Appendix: physical and financial calculation dictionary

The technical appendix defines the retained calculation as a reproducible instrument. It accepts a complete annual electricity input object, validates the schema and measure identities, computes sequential states, and returns physical, economic and diagnostic output. The same canonical module is used by the Studio and the research reproducer. The manuscript does not implement a competing spreadsheet or Python transition model. Retained inputs and complete outputs permit another analyst to reconstruct the exact conditional calculation while keeping parameter validity and field performance as separate questions.

The input contract is more precise than a form label. Every required field has a numerical or structural type, an allowed range and a declared unit. Measure names must be unique within the package. Unknown fields are rejected rather than silently interpreted as additional model features. Missing fields, nonfinite values and values outside the supported numerical precision are errors. A legitimate zero remains a supplied value; a missing energy, price or cost does not become zero. The exported machine-readable schema is retained with the study files, and its identity is checked against the catalogued app schema.

The measure array supplies the state-transformation order. Each measure reduces the demand remaining at that step by its supplied percentage, then adds its supplied electrical demand. Its renewable quantity increases the cumulative annual supply available in the screen. The quantity used is capped at current demand, and grid energy supplies the remainder. The resulting emissions and energy cost follow the respective supplied factors and prices. This interpretation is central to replication: the percentage does not automatically apply only to a particular device, and the supplied renewable quantity is not necessarily the amount used after the cap.

The baseline state uses the supplied annual demand on the grid basis before listed measures. Incremental abatement compares the emissions immediately before and after a measure. Incremental energy-cost saving compares the corresponding energy expenditure. The measure cost combines equivalent annual capital, its supplied continuing expenditure and its energy-cost saving. The package comparison instead relates the final state to the baseline and includes all listed capital and continuing costs. These reference states should be retained when selecting an output pointer; a measure increment and a package result are different quantities.

The financial convention is a constant annual benefit with upfront capital. The discounted annuity factor converts that annual benefit over the supplied horizon and rate. At a zero supplied rate the factor uses the horizon directly, which avoids a spurious division problem. The package NPV applies that factor to net annual savings and subtracts total listed capital. Annualised net cost converts capital to an equivalent annual amount and subtracts the same annual saving. These are compatible descriptions of the retained simplified case. Neither includes debt, tax, commissioning, replacement or a time-varying benefit path.

The abatement-cost metric is defined when its computed annual abatement denominator is strictly positive. A small positive denominator produces a ratio and can magnify uncertainty in the inputs; there is no additional positive cutoff. A zero or negative denominator produces an unavailable ratio. In that case the frozen output retains null, and the publication renders it as not defined. The result must not be replaced by a numeric zero or sorted as a free reduction. A negative net cost with positive abatement is a different case: it indicates a conditional annualised saving per attributed reduction. The technical distinction is preserved in the small-denominator and zero-denominator studies.

The reverse diagnostic runs the same supplied measures in reversed order and returns final demand, emissions and NPV. It does not return a full reversed incremental ledger or a reversed package-abatement field. The manuscript therefore selects only quantities actually present in that diagnostic when reporting it. It does not invent a missing scalar through a separate calculation. The diagnostic can reveal a scope interaction, but it does not test feasibility of either order. Engineering must interpret whether a percentage can affect the demand introduced by another measure.

The built-in sensitivity tests retain the physical package and use the supplied prices, common price-level alternatives and a reduced grid-factor alternative. Both energy prices move together in the price-level tests, while measure operating expenditure remains supplied. The factor test changes grid attribution without changing price. These are deterministic selected conditions. They contain no assigned likelihood, forecast call or global optimisation. A relative-price change, such as the separately retained adverse-price study, is a distinct authored input case and should be described as such.

Warnings identify numerical interpretations that need attention. A measure with nonpositive incremental abatement has no meaningful reduction-cost ratio. Annual supply beyond demand receives no export revenue or extra emissions credit. A supplied renewable factor above the grid factor can make displacement adverse under the retained basis. A reversal that changes the physical result points to a sequential scope assumption. Warnings are part of the complete output, but their absence does not establish field feasibility or recognised reporting. A user should retain the method limits alongside every case.

The output has several representations of the same conditional state. Top-level fields support exact scalar bindings, measure records support the sequential ledger, and tables and metrics support readable app output. The research bindings select scalar input or output pointers and attach them reciprocally to published blocks. Reproduction recomputes the complete output before checking the selected claims. This prevents a paper from preserving only favourable summaries while the runnable case has changed. The ledger is an evidence link, not an independent source of truth that can override the canonical computation.

Verification combines exact reproduction with independent expected cases and invariants. Hand-selected physical expectations test demand, grid and renewable allocation, emissions direction, curtailment and supplied annual cash arithmetic. A zero-rate financial boundary tests the constant-benefit identity without constructing a competing discount model. Conservation, nonnegative used quantities and unavailable-ratio conditions test relations across outputs. Invalid and incomplete inputs test that errors remain errors. The paired overlap and reversed-demand checks test different sequence consequences. These checks improve confidence in the conditional engine while remaining separate from evidence that any fixture describes a real facility.

The retained figures use output pointers for every plotted coordinate. Deterministic drawing changes only coordinate scale and typography; it does not recompute transition economics. Adjacent specifications allow the audit to redraw the figures and compare their assets and scalar claims. Connectors between stages or selected tests organise the points and retain explicit reading limits. They do not add uncomputed intermediate states, probability curves or schedules. A reader should use the accompanying tables for exact values and the figure for the relationship it is designed to expose.

Fit an applied question to the instrument by tracing it through the available fields. A supported annual demand, factor basis, price and measure sequence can populate the retained screen. A duty-specific load interaction, payment for unused nominal supply or time-critical resilience objective needs a representation the screen does not provide. Identify that mismatch before entering a convenient substitute value. Preserve the complete input for replication and the omitted-mechanism explanation for interpretation. If another method is necessary, disclose its own basis and reproducibility separately. The calculation dictionary enables this fit test without treating a structurally valid input as evidence that the applied question has been answered.