{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__religious_studies_theology","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"religious_studies_theology","decision":"CANDIDATE","problem_id":"hidden_coupled_modes_in_religious_change","causal_lever_id":"longitudinal_modal_reconstruction_of_religious_change","proposal":{"problem":"Longitudinal studies of religious change often analyze doctrines, rituals, identities, and institutions as separate variables even when they shift as coupled configurations. This can make scholars mistake visible indicators for drivers, overlook weakly damped configurations preceding schism or reorganization, and produce explanations that fail across periods or communities.","actors_substrate":["religious-studies researchers","participating or historically documented religious communities","coded longitudinal surveys, interviews, texts, and institutional records","ethics and community-advisory bodies"],"observable_state":"Repeated, consistently coded observations show correlated changes across doctrinal statements, ritual participation, authority relations, identity labels, and institutional practices; coordinate-level models leave structured temporal residuals.","consequence":"Causal narratives overemphasize isolated beliefs or leaders, comparisons conflate distinct change configurations, and forecasts or historical reconstructions miss collective persistence, reversal, or instability.","affected_objective":"Produce bounded, interpretable explanations of coupled religious change while preserving residual evidence, uncertainty, community protections, and distinctions between description and causation.","structural_mapping":[{"archetype_element":"A transformation acts on coupled variables over repeated observations.","domain_realization":"Estimate a period-to-period mapping over consistently coded religious-life state vectors. HYPOTHESIS: a locally stable mapping exists within selected communities and periods.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Invariant directions reveal combinations that persist, grow, decay, or reverse.","domain_realization":"Latent combinations of doctrine, ritual, identity, authority, and institution are tested as approximate temporal modes rather than presumed substantive essences.","claim_kind":"INFERENCE"},{"archetype_element":"Scalar response ranks modal persistence or amplification.","domain_realization":"Estimated gains indicate which configurations decay, persist, oscillate, or grow within the declared window; they are not universal laws of religion.","claim_kind":"INFERENCE"},{"archetype_element":"Action-relevant selection requires consequence and fidelity checks.","domain_realization":"Retain modes only when they improve held-out reconstruction or explanation of prespecified outcomes without erasing consequential minority patterns.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual and drift checks constrain modal trust.","domain_realization":"Structured residuals, rotating modes, or a collapsing spectral gap trigger revision or retirement of the account.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"One named community or comparative stratum over a fixed historical interval and observation cadence."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Pre-registered coded measures of doctrine, ritual, identity, authority, and institutional practice, with missingness documented."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Approximate directions of joint religious change estimated from the longitudinal mapping."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Estimated gain or persistence for every retained and candidate mode."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes meeting held-out fidelity, stability, and consequence thresholds, not variance alone."},{"component":"Stable/Unstable Mode Partition","status":"adapted","domain_realization":"Classify configurations as decaying, persistent, oscillatory, or growing only inside the fitted period."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map analytic perturbations and alternative codings to modes; do not prescribe manipulation of communities."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Reconstruct held-out original variables and inspect both error magnitude and structured omissions."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Re-estimate across rolling periods and compare mode direction, ordering, and gain."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"State population, period, coding assumptions, descriptive status, and prohibited theological or causal readings."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degeneracy, cross-effects, coding dependence, and non-independent modes."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"Restrict claims to intervals without major measurement redesign or documented regime rupture."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Pre-register the minimum separation and bootstrap stability needed to call a mode dominant."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicitly estimated square transition operator, reporting conditioning and uncertainty rather than treating it as known exactly.","counterfactual_removal":"Without invariant directions and gains, the proposal reverts to coordinate-level trend analysis."},{"slug":"modal_sensitivity_sweep","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Perturb coding choices, modal coordinates, and gains in silico to rank consequence sensitivity and expose cross-effects.","counterfactual_removal":"The decomposition remains descriptive, but leverage and coupling claims lose their test."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify temporal modes within the declared historical window, with uncertainty around stability boundaries.","counterfactual_removal":"The account cannot distinguish persistent or growing configurations from merely large current patterns."},{"slug":"mode_shape_testing","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor placement do not transfer ethically or literally to religious communities; observational validation is supplied by held-out reconstruction.","counterfactual_removal":"No material change because this mechanism is not used."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Node importance answers a different question from coupled temporal configurations and risks reducing religious change to influential actors.","counterfactual_removal":"No material change to the temporal-mode causal chain."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only estimate is insufficient because rival and minority modes plus the gap must remain visible.","counterfactual_removal":"No change; full decomposition is retained."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions may summarize data but do not represent the period-to-period transformation or temporal gain.","counterfactual_removal":"No change to transformation-based inference."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Use a small descriptive simulator for held-out reconstruction and analytic counterfactuals only within the fitted window.","counterfactual_removal":"Modes could still be identified, but fast comparative testing of retained-mode sufficiency would be lost."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Test held-out reconstruction by variable and subgroup, inspecting structured residuals rather than aggregate error alone.","counterfactual_removal":"Compression could erase minority or low-variance religious patterns without detection."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use SVD as a robustness diagnostic when the estimated transition is ill-conditioned or non-normal, not as proof of invariant temporal modes.","counterfactual_removal":"The main analysis remains possible, but fragility of eigen-based claims is harder to diagnose."},{"slug":"spectral_decomposition_report","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Publish gains, residuals, couplings, uncertainty, permissible readings, and explicit bans on essentialist or theological ranking claims.","counterfactual_removal":"Tentative descriptive modes could be mistaken for causal, normative, or universal religious types."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track bootstrapped gap and directional drift across rolling periods; suspend dominance claims when thresholds fail.","counterfactual_removal":"A once-valid reduction could remain in use after modes rotate or become indistinguishable."}],"causal_chain":["Separate-variable analysis obscures repeatable combinations of religious-life variables.","A scoped longitudinal mapping represents how those combinations change between observations.","Decomposition estimates approximate invariant directions and their temporal gains.","Stability and sensitivity analyses distinguish consequential persistent or growing modes from merely conspicuous variables.","Held-out reconstruction, gap, coupling, and drift checks bound which modal explanations remain usable.","A scoped report improves explanation without converting descriptive modes into universal, causal, or normative claims."],"baseline":"Analyze each coded doctrine, ritual, identity, authority, or institutional variable with separate trends or regressions and synthesize the results narratively.","nearest_rival":"A PCA or factor analysis that compresses correlated observations by variance but does not model the temporal transformation, stability, or gain of configurations.","authority_safety":{"affected_parties":["members and former members represented in data","small or stigmatized religious communities","researchers and downstream interpreters","archives and data stewards"],"decision_authority":"The research team may choose analytic models only under institutional ethics approval, data-use agreements, and any applicable community-governance process; it has no authority to alter religious practice or label communities as stable, deviant, or dangerous.","authorized_first_step":"Run a preregistered retrospective pilot on one deidentified, already-authorized longitudinal dataset: train on earlier waves, predict one held-out wave, bootstrap modes and gaps, and compare subgroup residuals against the baseline and PCA rival.","excluded_actions":["recruiting or manipulating adherents without separate consent and review","targeting leaders or communities for influence","publishing identifiable small-group scores","treating modes as theological truth, essence, pathology, or causal proof","extrapolating beyond the registered population and period"],"halt_rollback":"Stop and suppress substantive mode labels if identities become inferable, subgroup residuals exceed the registered harm/fidelity budget, modes are bootstrap-unstable, the gap falls below threshold, or community/ethics authority withdraws permission; revert to aggregate descriptive reporting."}},"negative_tests":{"strongest_counterevidence":"Apparent modes may be artifacts of coding conventions, survey redesign, demographic turnover, missingness, or singular historical shocks; different operationalizations may yield incompatible bases.","analogy_break":"Religious meanings are reflexive, contested, historically situated, and partly constituted by interpretation. Unlike physical state variables, they need not obey a stationary linear operator, and statistical modes are not ontological kinds.","failure_condition":"The transfer fails if no bounded interval yields stable, interpretable modes with acceptable held-out residuals and traceability to original variables.","problem_falsifier":"Across credible codings and longitudinal strata, separate-variable models leave no repeatable structured residuals and coupled models provide no meaningful held-out explanatory improvement.","intervention_falsifier":"The problem exists, but the modal workflow is falsified if its modes, gains, or selected set are bootstrap-unstable, fail held-out reconstruction, omit consequential subgroup patterns, or perform no better than the baseline and PCA rival.","risks":["Essentializing traditions or communities from statistical modes","Reidentifying small or stigmatized groups","Confusing descriptive persistence with causation or theological validity","Encoding researcher categories as if they were participant meanings","Using instability labels to justify surveillance or intervention","Missing abrupt nonlinear change outside the fitted window"]},"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":0.78,"generator_notes":"Closed-book structural transfer. Empirical existence, stability, and usefulness of the proposed religious-change modes remain hypotheses for the bounded pilot."}