# World Ledger 2026: evidence and mathematical methods

Prepared 16 October 2026. Thirty retrospective essays cover January through 16 October, three per month. Publication is October 16; monthly focus is not an assertion of earlier authorship. The inherited research contains 382 dated claim lines and 363 distinct URLs. That is an inventory, not 382 independently established facts. Each writer's research note records the primary sources selected and access limitations.

## Reading the two founding documents

The user's World State forecast, dated October 13, distinguishes observations, estimates, institutional forecasts and judgment. Its 100,000 scenario draws cannot establish predictive calibration. We preserve that evidence boundary. Its five scenario weights are judgments, not observed frequencies. The new accounting calculations below do not fit or validate those weights and do not generate market targets.

Kenya Vision 2060 is Derrick Macharia's founder-authored operating thesis, not an adopted Kenyan government plan. Its central insight is that abundant intelligence increases the value of scarce complements: reliable energy, food systems, trusted institutions, physical infrastructure, clinical capacity, and productive ownership. Its 7% real-growth trajectory is an ambition. Its AGI planning windows are conditional, not a dated scientific consensus.

## What this model can say

Forty-five named parameters feed five joint accounting scenarios: reference, adaptation, supply shock, credit squeeze, and compound disruption. All changes are exposed in model-results.json. These are conditional calculations, with no scenario probabilities or fitted causal coefficients. The crisis paths are stress cases, not measured odds. We do not manufacture quantitative measures of planetary psychology, gender conflict, war escalation, AGI arrival or institutional collapse.

Four historical inputs come from the Treasury's January 2026 debt strategy and KNBS's September CPI release. External debt share is derived from two historical Treasury amounts. The other parameters are assumptions, including the two rounded population anchors carried from Vision 2060. Parameters labelled J are not current observations. The effective debt rates are illustrative averages, not policy rates. Token pricing is hypothetical, not a vendor quotation. A model with 45 inputs is not 45 independent pieces of evidence.

The sovereign illustration starts from the Treasury's end-June 2025 debt balance of 67.8% of GDP, and its external-debt fraction of 5,488.46/11,814.47. It does not silently relabel this historical balance as October 2026. Model years 1–3 are three annual accounting steps from a hypothetical balance sheet with that historical composition; they are not 2027–29 official forecasts. External debt approximates FX debt, which is an imperfect proxy. Contingent liabilities and sovereign restructuring are absent.

## Equations and conventions

Nominal GDP growth is (1 + real growth) × (1 + GDP deflator) − 1. The deflator and CPI are different variables. This prevents adding real growth and inflation while omitting their product.

For each annual step, debt/GDP = previous debt/GDP × [(1 − external share) × (1 + domestic effective rate) + external share × (1 + foreign effective rate) × (1 + FX depreciation)] / (1 + nominal GDP growth) − primary surplus/GDP + stock-flow adjustment/GDP. Primary surplus is positive; deficits are negative. FX depreciation means more KES per unit of foreign currency. FX is applied at the end of the annual step in this simplified convention. After interest, exchange-rate revaluation and GDP growth, new financing or repayment follows the resulting debt composition. This is an explicit issuance assumption; it does not forecast Treasury's financing choices.

Illustrative household inflation = sum of fixed budget weights × division inflation. Weights describe an example household, not KNBS national weights. Real-income change = (1 + nominal wage growth)/(1 + household inflation) − 1. Holding division rates constant is a designed scenario, not an extrapolation supported by a fitted inflation process. Income support, substitution and changes in employment are omitted.

Food-preservation net monthly benefit = gross pre-loss produce value × (initial spoilage − final spoilage) × (1 − recovered-revenue variable-cost fraction) − intervention cost. Break-even gross value = intervention cost / [(initial spoilage − final spoilage) × (1 − variable-cost fraction)]. A change in grades or selling prices would require additional inputs. These are incremental operating benefits before capital costs, finance, tax and depreciation.

Clinic capacity = staff × patients per staff per day. Utilization = arrivals/capacity. Daily backlog addition = max(0, arrivals − capacity). This deterministic capacity calculation is not a queueing forecast: variability can create waiting even below 100% utilization, and disease severity changes service times. No Ebola reproduction number or case projection is estimated.

AI workflow cost = tasks × tokens per task × blended price per million / 1,000,000 + tasks × review minutes/60 × reviewer hourly rate + tasks × failure fraction × extra rework minutes/60 × reviewer hourly rate. Every task is reviewed. Failed tasks receive additional human rework, assumed successful. Taxes, platform overhead, exchange costs and autonomous retries are excluded. This shows why token costs alone are not the cost of verified work.

Monthly facility energy = IT kW × PUE × monthly hours × operating fraction. Power cost = energy × tariff. Hours use 730, a 365-day-year monthly average. The 10 kW facility illustration is independent of the AI workflow: combining them would require measured compute per task. Reduced uptime lowers billed electricity while also reducing available service; it is not a productivity gain.

Bond price change approximation = −modified duration × yield change + 0.5 × convexity × yield change squared. It omits coupon income, spread changes and higher-order terms. Long-run real output multiple = (1 + real growth)^years. Per-capita multiple divides this by the population ratio.

## Reproduced reference calculations

Example household: 45% food at 9.5%, 15% transport at 15.6%, and 40% other costs at an assumed 3.2% yield 7.895% basket inflation. With assumed 5% wage growth, purchasing power changes by -2.683%, not 5 − 7.895 exactly.

Food pilot: KES1 million gross monthly produce value, spoilage falling from 25% to 15%, 20% variable costs on recovered sales and KES60,000 monthly intervention cost yield KES20,000 net monthly incremental benefit. Break-even gross monthly value is KES750,000.

AI workflow: 10,000 tasks/month, 10,000 tokens/task and assumed USD2/million tokens cost USD200 for inference. Two minutes of review on every task at USD6/hour cost USD2,000; ten minutes of extra rework on 10% cost USD1,000. Total = USD3,200/month or USD0.32/completed task.

Clinic: 100 arrivals/day against 10 staff × 12 patients/day yields 83.33% deterministic utilization. At 170 arrivals and eight staff, capacity is 96/day and backlog grows by 74/day without response. Clinical triage, overtime, referral and staffing reactions are absent, so this is a trigger for intervention, not a forecast of an inevitable queue.

Bond illustration: duration8, convexity75, yield increase100bp gives an approximate price change of -7.625%, before income. Vision ambition: 7% compounded for35 years gives 10.6766× real output and 6.7077× per-capita output using the report's rounded population assumptions.

## Joint stress results

- Reference: illustrative debt/GDP at annual steps1/2/3 = 65.22%, 62.73%, 60.33%; example household real income after one year changes -2.68%; food-preservation incremental benefit KES20,000/month; clinic utilization 83.3%.
- Adaptation: illustrative debt/GDP at annual steps1/2/3 = 63.65%, 59.73%, 56.01%; example household real income after one year changes 1.73%; food-preservation incremental benefit KES44,000/month; clinic utilization 75.0%.
- Supply Shock: illustrative debt/GDP at annual steps1/2/3 = 69.57%, 71.41%, 73.33%; example household real income after one year changes -7.88%; food-preservation incremental benefit KES-20,000/month; clinic utilization 108.3%.
- Credit Squeeze: illustrative debt/GDP at annual steps1/2/3 = 77.99%, 89.69%, 103.14%; example household real income after one year changes -7.32%; food-preservation incremental benefit KES0/month; clinic utilization 91.7%.
- Compound Disruption: illustrative debt/GDP at annual steps1/2/3 = 81.21%, 97.43%, 117.15%; example household real income after one year changes -15.35%; food-preservation incremental benefit KES-74,000/month; clinic utilization 177.1%.


Debt ratios can decline when inflation raises nominal GDP, even while household welfare deteriorates. A falling debt ratio alone is therefore not proof of adaptation. Adverse scenarios do not assume immediate stabilizing fiscal or monetary reactions. In practice policy choices can change outcomes; fiscal capacity, exchange intervention, aid and clinical response belong in the next model version.

## Sensitivity, validation and reassessment

The executable performs 19 one-at-a-time parameter increases and records changes in six outputs. Perturbations use each variable's own units; their raw magnitudes are not comparable importance rankings. They are local sensitivities, not fitted effects, correlations or elasticities estimated from 2026. Joint scenarios expose interactions that one-at-a-time changes omit.

Numerical assertions independently reconcile the first annual debt identity, food-pilot arithmetic, AI full costs, household basket and clinic utilization. JSON rejects nonfinite values. These checks establish computational consistency, not out-of-sample predictive accuracy. No Monte Carlo sample size is used as evidence of skill.

The earlier session's F1–F12 probabilities remain inherited subjective judgments and uncalibrated. They are not outputs of this accounting model. To evaluate them, preserve exact event definitions, venues, time zones, observation dates and missing-data rules before resolution. A Brier score is (p − y)^2. A constant50% forecaster scores0.25 on each binary question; meaningful skill assessment also needs event-appropriate base rates and enough resolved forecasts. There are no resolved future events in this release and no claimed forecast track record.

The five leading tripwires are verified shipping availability and delivered fuel costs; local food/transport CPI; debt refinancing and FX liquidity; laboratory-confirmed transmission with consistent case definitions; and measured AI completed-task costs and reliability. Reassess after a material official change, rather than extrapolate a narrative indefinitely.

## Full parameter register

O = historical observation. J = analyst-specified illustrative assumption or user-report anchor not independently re-extracted. No source URL certifies a J parameter.

- debt_ratio: 0.678 GDP fraction [O]. End June 2025, not October 2026. Source: [MTDS](https://www.treasury.go.ke/sites/default/files/Latest%20updates/2026%20MTDS%20FINAL.pdf)
- external_share: 0.4645540596 fraction of debt [O]. End June 2025; external debt proxy for FX debt. Source: [MTDS](https://www.treasury.go.ke/sites/default/files/Latest%20updates/2026%20MTDS%20FINAL.pdf)
- domestic_rate: 0.1 annual effective rate [J]. Illustrative planning assumption.
- foreign_rate: 0.05 annual effective rate [J]. Illustrative planning assumption.
- primary_surplus: 0.01 current-year GDP fraction [J]. Illustrative planning assumption.
- stock_flow_adjustment: 0 current-year GDP fraction [J]. Illustrative planning assumption.
- real_growth: 0.05 annual fraction [J]. Illustrative planning assumption.
- gdp_deflator: 0.05 annual fraction; distinct from CPI [J]. Illustrative planning assumption.
- fx_depreciation: 0 annual fraction increase in KES per foreign currency [J]. Illustrative planning assumption.
- food_weight: 0.45 illustrative household basket fraction [J]. Illustrative planning assumption.
- transport_weight: 0.15 illustrative household basket fraction [J]. Illustrative planning assumption.
- other_weight: 0.4 illustrative household basket fraction [J]. Illustrative planning assumption.
- food_inflation: 0.095 year-on-year fraction [O]. September 2026 division, held constant only in scenario. Source: [KNBS](https://www.knbs.or.ke/wp-content/uploads/2026/09/Kenya-Consumer-Price-Indices-and-Inflation-Rates-September-2026.pdf)
- transport_inflation: 0.156 year-on-year fraction [O]. September 2026 division, held constant only in scenario. Source: [KNBS](https://www.knbs.or.ke/wp-content/uploads/2026/09/Kenya-Consumer-Price-Indices-and-Inflation-Rates-September-2026.pdf)
- other_inflation: 0.032 annual fraction; assumed composite, not measured housing division [J]. Illustrative planning assumption.
- wage_growth: 0.05 annual nominal fraction [J]. Illustrative planning assumption.
- monthly_income: 40000 KES/month [J]. Illustrative planning assumption.
- gross_produce_value: 1000000 KES/month before losses [J]. Illustrative planning assumption.
- spoilage_before: 0.25 fraction of gross produce value [J]. Illustrative planning assumption.
- spoilage_after: 0.15 fraction of gross produce value [J]. Illustrative planning assumption.
- variable_cost_share: 0.2 fraction of recovered revenue [J]. Illustrative planning assumption.
- intervention_cost: 60000 KES/month [J]. Illustrative planning assumption.
- health_arrivals: 100 patients/day [J]. Illustrative planning assumption.
- staff_count: 10 staff [J]. Illustrative planning assumption.
- capacity_per_staff: 12 patients per staff per day [J]. Illustrative planning assumption.
- ai_tasks: 10000 tasks/month [J]. Illustrative planning assumption.
- tokens_per_task: 10000 billable tokens/task [J]. Illustrative planning assumption.
- token_price: 2 USD per million blended tokens; hypothetical vendor price [J]. Illustrative planning assumption.
- task_failure_rate: 0.1 fraction requiring rework [J]. Illustrative planning assumption.
- review_minutes: 2 minutes per task; every task reviewed [J]. Illustrative planning assumption.
- review_rate: 6 USD/hour [J]. Illustrative planning assumption.
- rework_minutes: 10 minutes per failed task, additional to review [J]. Illustrative planning assumption.
- power_kw: 10 kW IT load [J]. Illustrative planning assumption.
- pue: 1.4 total facility energy / IT energy [J]. Illustrative planning assumption.
- power_price: 0.15 USD/kWh [J]. Illustrative planning assumption.
- uptime: 0.95 fraction of monthly hours operating [J]. Illustrative planning assumption.
- hours_per_month: 730 hours; 365-day-year monthly average [J]. Illustrative planning assumption.
- fx_kes_usd: 130 KES/USD; rounded illustrative conversion [J]. Illustrative planning assumption.
- bond_duration: 8 years, modified duration [J]. Illustrative planning assumption.
- bond_convexity: 75 years squared [J]. Illustrative planning assumption.
- yield_shock: 0.01 yield fraction, 100 basis points [J]. Illustrative planning assumption.
- population_2025: 57.53 million [J]. User Vision 2060 rounded UN WPP anchor, not independently re-extracted.
- population_2060: 91.57 million [J]. User Vision 2060 rounded UN WPP projection, not independently re-extracted.
- vision_growth: 0.07 annual real fraction; ambition, not forecast [J]. Illustrative planning assumption.
- vision_years: 35 years from 2025 to 2060 [J]. Illustrative planning assumption.

## Reproduction

Run `python3 scenario_model.py` with Python3.9 or newer. No dependencies, credentials or network calls are required. model-results.json retains unrounded outputs, sources, all scenario overrides and sensitivities. Narrative rounding does not replace the full precision file.