Appendix: illustrative commercial engines

The illustrative study slate is a set of mechanism and boundary cases, not a sample of businesses. It has no declared empirical population, frequency distribution or intervention-effect estimator. The cases were authored as complete typed input objects before their numerical conclusions were written. Each result is produced by the same canonical Growth engine. The selection is useful because it challenges different shortcuts in commercial reasoning, including endpoint ranking, positive customer ratios, empty acquisition paths and unsupported payment terms.

The foundation reproduces the app’s supplied recurring-service reference. Each isolated intervention changes only its named field. The discount-and-acquisition package changes both starting price and acquisition budget explicitly. The complete-churn case also removes retained-price expansion so its timing boundary is easy to interpret. Every other field remains the foundation value. The input files retain all fields rather than storing an ambiguous partial difference that depends on whichever default happens to be current.

The fixed horizon and homogeneous assumptions are part of each case’s scope. A price intervention holds the customer path; a collection intervention holds operating performance; an opening-cash intervention holds every operating flow. These invariants help interpret the exact results. They also reveal the missing evidence needed for real use. If a proposed programme changes several relationships, the isolated case cannot be described as its complete forecast. The team must author and recompute a joint case before making numerical claims about that package.

The table states the literal changes. It is an input registry, not a recommendation to adopt those amounts. The controller should use the complete named file to reproduce a case and use the claim ledger to trace printed outputs. A reader can inspect a favourable result beside the unchanged assumptions that make it favourable. The same registry also preserves adverse and unavailable cases, preventing a selective presentation of only the outcomes that support a preferred growth narrative.

The foundation challenges the positive-ratio shortcut. A customer can have favourable finite recurring contribution while the organisation needs resources for acquisition, shared operations and working capital. The case therefore supports a hold on an unsupported implementation path while allowing a useful internal evidence task. It does not establish that the offer is commercially attractive in a real customer universe. Its value lies in the simultaneous conditional outputs and the action boundary they require.

The collection case challenges the belief that better cash must reflect better operating profit. It changes a payment timing input while preserving customer value and the operating ledger. This isolates a working-capital mechanism. The remaining funding gap matters: the improvement does not make the declared path fully self-funded. A real programme would need evidence for the timing change and its costs, which are not included in the isolated intervention.

The price case challenges the promotion of a favourable conditional result into a demand forecast. It retains acquisitions and churn while increasing the supplied starting price. The numerical improvement is exact under those held assumptions. The committee still needs offer-specific response and contractual evidence. The remaining funding gap prevents a self-funded launch claim even before service readiness is tested. A promising price review and an approved rollout remain different actions.

The volume case challenges endpoint ranking. Greater supplied acquisition spending produces more expected customers at unchanged CAC and can produce an attractive final cash balance. The earlier resource need remains positive. The case demonstrates why the final outcome cannot retroactively fund the campaign. It also identifies the acquisition and service premises that a real volume proposal would need to support, including whether the constant CAC relationship remains credible.

The discount-and-acquisition package challenges an unqualified customer-count story. It supplies a lower price and more spending jointly, while holding customer-response and service assumptions. More expected accounts do not establish a cheaper funded path. The discount has not been shown to cause acquisition, and its recurring contribution tradeoff remains visible. A revised concession proposal should state the customer action it purchases and author a complete new case rather than combining favourable results from separate interventions.

The higher-envelope case challenges the use of an unchanged customer ratio as proof of unchanged affordability. The unit curve excludes fixed costs, so its contribution value is preserved while business cash deteriorates. The case represents an externally supplied operating envelope throughout the window. It cannot estimate the required staff, a capacity trigger or a start date. The service acceptance and cost representation must therefore be completed separately before implementation.

The retention case challenges the equation of a lower churn input with a successful programme. The survival mechanism improves under the supplied parameter, but programme cost, customer selection and efficacy are absent. The event protocol and relevant customer model determine whether a measured rate can replace the illustrative assumption. A homogeneous expected curve remains useful for learning while a real retention allocation decision may require age or segment evidence.

The supplier-credit case challenges the conversion of an optimistic term into available liquidity. Its cash mechanism is favourable relative to the reference, while terms eligibility remains outside compute. The negative inventory/payable component requires a supported operating arrangement. The committee holds reliance on TERM-A until the relevant terms and eligible costs are documented. The case is not a borrowing offer or an accounting determination of supplier finance.

The cash-funded case changes resources rather than customer economics. It preserves the reference unit curve and operating flows while eliminating the modelled additional opening-cash requirement. This invariant makes it the appropriate case for the independent service and terms branch tests. The numerical result is favourable on the stated funding condition. A missing READY or applicable TERM declaration still holds the next commitment without changing the output.

The adverse-margin case challenges selective omission of an unavailable result. Starting price is below the recurring variable cost, so the engine returns no starting-price break-even count. The finite customer contribution value and cash path are unfavourable inside the supplied window. Meridian’s recurring-service policy rejects that perimeter. A strategic exception would need a new mandate and stated benefit rather than silently treating unavailable break-even as zero.

The no-acquisition case challenges the assumption that a hypothetical unit appears in the business. The one-customer curve remains favourable because its assumptions are unchanged, but the monthly path acquires no accounts and still pays the fixed envelope. The policy correctly holds funding rather than calling the unit adverse. This boundary also verifies that the recurring-perimeter gate reads unit contribution, not the business’s zero customer contribution.

The complete-churn case challenges timing intuition. New cohorts still receive acquisition-month service, while later survival is absent. The business can therefore have active customers each month from new acquisitions even though no earlier cohort continues. Contribution payback is unavailable in the supplied window. The example makes the first-service convention inspectable and gives the reader a reason to compare it with a real activation and cancellation process.

The shorter-horizon case challenges an unqualified lifetime label. Its customer curve omits later ages, and its business path ends before the reference’s final months. It neither releases working capital nor adds residual customer value. The finite-window result is meaningful as stated. It cannot establish that relationships continuing beyond the window have no value or that the business has liquidated its operating assets.

The contracting-price case challenges the substitution of revenue retention for logo survival. Logo churn stays at the foundation assumption while retained customer price declines with age. The resulting contribution and cash differ through price, not through a discovered change in relationship duration. A real diagnosis should preserve those mechanisms and identify whether the price path is a contractual term, a supplied estimate or an intervention assumption.

Together the cases support a disciplined comparison rather than a universal commercial ranking. The slate is complete for its stated mechanism questions and incomplete as a search over all strategies. An admissible combined offer, dated contract or heterogeneous customer base can require another model. The original protocol should allow that escalation while preserving the reference files, so later readers can see which premise changed and why the decision changed with it.