement do not match observational venture-state data.","counterfactual_removal":"No change; empirical validation is supplied by shadow prediction and bounded perturbation."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The state is a transition vector, not a node-importance network.","counterfactual_removal":"No change to the causal chain."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The matrix is small and the full spectrum, including unstable non-leading modes, is required.","counterfactual_removal":"No change because full decomposition supplies the spectrum and gap."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions do not identify week-to-week dynamics or intervention leverage.","counterfactual_removal":"No change; excluding it avoids substituting covariance for transformation."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable surrogate adds complexity before predictive and intervention validity are shown.","counterfactual_removal":"No change to the bounded diagnostic and intervention test."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Evaluate retained-mode next-state reconstruction out of sample and inspect residual structure.","counterfactual_removal":"There is no hard fidelity gate against omitted venture behavior."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"SVD may diagnose conditioning but its reconstruction-optimal directions are not invariant transition modes.","counterfactual_removal":"No change to the primary test; conditioning failure instead halts the eigen interpretation."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document meanings, prohibited causal readings, uncertainty, couplings, and regime limits.","counterfactual_removal":"The mathematics remains, but safe shared interpretation is materially weakened."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Re-estimate separation and direction drift during the shadow and intervention periods.","counterfactual_removal":"A changing venture could continue receiving recommendations after its retained basis lost validity."}],"causal_chain":["[INFERENCE] A fixed-regime weekly state makes the coupled transition estimable.","[HYPOTHESIS] Decomposition reveals persistent or growing combinations missed by isolated KPI review.","[INFERENCE] Residual, conditioning, gap, and drift gates remove untrustworthy interpretations.","[HYPOTHESIS] Sensitivity analysis identifies a feasible small portfolio change aligned with an objective-relevant mode.","[HYPOTHESIS] That change improves learning or cohort contribution per runway without breaching harm limits."],"baseline":"Ordinary weekly dashboard review in which owners set thresholds for individual KPIs and negotiate budget changes from recent movements.","nearest_rival":"A preregistered regularized multivariate cohort-transition model that predicts the same objective and recommends controls without modal decomposition.","authority_safety":{"affected_parties":["customers exposed to experiments","employees whose work priorities may change","founders and functional leads","investors whose runway is consumed"],"decision_authority":"Founders plus the accountable product, growth, finance, and data leads; customer-impacting changes require the existing ethics or experiment owner.","authorized_first_step":"For one consenting venture, fit on 26–52 comparable historical weeks, run four weeks in shadow mode, and—only if all gates pass—test one reversible two-week reallocation capped at 5% of an existing experiment budget against a preregistered holdout.","excluded_actions":["automated budget or product decisions","pricing, eligibility, or service changes across protected groups","hiring, firing, compensation, or fundraising decisions","claims that modes are causal entities","use outside the declared regime"],"halt_rollback":"Stop recommendations and restore the prior allocation if residual tolerance fails, modes are ill-conditioned, the spectral gap or direction-stability gate fails, the regime changes, or any customer, employee, cash, or compliance guardrail is breached."}},"negative_tests":{"strongest_counterevidence":"Startup histories are often short, strategically nonstationary, and confounded by prior management actions; stable modes may therefore be artifacts with no usable prediction window.","analogy_break":"Unlike a fixed physical operator, a venture learns and changes its own transition rules; people also react to the analysis, so a measured mode can vanish when acted upon.","failure_condition":"The method fails if no locally stable window exists, estimates are ill-conditioned or gapless, residuals remain structured, feasible controls cannot move selected modes, or data definitions drift.","problem_falsifier":"The diagnosed problem is falsified if isolated KPI or nearest-rival models match or exceed out-of-sample transition and objective prediction, decisions show little recurring cross-metric reversal, and no stable coupled pattern appears across resamples.","intervention_falsifier":"The intervention is falsified if the capped mode-guided change does not move the predicted combination in the preregistered direction or does not outperform the rival recommendation on learning or cohort contribution per runway within uncertainty and safety bounds.","risks":["Spurious modes from sparse or endogenous data","False causal interpretation of descriptive modes","Metric gaming or suppression of low-variance customer harms","Regime shifts mistaken for instability","Sensitive customer or employee data leakage","Overconfident action from near-degenerate modes"]},"null_rationale":null,"classification":{"candidate_kind":"TESTABLE_CONJECTURE","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":0.72,"generator_notes":"Closed-book structural transfer. The fit is plausible only for a bounded, locally stationary venture regime; nonstationarity and endogenous decisions are primary hard gates."}