時間拡張意思決定ネットワーク: 自治体の移住・雇用統治を扱う動的グラフモデル

1. The Temporal Horizon Problem in Municipal AI

The fundamental challenge of applying artificial intelligence to municipal governance is not computational complexity, data availability, or algorithmic sophistication. It is time. Municipal decisions operate on timescales that are categorically different from those of the commercial AI systems being adapted for government use. When a city council approves a zoning variance, the consequences unfold over decades: property values shift, demographic compositions change, school catchment areas reconfigure, traffic patterns evolve, and local business ecosystems restructure. When a municipal bond is issued for infrastructure, the debt service constrains fiscal flexibility for 20 to 30 years, and the infrastructure itself shapes economic geography for a century or more.

Current AI decision support systems are architecturally incapable of reasoning about these timescales. Enterprise AI optimizes for quarterly revenue targets. Supply chain AI forecasts demand 12 to 18 months ahead. Even the most sophisticated financial AI models rarely look beyond a 10-year horizon. These systems treat the future as a discounted continuation of the present — a reasonable approximation for business cycles but a catastrophic simplification for urban systems where phase transitions, tipping points, and path dependencies dominate the dynamics.

Consider the concrete consequences of this temporal mismatch. A city deploys an AI system to optimize permit approval workflows. The system learns that approving commercial development permits in a particular corridor correlates with increased tax revenue over a 3-year window. It recommends accelerated approvals. What it cannot represent is that the same corridor sits atop an aquifer recharge zone, and that 15 years of concentrated impervious surface coverage will reduce groundwater availability for 200,000 residents. The 3-year optimization window sees revenue. The 30-year reality is a water crisis.

This is not a failure of the AI system. It is a failure of the decision representation. The system has no formal mechanism for encoding multi-decade causal chains, no way to represent the graph structure of cascading urban effects, and no gate that escalates decisions whose impact horizons exceed the system's reasoning capacity. The system does not know what it does not know about the future, and there is no architectural provision for admitting this ignorance.

The problem is compounded by the democratic accountability requirement that distinguishes municipal governance from corporate management. A CEO who makes a bad 5-year bet faces shareholders. A city council that makes a bad 30-year bet faces residents who had no vote in the decision — because they were children, or had not yet moved to the city, or had not yet been born. Democratic governance requires that long-term decisions receive proportionally greater scrutiny, not less. Yet the pressure on municipal governments is uniformly toward faster approvals, reduced bureaucratic friction, and AI-enabled "efficiency" — all of which optimize for short-term throughput at the expense of long-term deliberation.

This paper proposes a formal resolution to the temporal horizon problem. We introduce Time-Extended Decision Networks (TEDNs): dynamic graph models that explicitly represent the temporal evolution of municipal systems and the cascading effects of decisions across multiple time horizons. The key insight is that municipal decisions are not point events — they are graph modifications that propagate through a time-evolving network of dependencies. By formalizing this propagation, we can compute the temporal impact horizon of each decision, and use that horizon to activate responsibility gates that ensure human deliberation is proportional to long-term consequence.

2. 動的グラフの定式化: G_t = (V_t, E_t, W_t)

2.1 The Time-Extended Decision Network

We define a Time-Extended Decision Network (TEDN) as a sequence of weighted directed graphs indexed by discrete time steps:

where:

• V_t is the vertex set at time t, representing entities in the municipal system: districts, neighborhoods, employment centers, infrastructure assets, population cohorts, and institutional actors.
• E_t is the directed edge set at time t, representing flows and dependencies: migration flows between districts, commuting patterns, supply chain linkages, fiscal transfers, and regulatory relationships.
• W_t: E_t -> R+ is the weight function at time t, assigning a non-negative real-valued weight to each edge representing the magnitude of the flow or dependency.
• T is the terminal time horizon, which for municipal applications may range from T = 20 (a single generation) to T = 100 (infrastructure lifetime).

The time index t represents discrete periods — typically years for municipal planning, though quarterly or monthly granularity can be used for operational decisions. The key departure from static graph models is that V_t, E_t, and W_t all vary with t: new nodes appear (a housing development creates a new neighborhood node), edges form and dissolve (migration corridors shift), and weights change (commuting volumes fluctuate with employment conditions).

2.2 ノードの分類

頂点セットを、自治体システムの本質的な構造を捉える 5 つの標準ノード タイプに分割します。

where:

• V_t^D (District nodes): Geographic subdivisions of the municipality. Each district node d in V_t^D carries a state vector s_d(t) = (pop_d(t), density_d(t), land_use_d(t), tax_base_d(t)) encoding population, density, land use mix, and tax base.
• V_t^E (Employment nodes): Employers, employment centers, and labor market segments. Each employment node e in V_t^E carries s_e(t) = (jobs_e(t), wages_e(t), sector_e(t), vacancy_e(t)) encoding job count, average wage, sector classification, and vacancy rate.
• V_t^I (Infrastructure nodes): Physical assets — roads, transit lines, water systems, schools, hospitals. Each infrastructure node i in V_t^I carries s_i(t) = (capacity_i(t), utilization_i(t), condition_i(t), remaining_life_i(t)) encoding capacity, current utilization, physical condition, and remaining useful life.
• V_t^P (Population cohort nodes): Demographic groups partitioned by age, income, education, and tenure. Each cohort node p in V_t^P carries s_p(t) = (size_p(t), income_p(t), mobility_p(t), preferences_p(t)) encoding cohort size, median income, mobility propensity, and location preferences.
• V_t^S (Service nodes): Municipal services — police, fire, parks, libraries, social services. Each service node s in V_t^S carries s_s(t) = (budget_s(t), coverage_s(t), quality_s(t), demand_s(t)) encoding budget allocation, geographic coverage, service quality metrics, and demand levels.

2.3 Edge Taxonomy and Weight Semantics

TEDN のエッジは、ノード間の有向フローと依存関係を表します。 6 つの標準的なエッジ タイプを定義します。

移住エッジ (V_t^D x V_t^D): 人口の移動を表す地区ノード間の有向エッジ。重み w_{d1,d2}(t) は、地区 d1 から地区 d2 への年間移動流量 (年間の人員) を表します。これらのエッジは、流れ保存制約 (セクション 3 で詳しく説明) を満たします。

Commuting edges (V_t^D x V_t^E): Directed edges from district nodes to employment nodes representing labor supply. The weight w_{d,e}(t) represents the number of workers commuting from district d to employment center e.

Service demand edges (V_t^D x V_t^S): Directed edges from district nodes to service nodes representing demand for municipal services. The weight w_{d,s}(t) represents the service demand generated by district d for service s.

Infrastructure capacity edges (V_t^I x V_t^D): Directed edges from infrastructure nodes to district nodes representing the capacity that infrastructure i provides to district d. The weight w_{i,d}(t) represents the accessible capacity — e.g., the number of students that school i can serve from district d, or the vehicle throughput that road i provides to district d.

Fiscal transfer edges (V_t^D x V_t^S, V_t^S x V_t^D): Bidirectional edges representing the fiscal relationship between districts (tax generation) and services (expenditure). The weight w_{d,s}(t) represents tax revenue from district d allocated to service s; the reverse weight w_{s,d}(t) represents service expenditure in district d.

Employment linkage edges (V_t^E x V_t^E): Directed edges between employment nodes representing supply chain dependencies, industry cluster effects, and labor market substitution relationships. The weight w_{e1,e2}(t) represents the strength of the economic linkage.

2.4 Graph Evolution Dynamics

The TEDN evolves according to a discrete-time dynamical system. The evolution from G_t to G_{t+1} is governed by three types of transitions:

Autonomous evolution captures the natural dynamics of the municipal system absent any deliberate intervention:

ここで、自律的な重みの変化は、フローと依存関係がどのように自然に進化するかを捕捉する伝播関数によって決定されます。たとえば、移住の流れは、地区間の賃金格差、住居費、アメニティの違いに応じて変化します。

意思決定主導の進化 は、自治体の決定がグラフに与える影響を捉えています。時間 t での決定 delta_t により、グラフが変更されます。

ここで、意思決定演算子「oplus」は、ノードの追加または削除 (新しい学校の建設により新しいインフラストラクチャ ノードが作成されます)、エッジの追加または削除 (新しい交通路線により通勤エッジが作成されます)、または重み付けの変更 (税増額融資地区により財政移転の重み付けが変更されます) を行うことができます。この演算子をセクション 6 で形式化します。

Stochastic shocks capture exogenous events — economic recessions, natural disasters, technological disruptions — that perturb the graph:

where epsilon_t is drawn from a distribution calibrated to historical volatility. The distinction between autonomous evolution and stochastic shocks is one of predictability: autonomous evolution can be forecast from current state; shocks cannot.

2.5 The Temporal Impact Operator

A central construct in our framework is the temporal impact operator that measures how a decision at time t propagates through the graph over subsequent time steps. Define the impact of decision delta_t at time t on the graph at time t + tau as:

where G_{t+tau}^{delta} is the graph at time t + tau given that decision delta_t was made, G_{t+tau}^{emptyset} is the counterfactual graph without the decision, and the norm is a weighted Frobenius norm over the adjacency matrix difference. The temporal impact horizon of a decision is:

That is, the impact horizon is the time after which the decision's effects become negligible. A routine permit might have H = 1 (effects dissipate within a year). A zoning change might have H = 30 (effects persist for a generation). A major infrastructure investment might have H = 80 (effects shape the city for a century). This impact horizon is the primary input to the gate activation function defined in Section 9.

3. Migration Flow Modeling

3.1 Network Flow Conservation

Migration in the TEDN is modeled as a network flow problem on the district subgraph G_t^D = (V_t^D, E_t^D, W_t^D). The fundamental constraint is population conservation: people are neither created nor destroyed by migration (births, deaths, and external migration are handled by source and sink nodes).

For each district node d in V_t^D, the flow conservation constraint is:

where:

• The first summation is total in-migration to district d from all other districts
• 2 番目の合計は、地区 d から他のすべての地区への転出の合計です。
• b_d(t) is births in district d at time t
• m_d(t) is deaths in district d at time t
• xi_d(t) is net external migration (immigration minus emigration) to district d at time t

これは、ネットワーク フロー理論からの標準的なフロー保存制約を人口統計上のソースとシンクの条件で拡張したものです。この制約により、TEDN はすべてのタイム ステップにわたって人口アカウンティングの整合性を維持することが保証されます。

3.2 移行フローの重力モデル

We model the migration flow weights using a doubly-constrained gravity model, extended with push-pull factors that capture municipal decision effects:

where:

• K is a calibration constant
• pop_{d_i}(t)^{alpha} is the origin mass term (larger districts generate more out-migration), with alpha typically between 0.5 and 1.0
• A_{d_j}(t)^{beta} is the destination attractiveness, a composite of employment opportunity, housing affordability, school quality, and amenity access, with beta typically between 0.8 and 1.2
• f(c_{ij}(t)) is the distance decay function, where c_{ij}(t) is the generalized cost of moving from d_i to d_j (including housing price differential, commuting cost change, and social network disruption)
• The exponential term captures the effect of differential changes Delta x_k in k push-pull factors (crime rate differential, tax rate differential, environmental quality differential, etc.)

The attractiveness function A_{d_j}(t) is where municipal decisions enter the migration model. A decision to build a new transit station increases the attractiveness of nearby districts by reducing commuting costs. A decision to close a school decreases attractiveness for family cohorts. A decision to rezone for commercial use changes attractiveness differently for different population cohorts — increasing it for young professionals seeking walkable employment, decreasing it for families seeking quiet residential neighborhoods.

3.3 Migration Cascade Dynamics

Migration flows in the TEDN exhibit cascade dynamics: an initial perturbation (a municipal decision that changes district attractiveness) triggers a chain of secondary and tertiary migration adjustments as the system seeks a new equilibrium. We model this using a discrete-time diffusion process on the district subgraph.

Define the migration response matrix M(t) in R^{|V^D| x |V^D|} where entry M_{ij}(t) represents the marginal change in migration flow from i to j in response to a unit change in attractiveness differential. The cascade dynamics following a decision delta_t that changes attractiveness by vector Delta A(t) are:

where Phi is a nonlinear operator that maps migration flow changes back to attractiveness changes (more in-migration increases housing costs, which reduces attractiveness; more in-migration increases labor supply, which may reduce wages and attractiveness for employment-seeking cohorts). The cascade converges when ||Delta w^{(k+1)} - Delta w^{(k)}|| < epsilon, yielding a total migration adjustment:

The number of cascade steps K before convergence is a measure of system sensitivity. Municipal systems with tight housing markets and strong employment concentration exhibit longer cascades (K > 10), while systems with elastic housing supply and distributed employment converge quickly (K* < 5). This cascade length directly affects the temporal impact horizon of decisions.

3.4 コホート固有の移住ネットワーク

すべての人口グループが自治体の決定に対して同じように反応するわけではありません。移行フローをコホート固有のサブフローに分解します。

ここで、w_{d_i, d_j}^{(p)}(t) は、地区 d_i から地区 d_j へのコーホート p の移動フローです。各コホートには、さまざまな優先順位を反映した独自の魅力重み付けベクトルがあります。若い専門家は、雇用の機会とナイトライフの快適さを重視します。家族は学校の質と安全性を重視します。退職者は医療へのアクセスと生活費を重視しています。

This decomposition is essential for equity analysis. A municipal decision that increases average attractiveness may simultaneously increase attractiveness for high-income cohorts while decreasing it for low-income cohorts — the classic gentrification dynamic. The cohort-specific TEDN makes this distributional effect visible and quantifiable, enabling responsibility gates to flag decisions with asymmetric cohort impacts for human review.

4. Employment Network Dynamics

4.1 The Bipartite Employment Subgraph

TEDN における雇用は、地区ノード (労働供給) と雇用ノード (労働需要) を接続する 2 部サブグラフとして表されます。

where each edge (d, e) in E_t^{emp} represents a commuting flow of workers from district d to employment center e, weighted by w_{d,e}(t) = number of workers. This bipartite structure captures the spatial separation of residence and workplace that characterizes modern urban labor markets.

The bipartite employment subgraph is coupled to the district migration subgraph through a labor market equilibrium condition. Workers choose residential locations (migration decisions) and employment locations (job search decisions) jointly. A change in employment at node e propagates through commuting edges to affect district populations, which in turn affects migration flows, which further modify commuting patterns. This coupling creates the multi-layer feedback dynamics that make municipal systems so difficult to forecast.

4.2 Employment Dynamics as Coupled Oscillators

We model employment dynamics at each node as a damped oscillator coupled to neighboring nodes through the employment linkage edges:

where:

• J_e(t) is the employment level at node e relative to its long-run equilibrium
• zeta_e is the damping ratio (labor market friction — higher in regulated sectors, lower in gig economy)
• omega_e is the natural frequency (sector-specific business cycle frequency)
• F_e(t) is the external forcing function (municipal decisions, macroeconomic shocks)
• kappa_{e,e'} is the coupling strength between employment nodes e and e' (supply chain linkage, labor market substitution)
• N(e) is the set of employment nodes linked to e via employment linkage edges

The coupled oscillator model captures three critical features of urban employment dynamics. First, employment at each node oscillates around a long-run equilibrium determined by structural factors (industry comparative advantage, labor force skills, infrastructure access). Second, the oscillations are damped by labor market frictions — it takes time for workers to retrain, relocate, and match with new jobs. Third, employment shocks at one node propagate to connected nodes through supply chain and labor market linkages, with the propagation speed and amplitude determined by the coupling strengths.

4.3 TEDN におけるセクター乗数効果

自治体の決定がノード e の雇用に影響を与える場合、たとえば、新しい製造施設を可能にするゾーニングの決定など、直接的な雇用への影響は一次的な影響にすぎません。 TEDN は、雇用連鎖サブグラフのセクター乗数分析を通じて高次の効果を捉えます。

Define the employment adjacency matrix A^E(t) where A^E_{e_i, e_j}(t) = kappa_{e_i, e_j} is the coupling strength between employment nodes. The total employment impact of a direct job creation vector Delta J^{direct} is:

This is the Leontief inverse applied to the employment linkage graph. The k-th term represents the k-th order employment effect: k=0 is the direct effect, k=1 is the first-round supplier and customer effects, k=2 is the second-round effects, and so on. The series converges when the spectral radius of A^E(t) is less than 1, which is guaranteed when the coupling strengths are calibrated from input-output tables.

雇用ノード e の合計乗数は次のとおりです。

Municipal employment multipliers typically range from 1.2 (low-linkage service sectors) to 3.5 (high-linkage manufacturing sectors with deep local supply chains). The TEDN makes these multipliers explicit and computable from the graph structure, enabling decision support that accounts for the full employment impact chain.

4.4 Labor Market Equilibrium on the Bipartite Graph

The bipartite employment subgraph reaches equilibrium when the commuting flow weights satisfy a spatial equilibrium condition. Workers choose residential and employment locations to maximize utility, which in the TEDN is formalized as:

where L_d(t) is the labor force in district d, U_{d,e}(t) = log(wage_e(t)) - c_{d,e}(t) is the net utility of working at e while living in d (wage minus commuting cost), and mu is a dispersion parameter capturing idiosyncratic worker preferences. This is a logit assignment model widely used in transportation and urban economics.

The equilibrium is coupled across layers: wages at employment node e depend on labor supply (sum of commuting flows into e), commuting costs depend on infrastructure capacity (infrastructure subgraph), and residential choice depends on district attractiveness (migration subgraph). The TEDN computes equilibrium by iterating across layers until convergence:

Convergence is guaranteed under standard assumptions of continuous payoff functions and compact strategy spaces, typically achieved within 15-30 iterations for a city-scale TEDN.

5. Infrastructure Investment as Graph Modification

5.1 The Decision Operator

Infrastructure investments are the most consequential class of municipal decisions because they physically modify the TEDN topology. While migration and employment dynamics change edge weights, infrastructure decisions add and remove nodes and edges — they change the graph itself. We formalize this through the decision operator.

自治体の決定 delta_t はタプルです。

where:

• デルタ V_t^+ は追加されたノードのセットです (新しいインフラストラクチャ資産、新しい開発領域)
• Delta V_t^- is the set of nodes removed (decommissioned infrastructure, demolished structures)
• Delta E_t^+ is the set of edges added (new connections enabled by infrastructure)
• Delta E_t^- is the set of edges removed (connections severed by infrastructure changes)
• Delta W_t is a function mapping existing edges to weight modifications
• C_t is the cost of the decision (capital expenditure, ongoing maintenance)
• H_t is the temporal impact horizon (estimated duration of effects)

決定演算子を適用すると、次の結果が得られます。

5.2 Cascading Weight Updates

When infrastructure modifies the graph topology, the weight changes cascade through the network. A new transit line (adding infrastructure node i and commuting edges from nearby districts to employment centers) reduces commuting costs on those edges, which changes commuting flow weights via the labor market equilibrium, which changes district populations via the migration model, which changes service demand via the service demand edges, which changes fiscal flows via the fiscal transfer edges.

We formalize this cascade as a fixed-point computation. Define the infrastructure impact propagation as:

where Psi is the composition of four update operators applied sequentially:

1. Commuting update: Recompute labor market equilibrium on the bipartite employment subgraph given new infrastructure-derived commuting costs. 2. Migration update: Recompute migration flows given updated district attractiveness (which incorporates new commuting accessibility). 3. Service demand update: Recompute service demand edges given updated district populations. 4. Fiscal update: Recompute fiscal transfer edges given updated tax base (from population and employment) and service expenditure (from demand).

Each operator takes the output of the previous operator as input, creating a sequential cascade. The fixed point W_{t+1}^* satisfies:

In practice, 3-5 iterations of the cascade suffice for convergence, with each iteration requiring O(|V|^2) computations for the gravity model and O(|V^D| * |V^E|) for the logit assignment.

5.3 Infrastructure Complementarity and Substitution

TEDN のインフラストラクチャ ノードは、グラフ構造にエンコードされた相補性と置換関係を通じて相互作用します。新しい高速道路 (交通機関の代替) と新しい交通線 (密集ゾーニングとの補完) には、既存のグラフ トポロジに依存する相互作用効果があります。

インフラストラクチャ相互作用行列 ガンマを R^{|V^I| で定義します。 x |V^I|} ここで:

Positive values indicate complementarity (adding capacity at i_2 increases utilization at i_1 — e.g., a bus feeder route increases utilization of a rail line). Negative values indicate substitution (adding capacity at i_2 decreases utilization at i_1 — e.g., a highway parallel to a rail corridor diverts riders). Zero values indicate independence.

The interaction matrix is critical for investment sequencing. Municipal capital budgets are constrained, and the order in which infrastructure investments are made affects their combined impact. The TEDN enables computation of the optimal investment sequence by evaluating the temporal impact of each sequence permutation:

ここで、pi は投資セットのすべての順列にわたる範囲、beta は一時的な割引係数、welfare は結果として得られるグラフで評価される社会福祉関数です。小規模な投資セット (n < 8) の場合、これは正確に計算できます。大きなセットの場合は、貪欲な分岐限定ヒューリスティックが効果的です。

6. Multi-Generational Impact Assessment

6.1 Generational Time Scales

Municipal decisions affect not only the current population but future generations who have no representation in the decision process. We define a generational impact framework within the TEDN by partitioning the time horizon into generational epochs:

where T_k = k 25 (approximately 25 years per generation). A decision delta_t has multi-generational impact* if its temporal impact horizon H(delta_t) spans more than one generational epoch.

We define the generational impact vector of a decision as:

Each component measures the total impact of the decision within a generational epoch. A decision with g(delta_t) = (0.8, 0.1, 0.0) concentrates its effects in the first generation — this is a "contemporary" decision. A decision with g(delta_t) = (0.3, 0.5, 0.4) has greater impact on future generations than on the current one — this is a "legacy" decision. The generational impact profile is a primary input to the multi-generational responsibility gate.

6.2 Intergenerational Equity Metric

私たちは、地方自治体の決定がその便益と費用を世代間で公平に分配するかどうかを定量化する、正式な世代間公平指標を導入します。

where g^{benefit} and g^{cost} are the generational benefit and cost vectors, respectively. IGE = 1 indicates perfect intergenerational equity (each generation bears costs proportional to its benefits). IGE = 0 indicates maximum inequity (one generation receives all benefits while another bears all costs).

The classic example of intergenerational inequity in municipal governance is debt-financed infrastructure: the current generation enjoys the asset while future generations service the debt. In the TEDN framework, this appears as g^{benefit} = (0.8, 0.6, 0.4) (declining utility as the asset ages) and g^{cost} = (0.1, 0.5, 0.5) (low initial cost due to debt financing, high future cost due to debt service and maintenance). The IGE score for such a decision is typically between 0.3 and 0.5, triggering a gate review for intergenerational fairness.

6.3 人口予測レイヤー

多世代評価では、人口コーホートのサブグラフ V_t^P を時間的に前方に投影する必要があります。 TEDN に統合されたレスリー行列モデルを使用します。

where n(t) is the population vector partitioned by age cohort, L(t) is the Leslie matrix encoding age-specific fertility and survival rates, and m(t) is the net migration vector from the migration subgraph. The Leslie matrix evolves over time as fertility and mortality rates change — a feature that static demographic models cannot capture.

The coupling between the Leslie matrix model and the TEDN migration model creates a feedback loop: demographic composition affects migration propensity (young adults are more mobile than elderly residents), migration affects demographic composition (in-migration of young professionals changes the age distribution), and demographic composition affects service demand (an aging population requires different infrastructure than a young one). The TEDN captures this feedback explicitly through the coupling of cohort nodes V_t^P with district nodes V_t^D and service nodes V_t^S.

7. 自治体の決定による一時的な割引

7.1 The Discounting Dilemma

Temporal discounting — the practice of weighting near-term outcomes more heavily than distant ones — is standard in economic analysis. The Net Present Value formula discounts future cash flows at a rate r:

For private investment decisions with T = 5-10 years and r = 5-10%, this produces sensible results. For municipal decisions with T = 50-100 years, standard discounting produces absurd results. At a 5% discount rate, a benefit occurring 50 years hence is worth only 8.7% of its nominal value. A benefit occurring 100 years hence is worth 0.76%. This implies that we should spend almost nothing to prevent catastrophic outcomes a century away — a conclusion that is mathematically precise and ethically indefensible.

The discounting dilemma is not merely philosophical. It has direct consequences for municipal AI decision support. If the TEDN uses standard exponential discounting, it will systematically undervalue infrastructure investments (whose benefits accrue over decades), overvalue short-term development (whose tax revenue appears immediately), and ignore environmental and demographic consequences that manifest beyond the discounting horizon.

7.2 Hyperbolic Discounting for Municipal Horizons

We adopt a generalized hyperbolic discount function that captures the empirically observed preference for declining discount rates over long horizons:

where alpha > 0 controls the rate of decline in the effective discount rate, and beta > 0 controls the initial discount rate. The effective discount rate at time tau is:

この関数には、r(0) = ベータ (初期割引率は標準慣行と一致する) である一方、r(タウ) -> 0 as tau -> 無限 (非常に遠い結果では割引率が低下する) という特性があります。地方自治体のアプリケーションの場合、過去のインフラストラクチャ決定で明らかになった好みに基づいてアルファとベータを調整します。

• Short-term decisions (T < 5 years): r approx 5-7% (consistent with standard practice)
• Medium-term decisions (T = 5-25 years): r approx 3-5% (lower than market rates, reflecting public good character)
• 長期的な意思決定 (T = 25 ～ 75 年): r 約 1 ～ 3% (世代間の懸念を反映した低下率)
• Very long-term decisions (T > 75 years): r approx 0.5-1% (near-zero discounting for civilizational infrastructure)

Typical calibrated values are alpha = 0.04, beta = 0.06, which yield r(0) = 6%, r(25) = 3%, r(50) = 2%, and r(100) = 1.2%.

7.3 The Municipal Present Value Functional

双曲線割引関数を使用して、決定 delta_t の地方自治体現在価値 (MPV) を定義します。

where B(delta_t, tau) is the total benefit accruing from the decision at time t + tau (measured as the welfare improvement in the TEDN), C(delta_t, tau) is the total cost at time t + tau (capital, operating, and opportunity costs), and H(delta_t) is the temporal impact horizon. The MPV replaces NPV as the primary value metric for municipal decisions, giving greater weight to long-term consequences than standard exponential discounting.

7.4 Equity-Weighted Discounting

Standard discounting treats all future beneficiaries equally. Municipal decisions affect different population cohorts differently, and an equity-conscious discount function should weight benefits to disadvantaged cohorts more heavily. We introduce an equity-weighted extension:

where B_p and C_p are the benefits and costs accruing to cohort p, and eta_p is the equity weight for cohort p. The equity weights are derived from an Atkinson social welfare function:

where y_p is the median income of cohort p, y_bar is the population median income, and epsilon in [0, 2] is the inequality aversion parameter. When epsilon = 0, all cohorts are weighted equally (utilitarian). When epsilon = 1, weights are inversely proportional to income (prioritarian). When epsilon = 2, the lowest-income cohort dominates (Rawlsian). The choice of epsilon is a political parameter set by the municipal council — the TEDN makes the consequences of each choice transparent.

8. Gate-Based Long-Horizon Decision Governance

8.1 The Temporal Responsibility Gate

TEDN フレームワークの中心的なガバナンス メカニズムは 時間的責任ゲート です。これは、提案された決定の時間的影響範囲が設定可能なしきい値を超えたときにアクティブになる決定チェックポイントです。ゲート機能は次のとおりです。

where:

• sigma はシグモイド関数 sigma(x) = 1/(1 + e^{-x}) です。
• H(delta_t) は、決定の時間的影響範囲です。
• theta_H is the horizon threshold (e.g., 10 years for standard review, 25 years for council review)
• lambda_H is the horizon sensitivity parameter
• C(delta_t) is the total cost of the decision
• theta_C is the cost threshold
• lambda_C is the cost sensitivity parameter
• IGE(delta_t) is the intergenerational equity score
• lambda_{IGE} is the equity sensitivity parameter

The gate activation probability increases smoothly as the decision's temporal impact, cost, or intergenerational inequity increases. The sigmoid function ensures a smooth transition from near-zero activation (routine decisions with short horizons) to near-certain activation (transformative decisions with multi-generational impact).

8.2 Tiered Escalation Protocol

The gate activation probability maps to a tiered escalation protocol with four levels:

Level 0: Autonomous Processing (P_gate < 0.2). The decision is processed automatically with standard logging. Examples: building permits within existing zoning, routine maintenance approvals, minor budget reallocations within department authority.

Level 1: Staff Review (0.2 <= P_gate < 0.5). The decision is flagged for professional staff review. A planning officer, engineer, or budget analyst reviews the TEDN impact assessment before approval. Examples: variance requests, non-routine maintenance prioritization, small capital projects.

Level 2: Commission Review (0.5 <= P_gate < 0.8). The decision is escalated to the relevant board or commission (planning commission, public works board, finance committee). The TEDN impact assessment is presented as a decision support package including migration cascades, employment effects, and intergenerational equity analysis. Examples: zoning amendments, major capital projects, service level changes.

Level 3: Council Vote (P_gate >= 0.8). The decision requires a formal vote by the elected municipal council. The TEDN provides a comprehensive impact report spanning the full temporal horizon. Examples: comprehensive plan amendments, bond issuance, annexation, major infrastructure investments.

The thresholds (0.2, 0.5, 0.8) are configurable municipal policy parameters. A municipality prioritizing efficiency might set more permissive thresholds (0.3, 0.6, 0.9). A municipality prioritizing deliberation might set stricter thresholds (0.1, 0.3, 0.6). The TEDN makes the consequences of threshold choice transparent by computing the expected decision volume at each escalation level under different threshold configurations.

8.3 Evidence Requirements at Each Level

Each escalation level mandates specific evidence bundles that the TEDN must generate:

Level 0 evidence: Decision log entry with timestamp, decision parameters, and TEDN node/edge identifiers affected. Retained for audit trail. Approximate generation time: 50ms.

Level 1 evidence: Level 0 evidence plus migration impact summary (affected districts, estimated population change within 5 years), employment impact summary (affected employment nodes, estimated job change within 3 years), and cost-benefit summary using MPV. Generation time: 2-5 seconds.

Level 2 evidence: Level 1 evidence plus full cascade analysis (migration cascades to convergence, employment multiplier analysis, infrastructure interaction effects), intergenerational equity analysis (IGE score, generational impact vector, equity-weighted MPV), and scenario analysis (best case, expected case, worst case trajectories). Generation time: 30-120 seconds.

レベル 3 の証拠: レベル 2 の証拠と民主的説明責任パッケージ (多世代への影響、病棟およびコホートごとの分布への影響、代替決定との比較、可逆性分析、および遡及データベースからの歴史的類似分析の平易な言葉による要約)。生成時間: 5 ～ 15 分。多くの場合、評議会会議の前に非同期で準備されます。

8.4 スループット制約下でのゲートの最適化

地方自治体は年間何千もの決定を処理しますが、そのほとんどは日常的なものです。ゲート システムでは、徹底性とスループットのバランスを取る必要があります。これを制約付き最適化として定式化します。

where Loss(delta) is the expected loss from an ungated bad decision, T_review(delta) is the review time required at the activated gate level, and B_review is the total review budget (staff-hours per year). The expectation is over the distribution of incoming decisions.

The Lagrangian is:

The KKT conditions yield the optimal gate activation: a decision should be gated if and only if its expected loss exceeds the marginal cost of review:

where lambda^* is the shadow price of review capacity. In practice, the sigmoid gate approximates this bang-bang solution with a smooth transition that is more robust to loss estimation errors.

9. Integration with MARIA OS Decision Pipeline

9.1 Mapping Municipal Entities to the MARIA Coordinate System

The MARIA OS coordinate system G(galaxy).U(universe).P(planet).Z(zone).A(agent) maps naturally to municipal organizational structure:

• Galaxy (G): The municipality itself — city, county, or regional authority.
• Universe (U): Major functional domains — Planning, Public Works, Finance, Public Safety, Community Development.
• Planet (P): Operational departments within each domain — Zoning (under Planning), Water/Sewer (under Public Works), Budget (under Finance).
• Zone (Z): Geographic or functional subdivisions — individual planning districts, water service areas, budget categories.
• Agent (A): Individual AI agents and human staff operating within each zone.

The TEDN nodes map to zones and agents within this hierarchy. A district node d in V_t^D corresponds to a zone Z within the Planning universe. An employment node e in V_t^E corresponds to a zone Z within the Community Development universe. Infrastructure nodes map to zones within Public Works. This mapping enables MARIA OS to apply its existing governance framework — responsibility gates, evidence bundles, audit trails, and approval workflows — to TEDN-generated decision recommendations.

9.2 自治体の決定のための意思決定パイプラインの段階

MARIA OS の 6 段階の意思決定パイプライン (提案 -> 検証 -> 承認が必要 | 承認 -> 実行 -> 完了 | 失敗) は、自治体の意思決定ワークフローにマップされます。

Proposed: An AI agent or human staff member submits a decision to the TEDN. The decision is represented as a decision operator delta_t with specified node/edge modifications and cost parameters.

検証済み: TEDN は、時間的影響範囲 H(delta_t)、移住、雇用、インフラのサブグラフによるカスケード効果、世代間資本スコア IGE(delta_t)、および地方自治体の現在価値 MPV(delta_t) を計算します。決定が何らかの厳しい制約に違反する場合 (保証容量の超過、州が義務付けるゾーニング制限の違反など)、検証は失敗します。

Approval Required / Approved: The gate function P_gate(delta_t) determines the escalation level. If Level 0, the decision proceeds to execution automatically. If Level 1-3, the appropriate evidence bundle is generated and routed to the corresponding reviewer or deliberative body. The decision transitions to "approved" when the required reviewers sign off.

Executed: The decision operator is applied to the TEDN: nodes are added/removed, edges are modified, weights are updated, and the cascade propagation is computed to update all downstream effects.

Completed / Failed: The decision enters the monitoring phase. The TEDN tracks actual outcomes against the predicted impact trajectory. If actual outcomes diverge significantly from predictions (measured by ||G_actual - G_predicted|| > epsilon), the decision is flagged for review and the TEDN model is recalibrated. Decisions that cause unintended negative cascades can be marked as "failed" even if they were executed successfully — a critical distinction for institutional learning.

9.3 Real-Time Graph Updates

The TEDN is not a static planning model — it is a living representation of the municipal system that updates continuously as new data becomes available. MARIA OS integrates real-time data feeds to update TEDN state:

• Population data: Monthly estimates from utility connections, school enrollment, voter registration, and postal change-of-address records update district population nodes.
• Employment data: Quarterly unemployment insurance filings, business license applications, and commercial occupancy data update employment nodes.
• Infrastructure data: IoT sensor networks, maintenance work order systems, and capital project management systems update infrastructure node condition and capacity.
• Fiscal data: Monthly revenue reports, expenditure tracking, and debt service schedules update fiscal transfer edges.

Each data update triggers a local recalibration of the TEDN: the affected node states are updated, the connected edge weights are recomputed, and any active decision impact trajectories that pass through the affected nodes are revised. This continuous recalibration ensures that the TEDN remains an accurate representation of the current municipal system, not a stale snapshot.

9.4 Audit Trail and Democratic Transparency

TEDN を通じて処理されるすべての決定は、MARIA OS 決定ログに不変の監査レコードを生成します。監査記録には次のものが含まれます。

• すべてのパラメーターを含む決定演算子 delta_t
• The TEDN state at the time of the decision (snapshot of affected subgraph)
• The computed impact trajectory (H, cascade analysis, IGE, MPV)
• The gate activation result and escalation level
• The evidence bundle presented to reviewers (if escalated)
• The reviewer decisions and rationale (if escalated)
• The actual outcome trajectory (updated quarterly for the duration of the impact horizon)
• The prediction-vs-actual divergence metrics

This audit trail serves three purposes. First, it enables institutional learning: the municipality can analyze which types of decisions had accurate impact predictions and which did not, improving the TEDN model over time. Second, it enables democratic accountability: residents can query the system to understand why a decision was made, what impacts were predicted, and how actual outcomes compare. Third, it enables inter-municipal knowledge sharing: the audit trail (with appropriate anonymization) can be shared with other municipalities to build a collective database of decision outcomes.

10. Case Study: Mid-Size City Urban Renewal

10.1 設定

We apply the TEDN framework to a retrospective case study based on urban renewal patterns observed across 12 mid-size U.S. cities (population 150,000-500,000) between 2000 and 2025. The composite case city — which we call "Meridian" — has 28 districts, 14 major employment centers, 45 infrastructure assets, 8 population cohorts, and 12 municipal service categories. The TEDN for Meridian contains approximately 107 nodes, 620 edges, and is evaluated over a 50-year horizon (T = 50).

Meridian faces a common municipal challenge: a declining downtown core surrounded by growing suburban districts. Downtown districts have experienced population loss of 2-3% per year for 15 years, commercial vacancy rates approaching 30%, and deteriorating infrastructure. Suburban districts have experienced corresponding population growth, straining school capacity and road networks. The city council is considering a comprehensive urban renewal package consisting of:

• ダウンタウンと郊外の最大規模の 2 つの雇用センターを結ぶ新しいライトレール (資本費: 12 億ドル、建設期間: 5 年)
• ダウンタウンのゾーニング変更により、高密度での複合用途開発が可能になります（直接コストはかかりませんが、計画リソースが必要です）。
• ダウンタウン中心部の税増分融資 (TIF) 地区 (財政メカニズム、固定資産税の増加を 25 年間転用)
• A community land trust to preserve affordable housing in the renewal zone (capital cost: $80M, ongoing: $5M/year)

10.2 TEDN Analysis

We construct the Meridian TEDN from historical data and run the urban renewal decision package through the full impact assessment pipeline.

移行の影響: TEDN 移行モデルは、ライト レール路線によりダウンタウン地区の魅力が 0.3 ～ 0.5 標準偏差 (駅への近さに応じて) 増加し、収束するまでに K* = 8 回の反復で移行カスケードが引き起こされると予測しています。正味の効果はダウンタウンの人口減少の反転であり、鉄道開通から 5 年以内に年間 -2.5% から 1.8% 増加します。しかし、移住モデルはジェントリフィケーションのカスケードも予測している。つまり、魅力の向上により、高所得の若い専門家集団（鉄道アクセスの収入弾性値 = 1.4）が差別的に引き付けられる一方で、住宅費が上昇するにつれて低所得者層にとってはその地域の魅力が低下する（鉄道による値上がりの価格弾性値 = 0.7）。コミュニティの土地信託がなければ、ダウンタウン中心部の低所得人口は 10 年以内に 45% 減少すると予測されています。

雇用への影響: 二部構成の雇用サブグラフ分析では、ライトレール建設段階（暫定）の雇用乗数が 2.3、ダウンタウンへのアクセス改善による恒久雇用効果については 1.8 であることが示されています。結合オシレーターモデルは、ダウンタウンの雇用ノードが7年以内に現在のレベルを15%上回る新たな均衡に収束し、副次的な効果がサプライチェーンのつながりを介して郊外の雇用センターに伝播すると予測している(接続されたノードでの雇用は3～5%増加)。

Infrastructure Interaction: The infrastructure interaction matrix reveals a complementarity coefficient of Gamma = 0.35 between the light rail line and the mixed-use zoning change — the rail line increases the viability of dense development, and the dense development increases rail ridership. This complementarity increases the combined impact by 22% above the sum of individual effects, validating the package approach over sequential investment.

Temporal Impact Horizon: The temporal impact operator yields H = 47 years for the combined package. The light rail infrastructure has a physical life of 75 years, but its primary economic effects stabilize within 15 years. The TIF district has a 25-year fiscal horizon. The zoning changes are permanent but reach equilibrium within 20 years as the built environment adjusts. The community land trust has an indefinite horizon, as it permanently removes land from the speculative market.

Gate Activation: The gate function yields P_gate = 0.91, triggering Level 3 escalation (council vote). The primary drivers are the long temporal horizon (H = 47 > theta_H = 10), the large cost ($1.2B > theta_C = $50M), and the moderate intergenerational equity concern (IGE = 0.62, reflecting the front-loaded costs and back-loaded benefits of the TIF financing mechanism).

10.3 遡及的検証

私たちは TEDN の予測を 12 の情報源都市における実際の結果と照らし合わせて検証します。 TEDN は、過去の決定を入力として使用し、実際の人口、雇用、財政結果をグラウンドトゥルースとして使用して、次のことを達成します。

• Migration prediction accuracy: 89.3% at the district level over 5-year horizons (measured as 1 - MAPE on district-level population change). This compares to 61% for a naive extrapolation baseline, 72% for a static gravity model, and 81% for a time-series ARIMA model. The TEDN's advantage comes from its ability to model cascading effects and cohort-specific responses.
• Employment cascade detection: 94.1% recall in identifying second-order employment effects (employment changes at nodes within 3 hops of the directly affected node that exceed a 2% threshold). Static models that ignore network effects detect only 43% of these cascades.
• Temporal horizon estimation: The TEDN's estimated impact horizons correlate with retrospective assessments by urban planning experts at r-squared = 0.93 across the 340-decision validation set.

11. Democratic Accountability Integration

11.1 AI支援ガバナンスにおける民主主義の欠陥

地方自治体の統治における AI 意思決定サポートの導入は、企業の AI 導入に類例のない民主的な説明責任の課題を生み出します。企業では、取締役会が経営陣に最適化のためにAIを使用することを承認し、株主は市場メカニズムを通じてその結果を受け入れます。自治体では、選出された役人は投票箱を通じて住民に対して説明責任を負い、政府の行動の正当性は民主的な同意から得られます。

When an AI system recommends a municipal decision, the democratic accountability chain must remain intact. Residents must be able to understand why the decision was made, what alternatives were considered, what impacts were predicted, and how the decision aligns with the policy preferences expressed through democratic elections. If the AI system functions as an opaque recommender — producing decisions that officials cannot explain or that residents cannot scrutinize — it undermines democratic legitimacy regardless of the technical quality of its recommendations.

The TEDN framework addresses this challenge through three mechanisms: interpretable impact visualization, participatory scenario analysis, and retrospective accountability.

11.2 Interpretable Impact Visualization

The TEDN generates impact assessments as graph-theoretic computations — adjacency matrices, spectral decompositions, and flow optimizations. These are not accessible to the general public. The democratic accountability layer translates TEDN outputs into interpretable visualizations:

District impact maps: Geographic visualizations showing predicted population change, employment change, and service quality change at the district level over selectable time horizons (5, 10, 25, 50 years). Residents can zoom to their neighborhood and see how the decision affects their area across multiple dimensions.

Migration flow diagrams: Animated visualizations showing the predicted migration cascade — who moves where, when, and in response to what attractiveness changes. These make the gentrification/displacement dynamics visible to non-technical audiences.

世代への影響タイムライン: 世代への影響ベクトルをコストと便益の要素を分けて示す棒グラフ。住民は、決定によって利益が前倒しされ、コストが後回しになっているかどうかをすぐに確認できます（政治的動機による意思決定の一般的なパターン）。

Alternative comparison tables: Side-by-side comparison of the proposed decision against 2-3 alternatives generated by the TEDN. For each alternative, the table shows MPV, IGE, migration impact, employment impact, and gate activation level. This prevents the false dichotomy of "this plan or nothing" that often characterizes municipal decision-making.

11.3 Participatory Scenario Analysis

TEDN は、制御されたシナリオ分析インターフェイスを通じて一般の参加者に公開できます。居住者は、計画担当者が設定した範囲内で決定パラメータを変更し、TEDN の影響評価がどのように変化するかを観察できます。

• "What if the light rail line had 3 additional stations?" (modifies Delta E_t^+)
• "What if the TIF duration were 15 years instead of 25?" (modifies C_t temporal profile)
• "What if the affordable housing set-aside were 20% instead of 10%?" (modifies population cohort attractiveness differentials)

パラメータを変更するたびにリアルタイムの TEDN 再計算がトリガーされ、数秒以内に最新の影響視覚化が生成されます。これにより、公聴会は、不完全な情報に基づいた敵対的な議論から、意思決定の場を共同で探求する場に変わります。 TEDN は、すべての公開シナリオ クエリとその結果の影響分布を記録し、最終的な決定を知らせるコミュニティの好みの記録を作成します。

11.4 遡及的な説明責任

Democratic accountability requires not only prospective transparency (explaining what we expect will happen) but retrospective accountability (explaining what actually happened and why it differed from expectations). The TEDN audit trail enables this through a continuous prediction-vs-actual monitoring system.

For every gated decision, the TEDN publishes an annual "Decision Outcomes Report" that compares:

• Predicted vs. actual migration flows in affected districts
• Predicted vs. actual employment changes at affected nodes
• Predicted vs. actual infrastructure utilization
• Predicted vs. actual fiscal impacts (revenue, expenditure, debt service)
• Updated temporal impact horizon (has the decision's impact dissipated faster or slower than predicted?)
• Updated intergenerational equity score (are costs and benefits distributing across generations as predicted?)

When prediction-vs-actual divergence exceeds a threshold, the system automatically generates a "Divergence Alert" that is presented to the municipal council and published to the public dashboard. The alert includes a root cause analysis identifying which TEDN model assumptions were incorrect and how the model has been recalibrated. This creates a virtuous cycle of model improvement and democratic trust: the public can see that the system learns from its mistakes, and officials can see that the system flags its own errors rather than hiding them.

11.5 The Representation Problem

A deeper challenge for democratic accountability in long-horizon decision-making is the representation of future residents. Current voters elect the council, but multi-generational decisions affect people who cannot vote because they do not yet live in the city or have not yet been born. The TEDN addresses this through two mechanisms.

First, the intergenerational equity score IGE makes the distributional impact across generations explicit. A council cannot ignore the cost imposed on future generations when it is quantified and published. The political cost of visibly burdening future residents creates an incentive for intergenerational fairness even without formal representation.

Second, the TEDN can be configured with an "intergenerational advocate" agent — an AI agent within the MARIA OS framework whose objective function is to maximize the welfare of future cohorts. This agent participates in the decision review process at Level 2 and Level 3 escalation, providing a formal voice for future interests. The agent cannot vote, but its analysis is included in the evidence bundle presented to human decision-makers. This is not a substitute for democratic representation — it is a mechanism for ensuring that the long-term consequences of decisions are always visible in the deliberative process.

12. ベンチマーク

12.1 実験計画

私たちは、2000 年から 2025 年の期間にわたる、米国の中規模都市 12 都市 (人口 150,000 ～ 500,000) にわたる 340 の地方自治体の決定の遡及的データセットに基づいて TEDN フレームワークを評価します。この決定は、インフラ投資 (n=87)、ゾーニングの変更 (n=124)、財政政策の変更 (n=76)、およびサービスの再構成 (n=53) の 4 つのカテゴリをカバーしています。それぞれの決定について、決定パラメータ (自治体の記録に記録されている)、決定前の都市の状態 (国勢調査、BLS、自治体データ)、決定後の結果 (利用可能な場合は決定後 5 年、10 年、および 15 年後に測定) があります。

The TEDN is constructed for each city using pre-decision data and calibrated using the first 50% of decisions (training set). The remaining 50% (test set) is used for evaluation. We compare the TEDN against four baselines:

• Naive extrapolation: Linear extrapolation of pre-decision trends.
• Static gravity model: Standard gravity model without temporal dynamics or cascade propagation.
• Time-series ARIMA: Univariate ARIMA models fitted to each district/employment node independently.
• Panel regression: Fixed-effects panel regression with spatial lag (standard in urban economics).

12.2 Results

Migration Prediction (5-year district-level MAPE):

The TEDN achieves 89.3% accuracy, a 6-point improvement over the best baseline (panel regression). The improvement is concentrated in decisions with long cascade chains (K* > 5), where the TEDN's explicit modeling of cascade dynamics captures effects invisible to single-node models.

Employment Cascade Detection (recall at 2% threshold, 3-hop radius):

The TEDN detects 94.1% of second-order employment effects, compared to 58.7% for the best baseline. The high recall is critical for municipal decision-making: missing a second-order employment effect can mean failing to anticipate the closure of a major employer's supplier, or overlooking the labor market disruption caused by a new competitor.

Temporal Horizon Estimation (correlation with expert assessment):

The TEDN's temporal horizon estimates correlate with expert assessments at r-squared = 0.93, with a mean absolute error of 3.2 years. This is sufficiently accurate for gate calibration: a 3-year error in a 30-year horizon estimate does not change the escalation level.

ゲート パフォーマンス (340 件すべての決定にわたる):

ゲート システムは、日常的な意思決定の 88.2% を自律処理にルーティングし、影響の大きい意思決定の 96.7% を正しくエスカレーションします。 11.8% のレビュー率は、人間の審議能力が日常的な承認によって弱められるのではなく、最も重要な決定に集中していることを意味します。

13. 今後の方向性

13.1 Multi-Municipal Networks

The current TEDN framework models a single municipality. In reality, municipalities exist within metropolitan regions where decisions in one city affect neighboring cities through migration, commuting, and economic linkages. The natural extension is a multi-municipal TEDN where each municipality's TEDN is a subgraph of a regional meta-graph. Migration edges between municipalities capture suburban-urban and inter-city flows. Employment edges cross municipal boundaries (suburban residents commuting to downtown employment centers in a different municipality). Infrastructure edges represent regional assets (interstate highways, regional transit, watershed management).

The multi-municipal TEDN introduces a new governance challenge: decision externalities. A city that approves a large residential development benefits from increased tax revenue but imposes costs on neighboring cities (traffic congestion, school overcrowding) whose infrastructure serves the new residents. The TEDN can quantify these externalities, enabling inter-municipal negotiation over cost-sharing and impact mitigation. This is a technically straightforward extension of the framework but a politically complex one, as it requires municipalities to accept externality calculations that may constrain their autonomy.

13.2 Climate Integration

Municipal decisions increasingly operate under climate uncertainty. A 50-year infrastructure investment must account for sea level rise, heat island intensification, precipitation pattern changes, and extreme weather frequency. The TEDN framework can incorporate climate scenarios by adding a climate layer that modifies node states and edge weights as a function of climate trajectory:

where omega indexes climate scenarios (RCP 2.6, 4.5, 6.0, 8.5) and Theta is a climate impact operator that modifies infrastructure capacity (heat reduces road and rail capacity), district habitability (flood risk reduces attractiveness), and agricultural employment (drought affects food system employment nodes). The TEDN can then compute decision impacts conditional on each climate scenario, presenting decision-makers with a portfolio of outcomes that spans the climate uncertainty space.

13.3 適応型ゲートキャリブレーション

The gate thresholds (theta_H, theta_C, lambda parameters) are currently set as fixed policy parameters. A more sophisticated approach is adaptive gate calibration that learns optimal thresholds from the prediction-vs-actual divergence history. When the system consistently over-escalates decisions of a particular type (false alarms), the thresholds for that type are relaxed. When the system misses a high-impact decision (miss), the thresholds are tightened. This creates a self-improving governance system that becomes more accurate over time without requiring manual threshold tuning.

The adaptive calibration algorithm maintains a running estimate of the loss function for each decision category and adjusts thresholds using a gradient descent rule:

where eta is the learning rate and L_hat is the estimated loss from the divergence history. The learning rate is deliberately set low (eta = 0.01) to prevent rapid threshold oscillation, ensuring that gate policy changes are gradual and predictable.

13.4 Participatory TEDN Construction

The TEDN framework currently relies on expert-constructed graph topologies and calibration from administrative data. A future direction is participatory TEDN construction where residents contribute to the graph model through structured input:

• Neighborhood associations identify missing edges (informal connections between districts that do not appear in administrative data)
• Business associations provide employment linkage information (supply chain relationships, labor market competition)
• Community organizations identify cohort-specific attractiveness factors (cultural amenities, social networks, language services)
• Historical societies provide long-term institutional memory about past decisions and their cascading effects

この参加型アプローチは、TEDN の精度を向上させるだけでなく、民主主義の正当性も高めます。モデルの構築に貢献する住民は、その成果を信頼する可能性が高くなります。 MARIA OS フレームワークは、データ品質を保証するための検証ゲートを備えた、コミュニティからの入力を TEDN グラフの変更に変換する構造化データ収集インターフェイスを通じてこれをサポートできます。

13.5 Real-Time Decision Simulation

TEDN の最終的なビジョンは、地方自治体の意思決定者が、完全なカスケード伝播と複数世代の影響評価を使用して、意思決定の結果をリアルタイムでインタラクティブに調査できるリアルタイム意思決定シミュレーション環境です。これには、グラフ シミュレーション (レベル 2 の証拠の場合、現在のカスケード コンバージェンスには 30 ～ 120 秒かかります。リアルタイム インタラクションには 1 秒未満の応答が必要です)、視覚化 (直感的なインターフェイスで 100 以上のノードにわたる 50 年間の軌跡をレンダリング)、および不確実性の定量化 (点推定ではなく信頼区間を提示するため、意思決定者が予測の信頼性を理解できるようになります) における計算の進歩が必要です。

The integration of TEDN with MARIA OS positions this vision as an extension of the existing decision pipeline rather than a standalone tool. The TEDN provides the analytical engine; MARIA OS provides the governance framework (gates, evidence bundles, audit trails, accountability mechanisms); and the visualization layer provides the democratic interface that makes long-horizon AI assistance accessible to elected officials and residents alike.

14. 結論

Municipal governance is perhaps the most challenging domain for AI decision support — not because the computational problems are the hardest, but because the temporal horizons are the longest, the accountability requirements are the strictest, and the consequences of error are borne by people who had no say in the decision. Traditional AI systems, designed for quarterly optimization in corporate settings, are not merely insufficient for this domain; they are actively dangerous, because they systematically undervalue long-term consequences and lack mechanisms for democratic accountability.

The Time-Extended Decision Network framework addresses these challenges through three contributions. First, it provides a formal mathematical representation of municipal systems as dynamic graphs that evolve over time, capturing migration flows, employment dynamics, infrastructure interactions, and fiscal relationships in a unified structure. Second, it introduces temporal responsibility gates that scale human deliberation in proportion to the decision's long-term impact, ensuring that transformative decisions receive council-level scrutiny while routine decisions are processed efficiently. Third, it integrates with the MARIA OS decision pipeline to provide full audit trails, evidence bundles, and retrospective accountability — the infrastructure required for democratic governance in an AI-assisted world.

12都市にわたる340の地方自治体の決定に関する遡及的検証は、TEDNが既存のモデルよりも大幅に正確な影響予測を生成することを示しています。移住予測の精度は89.3％（最良のベースラインの83.3％に対して）、雇用カスケード検出の再現率は94.1％（対58.7％）、r二乗 = 0.93で専門家の判断と相関する時間的ホライズンの推定です。ゲート システムは、長期的な影響が最も大きい意思決定の 12% に人間によるレビューを集中させ、一般的な手動レビューと比較してレビュー時間を 75% 節約し、ミス率を 3.3% 未満に維持します。

The deepest insight of this work is that long-horizon AI assistance is not in tension with democratic governance — it is a prerequisite for it. Without computational tools that make the multi-generational consequences of decisions visible and quantifiable, democratic deliberation about long-term issues is necessarily uninformed. With the TEDN, a city council considering a 50-year infrastructure investment can see the migration cascades, the employment effects, the intergenerational equity implications, and the distributional impacts across cohorts — all computed from a calibrated model of their specific city. This does not replace democratic judgment. It gives democratic judgment the information it needs to operate at the timescales that municipal decisions demand.

The challenge ahead is not technical but institutional. Municipal governments must develop the capacity to use AI decision support tools responsibly: training staff to interpret TEDN outputs, establishing governance frameworks for gate calibration, building public trust through transparent retrospective accountability, and navigating the political dynamics of quantified long-term impact. MARIA OS provides the technical infrastructure for this institutional transformation. The transformation itself is a human endeavor — exactly as it should be.