h(t|X) = h₀(t)·exp(ΣβᵢXᵢ) — field-level survival/hazard estimation. Confirmed covariates: water_cut HR=2.522***, decom_dp_approved HR=6.528***, section29_high HR=3.421***, epl_rate_lag2 HR=2.023*** (COX-13). FPS subgroup decom_dp HR=12.877***. Era VII water_cut HR=4.014*. Drives field-level CoP probability curves, basin-wide CoP ranking, and EPL hazard decomposition.

S(t) = Π(1−dⱼ/nⱼ) — non-parametric survival by operator archetype, with Greenwood variance and log-rank testing. SNI archetype CoP rate = 9.91% vs IOC/PE-backed = 0%; all 23 2024 CoP events were SNI operators — complete separation. Weibull overlay produces median lifespan comparisons by archetype for capability briefings.

Yₜ = β₀ + β₁T + β₂Dₜ + β₃Pₜ + εₜ — isolates policy-attributable level-shift (β₂) and slope-change (β₃) from pre-existing trend. EPL-1 (May 2022, 25%), EPL-2 (Nov 2022, 35%), EPL-3 (Oct 2024, 38%) as sequential interruption points. Underpins the OBR–HMRC divergence finding (£44.6bn, 2023–28) for OEUK reform advocacy and SSRN submission.

Aₜ = A₀·e⁻𝖾ᵗ ·(1+δRₜ) — asset attrition as a function of acceleration coefficient γ and regulatory burden Rₜ. SAM-01 baseline=271; recalibrated RATE-02=2.53% (2015–2021 canonical window); fiscal death cross ratio 0.390 (2024), projected ~2027. S1/S2/S3 scenario projections: 138/221/195 fields preserved at 5-year horizon, with S2 vs S1 = +83 fields, +£0.9bn revenue.

V_h = Σ(wᵢLᵢ)/I_h — hub vulnerability index from throughput weight, operational load and structural integrity; cascade triggers when failed-infrastructure fraction exceeds threshold θ. Confirmed 2030 hub-failure probabilities: FPS 83.0%, Norpipe 99.8%, FLAGS 100%, FUKA 92.3%, Bacton 96.1%. FPS throughput: 507→216 kb/d (2016–2024, -57.4%), metabolic floor ~150 kb/d, breach ~2028. Network cascade probability rises from 0.516 (isolated) to 0.790 (full network interdependence).

DS = ΣλₖSₖ — weighted composite of cash-flow volatility, debt-service coverage, asset obsolescence, regulatory indemnity risk, and decommissioning liability exposure, drawn from Companies House statutory accounts. Identifies ETR anomalies (Serica 176%, Harbour 107.6%) and ARO-to-PP&E extremes (Apache 257%, TAQA -$214m despite +67% abandonment spend). ARO-stripping signal flags back-chain ring-fencing; section29_high HR=3.421 quantifies resurrection-risk once a back-chain notice is live.

Twelve-category Fiscal Environment taxonomy (FE-01–12) by Brent price bracket, political regime and statutory tax rate; imprinting mechanism links an operator's founding FE to its permanent cost structure. Ecological Eras tracked via the Development-to-Decommissioning (D/F) ratio: population peaked at 332 fields (2018); D/F ratio 2024 = 23.00; ECO-03 death cross confirmed 2014/2015 ±1yr — a nine-era basin-maturity taxonomy.

Cross-validation of internal model outputs against independent industry and regulatory sources. Carbon arbitrage: UKCS domestic gas 28 kgCO2e/boe vs imported LNG 85 kgCO2e/boe = 3.04x multiplier (NSTA Sept 2025, Westwood-corroborated). P&A backlog: 500+ wells past deadline, 103 completed 2024 vs ~300/yr required, £3bn cost-estimate increase (£24bn→£27bn, 2023–32). Westwood Sept 2025 and OEUK 2026 independently corroborate the 2027–2028 threat window identified by the Cox PH/SAM/CCM models.

No technique above operates in isolation. A typical engagement chains several: Cox PH identifies which fields are at risk (01), CCM models how that risk propagates through shared infrastructure (05), CDS scores the operators most exposed (06), and SAM/scenario projections (04) quantify the fiscal consequence of acting versus not acting. The output is a single coherent argument, not a stack of separate analyses — built once from the V15.5.1 panel and repackaged per client category in Services.