{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp04_retrieval_first_paired20_20260802","cell_id":"invariant_mode_decomposition_design__political_science","arm":"PROPOSAL_FIRST","candidate_id":"cand_modal_budget_bargaining_001","hypothesis_id":null,"version":0,"title":"Modal Deadlock Map for City Budget Bargaining","problem":"During repeated city-budget bargaining rounds, officials track disagreement separately for revenues, staffing, capital projects, debt, reserves, and district allocations. Yet negotiators respond to packages rather than isolated items, so a coupled combination of otherwise moderate disagreements can persist, oscillate, or amplify across rounds. An issue-by-issue dashboard can therefore show no exceptional dispute while the negotiation moves toward deadline failure.","actors":["Elected city council members","Council caucus and coalition negotiators","Mayor or executive budget team","Neutral budget facilitator","Council clerk and public-data steward","Residents affected by delayed or disrupted budget adoption"],"observable_state":"For each bargaining round, a state vector records standardized, caucus-level proposal gaps across a fixed set of budget dimensions, using formally tabled proposals, amendments, recorded straw polls where lawful, and minuted negotiating positions. The observable warning state is a reproducible linear combination of these gaps whose estimated round-to-round gain is at or above the predeclared instability boundary, even though no single gap is unusually large.","consequence":"A growing or weakly damped disagreement mode can generate repeated package rejection, agenda cycling, rushed concessions, or failure to adopt a lawful budget by the deadline.","affected_objective":"Reach a timely, procedurally legitimate budget agreement while preserving elected representatives' authority over substantive fiscal choices.","intervention":"Create a facilitator-facing negotiation-mode dashboard for one bounded budget process. Estimate a local round-to-round transition operator over the standardized proposal-gap vector, decompose it into modes and scalar gains, classify growing, decaying, and oscillatory modes, and test how authorized procedural changes map into the action-relevant modes. When a retained mode crosses a predeclared gain or persistence threshold, the facilitator may recommend a reversible procedural response—such as reordering agenda items, separating a coupled package, convening a joint factual briefing, or requesting simultaneous clarification of the positions contributing to that mode. No recommendation changes a substantive offer or binds a vote. Re-estimate after each round and suspend modal guidance when the spectral gap, reconstruction residual, or mode drift breaches its tolerance.","structural_mapping":[{"archetype_element":"Transformation Scope","domain_realization":"The transformation is the locally estimated mapping from one formally documented city-budget bargaining round's proposal-gap vector to the next round's vector within the same budget process."},{"archetype_element":"State-Vector Definition","domain_realization":"Coordinates are standardized caucus-level gaps on a fixed, publicly specified set of fiscal dimensions; member-level ideology scores and private communications are excluded."},{"archetype_element":"Invariant Mode Basis","domain_realization":"Each mode is a weighted combination of fiscal disagreements that approximately preserves its direction as bargaining proceeds; complex pairs are represented as real oscillatory subspaces."},{"archetype_element":"Modal Gain Spectrum","domain_realization":"Each mode receives an estimated round-to-round gain and uncertainty interval indicating decay, persistence, oscillation, or amplification within the fitted window."},{"archetype_element":"Dominant Mode Selection Rule","domain_realization":"A mode becomes action-relevant only if it crosses a predeclared gain or persistence threshold, contributes to deadline-risk reconstruction, and remains identifiable under resampling."},{"archetype_element":"Stable/Unstable Mode Partition","domain_realization":"Modes are classified as decaying, marginal, growing, or oscillatory relative to the round-to-round stability boundary."},{"archetype_element":"Modal Intervention Map","domain_realization":"Authorized procedural levers are represented as bounded changes to the state transition and ranked by their modeled sensitivity on deadline risk and on the targeted mode."},{"archetype_element":"Reconstruction Residual Check","domain_realization":"The retained modes must reconstruct held-out round transitions within a declared error budget, with residuals inspected for omitted fiscal dimensions or structured caucus effects."},{"archetype_element":"Mode Drift Monitor","domain_realization":"After each new round, the system checks mode rotation, gain changes, ordering swaps, and changes in the retained-versus-dropped spectral gap."},{"archetype_element":"Interpretation Scope Contract","domain_realization":"The dashboard is explicitly descriptive and locally predictive, not a causal account of motives, a member ranking, or a mandate for substantive compromise."},{"archetype_element":"Local Linearization Window","domain_realization":"Results apply only while participants, fiscal constraints, bargaining rules, and issue definitions remain materially unchanged; a coalition break, legal ruling, fiscal shock, or new executive proposal ends the window."}],"mechanism_mapping":[{"mechanism_slug":"eigendecomposition_workflow","role":"Factors the explicit, small round-to-round transition operator into a complete set of disagreement modes and their gains.","counterfactual_removal":"Without it, the dashboard reverts to separate fiscal coordinates and cannot identify combinations preserved or amplified by the bargaining process."},{"mechanism_slug":"modal_stability_analysis","role":"Classifies each fitted mode as decaying, growing, marginal, or oscillatory within the current negotiation regime.","counterfactual_removal":"Without it, modes can be described but cannot supply an early-warning distinction between self-correcting disagreement and compounding deadlock."},{"mechanism_slug":"modal_sensitivity_sweep","role":"Perturbs each authorized procedural lever in the fitted model, ranks its influence on the risky mode and deadline outcome, and records cross-effects on other modes.","counterfactual_removal":"Without it, the largest mode might be mistaken for the most procedurally actionable one, and recommendations would lack a mode-to-lever trace."},{"mechanism_slug":"residual_reconstruction_test","role":"Tests retained-mode reconstructions on held-out bargaining transitions and exposes structured behavior that the modal summary omits.","counterfactual_removal":"Without it, a compact modal explanation could conceal consequential low-amplitude disputes or merely reproduce its fitting data."},{"mechanism_slug":"spectral_gap_monitor","role":"Tracks whether retained modes remain separated and directionally stable as new bargaining rounds arrive.","counterfactual_removal":"Without it, the facilitator could continue acting on a mode after near-degenerate modes swap, rotate, or lose their dominance."},{"mechanism_slug":"spectral_decomposition_report","role":"Documents mode meanings, prohibited interpretations, coupling, uncertainty, residuals, and the regime in which recommendations may be considered.","counterfactual_removal":"Without it, tentative mathematical patterns could be communicated as authoritative claims about political motives or blame."}],"causal_chain":["Budget positions on several dimensions jointly shape negotiators' next-round package responses.","The round-to-round transformation preserves, damps, oscillates, or amplifies particular combinations of proposal gaps rather than acting independently on each named issue.","A growing or weakly damped combination accumulates bargaining pressure while coordinate-level monitoring disperses it across several moderate disagreements.","Decomposition makes that combined direction and its gain observable, while stability and residual tests determine whether it is fit for bounded use.","A sensitivity sweep identifies which authorized procedural adjustment is projected to reduce excitation of the risky mode without selecting substantive policy positions.","The authorized facilitator recommends that reversible adjustment, and elected officials decide whether to adopt it.","Subsequent rounds reveal whether the mode decays, persists, rotates, or is displaced into residual behavior; breached validity thresholds suspend the dashboard."],"baseline":"The ordinary baseline is an issue-by-issue bargaining-gap dashboard combined with facilitator judgment: negotiators focus on the largest current fiscal disagreement, recent failed votes, and stated red lines without estimating the transformation governing coupled changes across rounds.","nearest_rivals":["Strongest rival: an issue-by-issue bargaining-gap dashboard with experienced facilitator judgment and deadline tracking","Coalition or voting-bloc network analysis that identifies aligned actors but does not classify round-to-round disagreement modes","A bargaining simulation based on fixed actor utilities and substantive concession ranges"],"remaining_contrastive_claim":"The candidate's testable contrast is whether a locally valid transformation-based combination of budget disagreements provides stable held-out reconstruction and actionable procedural sensitivity beyond the strongest rival's separate issue gaps and deadline indicators. This is not a novelty, prevalence, demand, or effect-size claim.","authority_safety":{"decision_authority":"The elected council retains authority over budget content and votes; only the body designated by council rules—such as the council president or agenda committee—may change meeting procedure. The neutral facilitator may analyze data and issue nonbinding procedural recommendations.","authorized_first_step":"With clerk or data-steward approval, conduct a retrospective, aggregate-level analysis of one city's archived bargaining rounds and present results only to an evaluation group; do not alter a live negotiation.","excluded_actions":["No automatic agenda, voting, or budget changes","No recommendation of substantive fiscal positions or concessions","No member-level loyalty, ideology, blame, or electability scores","No use of private communications, protected deliberative material, or undisclosed personal data","No public labeling of a caucus or member as destabilizing","No extrapolation across a coalition break, fiscal shock, legal change, or altered bargaining rules"],"halt_rollback":"Suspend recommendations immediately if residual, drift, spectral-gap, data-quality, or governance thresholds fail, or if participants begin treating modes as motive or blame scores. Revert to the ordinary issue-by-issue process, withdraw the affected report, preserve the underlying official record, and delete nonrequired derived analytic features under the approved retention rule."},"negative_tests":{"strongest_counterevidence":"Across archived rounds, separate issue gaps and deadline indicators predict transitions at least as well as the modal model, while estimated modes rotate under minor resampling, lack a usable spectral separation, or leave structured politically consequential residuals.","problem_falsifier":"The inferred transition is not sufficiently stationary or coupled for a bounded local analysis: no reproducible combination persists across held-out rounds, and bargaining outcomes are instead explained by singular shocks, explicit veto points, or one directly observable dispute.","intervention_falsifier":"Even when a risky mode is reproducible, simulated procedural levers show no stable selective influence on it, or a later authorized pilot shows the targeted mode does not decay relative to a predeclared matched baseline while residual deadline risk remains unchanged or worsens.","risks":["Sparse bargaining rounds may produce unstable or overfit operators.","Modes may encode recording practices rather than political dynamics.","Officials may mistake descriptive modes for causal accounts of motives.","A procedural recommendation could redistribute agenda power or visibility among constituencies.","Strategic actors could adapt positions to manipulate the dashboard.","An apparently damped retained mode could displace conflict into an omitted residual dimension.","Publishing mode labels could stigmatize caucuses or weaken legitimate bargaining privacy."]},"next_evidence_step":"Using only one city's authorized archival record, define no more than eight aggregate fiscal-gap coordinates and assemble consecutive states from a bounded set of prior bargaining rounds. Predeclare the stability boundary, resampling criterion, residual budget, spectral-gap threshold, and local-validity conditions. Fit the transition operator on earlier rounds; evaluate mode stability, reconstruction, and next-round prediction on withheld rounds against the issue-by-issue baseline; then run sensitivity sweeps only for procedurally authorized hypothetical levers. Stop before any live recommendation. Advance only if at least one action-relevant mode is resampling-stable, improves held-out reconstruction or prediction on the predeclared metric, leaves no structured high-consequence residual, and maps to a reversible lever without prohibited actor scoring.","prior_art_status":"UNSEARCHED","revision_record":{"parent_version":null,"progress_targets_addressed":[],"conceptual_changes":[],"operational_changes":[],"evidence_changes":[],"claim_changes":[]}}