{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__history_historiography","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"history_historiography","decision":"CANDIDATE","problem_id":"salient_event_periodization_of_coupled_historical_change","causal_lever_id":"transition_mode_periodization_with_residual_gates","proposal":{"problem":"Historians judging continuity versus rupture may place period boundaries around salient events or separately inspected indicators even when institutional, economic, demographic, and discursive variables change as coupled patterns. [HYPOTHESIS] This can make periodization sensitive to the historian's chosen coordinates rather than to reproducible directions of historical change.","actors_substrate":["historians and historiographers","archivists and historical-data curators","communities represented by the periodization","a bounded, time-indexed historical indicator dataset"],"observable_state":"Across adjacent intervals, several coded indicators move together, yet proposed boundaries change materially when indicators, scales, bins, or headline events change; held-out intervals retain structured reconstruction residuals. [HYPOTHESIS]","consequence":"Unstable boundaries can misclassify gradual change as rupture, conceal multi-domain transitions, and give contingent headline events more explanatory weight than the evidence warrants. [HYPOTHESIS]","affected_objective":"Produce transparent, reproducible continuity-versus-rupture judgments while preserving contingency, omitted evidence, and interpretive limits.","structural_mapping":[{"archetype_element":"Transformation acting on many variables","domain_realization":"An explicitly estimated map from the coded state of one historical interval to the next within one bounded place and period.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Invariant directions","domain_realization":"Combinations of indicators whose direction is approximately preserved by that estimated transition map.","claim_kind":"INFERENCE"},{"archetype_element":"Scalar modal response","domain_realization":"Estimated persistence, damping, growth, or reversal of each coupled indicator pattern across intervals.","claim_kind":"INFERENCE"},{"archetype_element":"Dominant or unstable modes","domain_realization":"Candidate patterns relevant to longue-duration continuity or an approaching rupture, not historical causes by themselves.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual visibility","domain_realization":"Events, local contingencies, coding error, and nonlinear changes not reconstructed by retained modes remain explicit.","claim_kind":"INFERENCE"},{"archetype_element":"Continuity-versus-rupture decision","domain_realization":"The packet identifies continuity versus rupture as an interpretive judgment about smooth change, threshold crossing, and causal severance.","claim_kind":"CORPUS"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"One named region, fixed interval range, and documented adjacent-interval transition operator."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Pre-registered indicators, units, missingness rules, sources, and binning for every interval."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Eigenvectors of the estimated transition operator, treated as approximate coupled-change patterns."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues with uncertainty estimates for persistence, growth, damping, or reversal."},{"component":"Dominant Mode Selection Rule","status":"direct","domain_realization":"Retain only modes passing held-out reconstruction, stability, consequence, and spectral-separation thresholds."},{"component":"Stable/Unstable Mode Partition","status":"adapted","domain_realization":"Classify modes only within the fitted historical window; do not equate mathematical growth with inevitability."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map documentary collection, coding, and model-specification changes to their effects on modes; no intervention on the past is implied."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Reconstruct held-out interval transitions and inspect both residual magnitude and historical structure."},{"component":"Mode Drift Monitor","status":"adapted","domain_realization":"Compare modes across rolling windows, alternative bins, and source subsets."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"State that modes are descriptive model objects, locally valid, and neither actors nor sufficient causal explanations."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degenerate, non-orthogonal, or specification-dependent modes that cannot be interpreted independently."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"The specified place, dates, bin width, and indicator ranges over which the transition approximation is tested."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"A pre-registered minimum separation and bootstrap stability requirement between retained and dropped modes."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicitly estimated adjacent-interval operator into approximate invariant patterns and gains.","counterfactual_removal":"Without it, the proposal has no transformation-defined modes or modal gains."},{"slug":"modal_sensitivity_sweep","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Perturb coding, bins, sources, and operator estimates; interpret leverage as specification sensitivity, not counterfactual history.","counterfactual_removal":"Robustness to researcher choices and cross-mode effects would be poorly identified."},{"slug":"modal_stability_analysis","disposition":"selected_supporting","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify fitted modes within the declared historical window only.","counterfactual_removal":"Continuity and rupture signals could not be distinguished by persistence or amplification."},{"slug":"mode_shape_testing","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor placement have no defensible analogue for an unreproducible past.","counterfactual_removal":"No change; held-out documents and intervals provide the empirical checks."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The proposed state is a time-indexed indicator vector, not a node-importance problem.","counterfactual_removal":"No change to the transition-mode analysis."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The bounded pilot needs multiple modes and a full spectrum; dominant-only estimation would hide competitors.","counterfactual_removal":"No change; full decomposition supplies the required gap."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions need not be directions preserved by historical transition.","counterfactual_removal":"No change; covariance structure is not the proposed causal lever."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable control surrogate adds unjustified simulation authority to a retrospective interpretive test.","counterfactual_removal":"No change to boundary evaluation."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Test retained modes on held-out intervals and inspect historically meaningful residual structure.","counterfactual_removal":"Compression could erase contingency or omitted patterns without detection."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Its paired reconstruction directions are not invariant temporal directions; retain only as a numerical diagnostic if needed.","counterfactual_removal":"The stated eigenmode chain remains intact."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Publish modes, uncertainty, residuals, couplings, coding choices, and prohibited causal readings.","counterfactual_removal":"Tentative descriptive modes would be substantially easier to reify as historical laws."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track gap and mode rotation across rolling windows and specification variants rather than live time.","counterfactual_removal":"Loss of mode identity across regimes could pass unnoticed."}],"causal_chain":["Pre-register a bounded historical state vector and estimate its adjacent-interval transformation.","Extract approximate invariant directions and scalar gains.","Retain modes only when separated, stable across specifications, and useful on held-out reconstruction.","Compare modal persistence or amplification with proposed continuity and rupture boundaries.","Keep structured residuals and mode couplings visible so singular events and contingency remain in the account.","Use the result as evidence about boundary robustness, not as a deterministic law of history."],"baseline":"Expert-led periodization organized around salient events and separate thematic timelines, with robustness assessed mainly through narrative argument.","nearest_rival":"Multivariate change-point detection on the same indicators using no transformation-defined modal basis.","authority_safety":{"affected_parties":["historians whose interpretations are compared","archives and source communities whose records define the state vector","people and communities represented by the historical categories","students and public audiences receiving the periodization"],"decision_authority":"A plural review panel of domain historians, data curators, and representatives of materially affected source communities controls coding, interpretation, and any publication claim.","authorized_first_step":"Run a preregistered pilot on one region, one 50-year window, fixed five-year bins, and at most 12 documented indicators; compare held-out boundary and reconstruction performance against the baseline and change-point rival, with bootstrap and source-subset checks.","excluded_actions":["declaring modes to be historical actors or universal laws","automatically replacing established period labels","using protected-group categories without contextual review","suppressing residual events or dissenting interpretations","extrapolating beyond the registered place and period"],"halt_rollback":"Stop interpretation if retained modes fail the gap or stability threshold, residuals cluster around consequential events or groups, or minor coding changes rotate the basis materially; revert to the baseline narrative analysis and publish the failed specification audit."}},"negative_tests":{"strongest_counterevidence":"Small changes in binning, source coverage, or coding produce different leading modes and boundaries, while close reading shows that apparent recurrence joins events with different meanings and causal structures.","analogy_break":"Historical processes are not repeatable stationary operators: evidence is selected and incomplete, meanings change, agency and contingency matter, and an eigenmode is a property of a fitted representation rather than of history itself.","failure_condition":"No locally stable transition representation exists, the operator is ill-conditioned or nonstationary, or residual consequences exceed the pre-registered budget.","problem_falsifier":"The ordinary baseline yields stable, well-supported boundaries and predicts held-out multi-indicator transitions, while no reproducible coupled residual pattern remains for modal analysis to explain.","intervention_falsifier":"Against the preregistered baseline and change-point rival, modal analysis does not improve held-out reconstruction or boundary stability, or its selected modes fail source-subset, binning, spectral-gap, or interpretive-review gates.","risks":["Reifying descriptive modes as deterministic historical forces","Encoding archival survival and elite documentation as structural importance","Erasing singular events, marginalized actors, or changing meanings through compression","Creating false precision around contested period boundaries","Mistaking local model sensitivity for causal intervention leverage"]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_ADAPTATION","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 candidate. Empirical applicability, stationarity, and comparative performance remain untested."}