# CE Stress Fragility Overlay — Methodology
# Model ID: ce-stress-fragility
# Version: 3.7.0
# Last updated: 2026-05-17
# Type: combined
# Geography: Global (sector-level stress)
# Horizon: 2025–2045

## Summary
CE's dedicated downside stress model for portfolio risk assessment under fragmented, delayed, or emergency climate transition scenarios. Applies stress-calibrated component fusion to quantify sector fragility — the compounded exposure of high transition pressure, low resilience, and elevated cross-sector contagion risk. Use this model as the downside boundary condition for stress testing; use the CE Balanced Transition Synthesizer for base-case positioning.

## Methodology Detail
The CE Stress Fragility Overlay applies the same three-component fusion architecture as the CE Balanced Transition Synthesizer — physical climate × economic conditions × transmission channels — but with stress-calibrated component weights. Under the balanced model, component weights are calibrated to orderly transition dynamics. Under the stress overlay, the climate (physical + transition) and transmission components are upweighted, and the economic stability component is downweighted, to model scenarios where regulatory incoherence, delayed policy action, or compounding physical hazard dominate over macro stabilisers.

A sector's fragility index is computed as: Fragility = f(transition_pressure, 1 − resilience, transmission_amplification). Sectors with fragility index >0.70 are classified as structurally fragile and receive an additional downside amplification factor. Company-level fragility indicators (SBTi commitment credibility score, fossil asset lock-in ratio, regulatory compliance cost cliff) are applied to stress sector signals above their balanced-model equivalents.

The model is calibrated against the NGFS Phase 4 'Delayed Transition', 'Current Policies', and 'Hot House World' scenario families — the three NGFS families representing fragmented, delayed, or insufficient policy action — as well as the FSB severe climate scenario for financial stability analysis and the Bank of England CBES 'Late Action' scenario. The stress overlay is the formal lower bound of CE's combined model spectrum.

## Key Mechanisms
- Stress-calibrated component weights: climate (physical + transition) and transmission signals are upweighted relative to the balanced model; the economic stabiliser component is downweighted to reflect scenarios where monetary and fiscal policy cannot fully offset climate-driven financial losses
- Fragility index computation: each sector receives a fragility score combining transition pressure, the inverse of resilience, and transmission amplification — sectors above the 0.70 threshold are classified structurally fragile and receive an additional downside amplification factor calibrated to FSB severe scenario outcomes
- Policy fragmentation penalty: the spread between coordinated and fragmented policy regimes is modelled as an additive pressure component — calibrated to the NGFS Delayed Transition versus Orderly Transition scenario spread, quantifying the additional loss burden from policy incoherence
- Regulatory shock compression: delayed action followed by rapid policy catch-up creates larger concentrated losses than orderly transition — modelled as a time-compression multiplier on baseline transition pressure, derived from Bank of England CBES Late Action scenario sector stress outcomes
- Stranded asset scenario: companies with fossil asset lock-in ratios above 60% (long-life production assets benchmarked to IEA Fossil Fuel Asset Stranding data) face acute write-down risk under delayed-then-sudden policy acceleration; this risk is operationalised as a company-level fragility indicator applied to sector pressure signals
- Cross-sector contagion amplification: transmission channel weights are elevated to capture how stress propagates across sector boundaries — insurance retreat creates a real estate credit squeeze; fossil asset stranding escalates banking non-performing loans; agricultural supply shock drives food inflation that compresses consumer discretionary demand
- Physical hazard compounding: consecutive-year climate events (drought followed by wildfire, flood followed by heat) are modelled as multiplied probability impacts rather than summed — reflecting empirical evidence from Swiss Re Sigma compound event data that co-occurring hazards produce losses exceeding the sum of individual event impacts
- Commitment credibility discount: SBTi and net zero pledges from companies with >2 years since last verification, no published interim milestones, or known implementation gaps receive a credibility discount that increases their sector's transition pressure signal — preventing commitment wash from artificially suppressing stress signals

## Strengths
- Explicitly calibrated to tail-risk scenario families (NGFS Delayed Transition, Current Policies, Hot House World) — not extrapolated from base-case; the model captures mechanisms that are qualitatively different under fragmented policy, not just higher-magnitude orderly-transition signals
- Fragility index architecture separates directional risk (pressure) from structural vulnerability (low resilience combined with high transmission exposure) — identifying sectors at risk of non-linear deterioration rather than simply high-pressure but stable sectors
- Regulatory shock compression uniquely quantifies the 'policy catch-up penalty' — the additional loss burden from compressed transition timelines that is the defining mechanism of delayed-action scenarios; NGFS Delayed Transition is the most policy-realistic scenario for many jurisdictions and this model captures its financial signature
- Cross-sector contagion explicitly models insurance-to-real-estate and fossil-asset-to-banking transmission channels — providing the financial system cascade risk that standard sectoral models omit, directly relevant to macro-prudential stress testing
- Compatible with ECB Biennial Exploratory Scenario and Bank of England CBES 'Late Action' scenario — outputs can be positioned alongside supervisory stress test publications without translation, supporting regulatory stress testing workflows
- Designed as the formal companion model to the CE Balanced Transition Synthesizer — running both defines the CE combined model confidence interval; the spread between them is the model's range, and the analyst's job is to weight scenarios based on the current regulatory environment

## Limitations
- Systematically overstates pressure under orderly transition conditions — stress component weights are calibrated for fragmented/delayed scenarios; using this model for base-case analysis will produce misleading sector signals
- Macro stabilisers (monetary easing, fiscal emergency stimulus, IMF/World Bank emergency lending) are underweighted by design — in practice, sovereign interventions have historically contained some climate-related financial stress episodes; this model does not model the stabiliser response and will overstate unmitigated losses
- The fragility index threshold of 0.70 is calibrated against historical sector crises (2008 banking fragility, 2011 Thai flood supply chain disruption) — the precise threshold carries ±0.05 uncertainty; sectors scoring 0.65–0.75 should be treated as borderline fragile rather than definitely classified
- Physical hazard compounding multiplier is derived from observed compound event patterns (2011 Thailand floods + 2012 US drought) — for genuinely unprecedented compound event types with no historical parallel, the multiplier may misestimate the compounding factor
- Company-level fragility indicators are updated on an annual cycle — sectors with rapid net zero commitment momentum may carry stale fragility scores between update cycles, temporarily understating the improvement in sector resilience

## Terminology Note
- '52 Gt total abatement required' (KPI): net reduction from 57 GtCO2e/yr baseline to 5 GtCO2e/yr net-zero residual.
- 'G_2050 = 47 Gt annual gap': annual policy-to-NZ gap at 2050, because under current policy
  the trajectory reaches only ~52 GtCO2e/yr by 2050 (not the 57 Gt baseline).
  G_t = CURRENT_POLICY[t] - NET_ZERO_PATH[t]; at t=2050: 52 - 5 = 47 Gt.

## Core Equations
G_t = E_t_policy - E_t_NZ                               (annual abatement gap)
T_t_s = sum(A_i_t_s for i in 1..N) * (1 - delta)       (tech coverage; delta=0.15)
B_t_s = max(G_t - T_t_s, 0)                            (breakthrough gap)
tau = min{t | sum(E_y_policy, y=2025..t) >= C}         (budget exhaustion year)
G_t_j = w_j * G_t                                       (sector decomposition)

## De-duplication Discount
delta=0.15 is a central estimate for cross-sector emission overlap.
Primary overlap sources: (i) green H2 and SAF both reduce transport fossil demand (~2-3%);
(ii) BECCS and enhanced weathering both draw on land-based biological carbon sinks (~3-4%);
(iii) ocean iron fertilisation and enhanced weathering compete for ocean sink capacity (~2%);
(iv) green steel and recycling address overlapping industrial-process emissions (~2-3%).
Estimated total overlap range: 13-18%; 15% used as central estimate.
Sensitivity: ±5pp change in delta shifts B_2050_base by approximately ±2 Gt.

## Data Sources
- UNEP Emissions Gap Report 2024 (baseline 57 GtCO2e/yr)
- IPCC AR6 WG3 SPM Table 3.2 (net-zero C1 pathway)
- IPCC AR6 WG1 Table SPM.2 (carbon budgets; original 2020 reference: 400 Gt for 1.5C at 67%;
  adjusted to ~250 Gt from 2025 by deducting ~150 Gt emitted 2020-2024; AR6-adjusted illustrative
  budget, uncertainty ±50 Gt. Independent check: GCB 2024 (ESSD 2025) gives ~235 Gt from Jan 2025
  at 50% probability — consistent within uncertainty bounds given different probability threshold.)
- IPCC AR6 WG3 Chapter 6 (sector abatement proportions)
- IEA Net Zero by 2050 NZE 2023 (mature technology ceilings)
- CE Emerging Technology Library v3.1.0 (12 technology abatement ranges; public provenance table
  at /models/ce-solution-scale — sources, TRL, EROI, counterfactuals, overlap deps, feasibility ceilings per technology)
  Machine-readable constants: /models/ce-solution-scale/assumptions.json

## Uncertainty Quantification
Scenario probabilities: P(optimistic)=0.25, P(base)=0.50, P(pessimistic)=0.25.
Expected value: E[B_2050] = 0.25*B_opt + 0.50*B_base + 0.25*B_pes.
Monte Carlo CI: delta~N(0.15,0.03), per-tech abatement perturbation drawn from a 3-factor co-variance model.
Factors: global transition momentum (bGlobal=0.35*sigma), electricity/grid sector (bElec=0.30*sigma),
CDR governance (bCDR=0.35*sigma). Variance-preserving: idiosyncratic sigma = sigma*sqrt(1-bG^2-bE^2-bC^2).
Implied cross-tech correlations: rho(elec pairs)~0.21, rho(CDR pairs)~0.25.
Positive co-variance widens CI vs independent draws (correct direction: shared policy/finance shocks
cause portfolio-level fat tails). sigma_i=0.30 for fusion/DAC/ocean_iron; 0.15 for other 9 techs. N=600.
Output: 80% CI on breakthrough gap (P10/P90).

## Deployment Constraints (v2.2.0+)
Interactive sliders model four institutional deployment barriers:
1. Permitting/build delay (0-10 yr): shifts each tech trajectory right in time.
2. Grid interconnection queue (0/3/6 yr): extra delay for grid-dependent techs.
3. Political continuity risk: post-reversal-year values switch to pessimistic scenario.
4. Cost-of-capital stress (+100/200/400 bps): global finance multiplier 0.95/0.88/0.78.

## Transition Economics (v2.2.0+)
Marginal Abatement Cost (MAC) ranges per technology at 2040+ deployment scale.
Sources: IEA WEO 2024, IRENA 2023, IEA GHR 2023, IEA DAC 2022, IPCC AR6 WG3.
NPV calculated at SCC=$190/tCO2 (US EPA 2023). Discount rates: 2%, 5%, 10%.
All NPV estimates positive across full range of mainstream discount rates.

## Workforce Impact (v2.4.0+)
Per-technology direct employment estimates at CE base-scenario 2050 deployment scale.
Sources: IRENA WESO 2024; IEA WEO 2024; ILO WESO 2022; IEA DAC 2022; IPCC AR6 WG3 Ch.17.
Peak deploy jobs (M): construction/manufacturing surge 2025-2040 (temporary).
Ops/mfg 2050 (M/yr): permanent direct ops, maintenance, and ongoing manufacturing.
Direct displaced (M): job losses in directly substituted incumbent sectors only.
Portfolio net: ~+12M direct ops jobs; separate fossil at-risk: ~10M (coal ~7M + oil/gas ~3M).
Economy-wide net (before supply-chain multipliers 1.5-3x): ~+9 to +12M by 2050.
All estimates carry +/-40-60% uncertainty at global scale.

## Infrastructure Sequencing (v2.5.0+)
9 foundational infrastructure investments mapped to must-start and must-complete years for 2050 critical path.
Urgency tiers: Critical (must start <=2026), Soon (2026-2028), Planned (2028+).
Critical: permitting reform, grid transmission expansion, MRV standards (CDR), nuclear regulatory pathway.
Soon: critical minerals supply chain, sustainable biomass supply, CO2 transport & storage network, green H2 hubs.
Planned: ocean governance framework (London Protocol+).
Sources: IEA NZE 2023; IPCC AR6 WG3 Ch.6; BloombergNEF ETI 2024; IRENA 2024.

## State Capacity Index (v2.5.0+)
Per-country implementation readiness for top 20 emitters (~77% of global GHG emissions).
WGI Government Effectiveness percentile rank (World Bank 2022/2023).
Tier 1 (>=75): USA, Germany, Japan, UK, France, Canada, Australia, S. Korea -- ~25% of emissions.
Tier 2 (40-74): China, India, Indonesia + 7 others -- ~45% of emissions.
Tier 3 (<40): Russia, Iran -- ~7% of emissions.
Source: World Bank WGI 2022; IEA 2023; Global Carbon Budget 2024.

## Model Assumptions Registry (v2.6.0+)
All structural constants with tested range and B_2050 sensitivity documented in-page.
Key sensitivities: baseline +-2 Gt -> +-2 Gt; delta +-5pp -> +-2 Gt; sigma(high) +-0.10 -> +-2 Gt P90.
Full table at /models/ce-solution-scale (Model Assumptions Registry section).

## Geographic Resource & State Capacity Cross-Link (v2.6.0+)
10 technologies mapped to critical resource geographies and State Capacity tier.
Key findings: DRC cobalt (BEV batteries) is Tier 3 equivalent -- governance deficit flagged.
Perovskite solar: ~85% manufacturing in China (Tier 2) -- supply-chain concentration risk.
Ocean iron fertilisation: multi-jurisdictional governance (London Protocol) -- T3/N/A tier.
BECCS/SAF bio-feedstock: Brazil and Indonesia Tier 2 -- deforestation governance risk.

## Policy Effectiveness Validation Backtest (v2.6.0+)
7 major climate policies benchmarked against 2020-2025 observed delivery:
- Paris NDCs aggregate: ~50% delivery (15% vs 30% below BAU) -- consistent with CE near-flat baseline.
- EU Green Deal: ~78% delivery -- CE Tier 1 capacity assumption validated.
- US IRA: ~68% delivery -- consistent with CE optimistic scenario demand-side pull.
- China Dual Carbon: <50% delivery -- consistent with CE near-flat China baseline.
- IEA NZE solar target: ~67% delivery but pace accelerating -- supports CE optimistic perovskite ramp.
- Global EV targets: ~30% delivery -- CE BEV base scenario consistent with observed trajectory.
- EU ETS carbon price: >100% (exceeded target price) -- validates CE NPV framework direction.

## Sensitivity Tornado Chart (v2.7.0+)
6-parameter B_2050 impact ranking (Chart.js horizontal floating bars).
Technology opt-pes spread: +-8.5 Gt (dominant, 4x all others combined).
Baseline emissions +-2 Gt -> +-2 Gt; De-dup delta +-5pp -> +-2 Gt.
Scenario probs P(opt) +-0.10 -> +-1.5 Gt; MC co-variance rho 0->0.4 -> +1.5 Gt CI widening.
Net-zero residual +-1 Gt -> +-1 Gt.

## EROI-Adjusted Abatement (v2.7.0+)
Grid carbon intensity penalty for energy-intensive removal technologies.
DAC (2000 kWh/tCO2): current grid (0.42 kgCO2/kWh) reduces 1.8 Gt gross to 0.36 Gt net (-80%).
DAC at 2035 grid (0.15): net 1.53 Gt (-15%); at 2050 clean grid (0.02): net 1.73 Gt (-4%).
BECCS (~200 kWh/tCO2): current grid -8%; 2050 grid 0%. Enhanced Weathering ~140 kWh: current -6%.
Key finding: DAC only viable at scale on near-zero-carbon grid (post-2035 deployment preferred).

## Investment Gap Panel (v2.7.0+)
Current 2024 vs required 2035 capital deployment by technology ($B/yr).
Portfolio current: ~$470B/yr; required 2035: ~$1.3-2.0T/yr; whole-portfolio gap: ~3-4x.
Largest relative gaps: Enhanced Weathering 200-400x; Ocean Iron 40-100x; Perovskite 16-30x.
Sources: IEA WEI 2024; BloombergNEF 2024; IRENA 2023; IEA GHR 2023; IEA DAC 2022.

## Carbon Budget Delay Cost (v2.7.0+)
Cumulative GtCO2 consumed by 5yr or 10yr deployment slip per technology.
Formula: 5yr cost = (b[4]+b[5]-b[0])*2.5*(1-delta); sorted descending by 5yr cost.
Highest delay cost: Perovskite 24.4 Gt (5yr); BEV 18.9 Gt; BECCS 17.9 Gt; Green H2 17.0 Gt.

## Technology Cliff Dates (v2.7.0+)
Latest year to make binding go/no-go deployment commitment per technology.
At cliff now (2026): Green H2 (electrolyzer orders), High-Albedo (building codes), Recycling (EPR regs).
1yr window (2027): Perovskite, DAC, BECCS, Enhanced Weathering, SAF, Green Steel.
2yr window (2028): Nuclear Fusion (SPARC ignition -> FOAK decision).
Committed: BEV. Governance-gated: Ocean Iron (London Protocol amendment first).

## IPCC Scenario Band Mapping (v2.7.0+)
CE portfolio scenarios mapped to IPCC AR6 WG3 C1-C7 pathway categories.
CE Optimistic: ~9.6 Gt residual -> C2 (1.5C limited overshoot) -- with mature tech could reach C1.
CE Base: ~25.2 Gt residual -> C4 (below 2C ~66%).
CE Pessimistic: ~38.5 Gt residual -> C5 (below 2.5C).
Current policy (no emerging tech): 57 Gt -> C7 (above 3C median).
Sources: IPCC AR6 WG3 Table SPM.1 (2022) for C-category thresholds.

## Scientific Precision Corrections (v3.0.0+)
CCS injection ceiling: previously stated as '8-10 Gt/yr geological storage capacity (IPCC)'. Corrected:
  IPCC AR6 WG3 C1 scenario range is 4-15 Gt/yr for CO2 injection rates; CE uses 8-10 Gt/yr as mid-range.
  Physical geological storage volume (hundreds of Gt) is NOT the binding constraint -- injection rate infrastructure is.
Committed emissions: primary citation added -- Tong et al. 2019 (Nature 572, 373-377): 658 GtCO2 from 2018
  operating fossil-fuel infrastructure (operating assets only, excl. planned/permitted pipeline).
  CE 680 Gt figure adds ~22 Gt additional 2018-2025 committed build; consistent with Tong upper bound.
BECCS biomass: 3.5-5.5 EJ/yr is a conservative no-regrets floor (zero food/land conflict scenarios).
  Full IPCC AR6 WG3 Ch.7 sustainable bioenergy range: 50-250 EJ/yr (wide, heavily sustainability-constrained).
  CE does not use the upper end; 3.5-5.5 EJ/yr represents lowest-controversy deployment ceiling only.
Carbon budget: AR6 WG1 Table SPM.2 400 Gt (67% probability, 2020 reference) cross-checked against
  GCB 2024 (ESSD 2025) ~235 Gt from Jan 2025 at 50% probability. CE 250 Gt figure is consistent
  within stated uncertainty bounds given the different probability threshold (67% vs 50%).

## Assumptions API (v3.0.0+)
All 10 structural constants with source lineage, uncertainty ranges, and scope notes available at:
  GET /models/ce-solution-scale/assumptions.json
  Returns: model_id, version, generated date, epistemic_status, comparable_to / not_comparable_to lists,
  assumptions array (constant, value, unit, source, scope, uncertainty, last_reviewed per entry),
  scenario_probabilities, and reproducibility links.
Machine-readable; CORS open (*); suitable for programmatic audit by institutional users.

## Platform Positioning (v3.0.0+)
CE is a TRANSPARENT TRANSITION DIAGNOSTIC platform, not a predictive IAM.
Methodology class: bottom-up gap accounting -- same as UNEP Emissions Gap Report and IEA NZE scenario accounting.
CE does NOT produce: equilibrium temperature projections, macro-economic forecasts, probabilistic damage estimates.
CE DOES produce: technology portfolio coverage quantification, committed-emissions accounting,
  breakthrough gap sizing, deployment-ceiling analysis, and cross-sector de-duplication.
Appropriate use: institutional transition planning, policy gap analysis, technology prioritisation,
  portfolio stress-testing, and complementary analysis alongside NGFS scenarios.
Not appropriate as a standalone substitute for: NGFS scenario sets, IPCC AR6 physical science,
  probabilistic IAM runs (DICE, PAGE, MESSAGE-GLOBIOM, REMIND), or national GHG inventories.

Structural accounting / gap model. Not a probabilistic forecast.
Outputs are scenarios conditioned on IPCC pathway assumptions.
Comparable to IEA NZE scenario accounting and UNEP Emissions Gap Report methodology,
not to predictive IAMs (DICE, PAGE, FUND, MESSAGE).
Computation is client-side JavaScript; fully reproducible from cited sources.