Appendix: worked illustrative portfolios

The worked-study appendix is a replication register, not a sample of investment outcomes. Each named study has a complete input file, canonical output file and scalar-binding file. The names identify the experiment being performed. The app schema supplies the units and structural limits, while the study metadata records the purpose, sensitivity and limitations. A reader can load a named input and recompute it using the paired current app under its supported version. The resulting calculation remains illustrative even when it reproduces exactly.

The studies deliberately vary different parts of the architecture. The balanced, impact-led and initial-capital cases hold raw performance and universe fixed while changing weights. The range-artifact case holds original performances and weights fixed while adding a dominated reference proposal. The close contest changes both the candidate profiles and the tradeoff reference to examine ties. The dominance example isolates an impact-only preference. The paired evidence cases hold the universe and vector fixed while revising the logistics readiness and risk interpretations. These are distinct experiments with different decision readings.

Read the study register as a contrast map. The mandate studies hold raw performances fixed and change preference; the evidence pair holds the mandate fixed and changes a supplied interpretation; the range experiment holds the original proposals fixed while extending the comparison set; the dominance case inspects a raw advantage that a zero-weight criterion can hide. Match each contrast to the question it can answer before comparing leaders. A preference disagreement calls for mandate work, whereas unsupported performance calls for evidence work. Counting favourable leaders across these unlike contrasts would combine different experiments into a statistic with no defined sampling or decision meaning.

The balanced reference represents a fictional committee that values the cost, impact, readiness and risk swings through a declared compensatory vector. The reliability proposal leads because several represented contributions support it, rather than because it dominates every raw attribute. The capacity proposal retains the greatest represented impact while paying a preference cost for its other positions. This establishes a conditional comparison among tradeoffs. It does not establish that the reliability intervention is superior under every legitimate objective or that the larger capacity proposal should be abandoned.

The appropriate next action depends on the charter. If the present envelope concerns a bounded near-term operating investigation, the leader can support that action subject to its evidence and eligibility conditions. If the envelope concerns a funded package or strategic expansion, the standalone reference is insufficient. The study therefore provides a useful baseline and a falsifiable interpretation, not a universal project recommendation. Its contribution ledger and raw table are the first replication check before applying any sensitivity reading.

The impact-mandate study changes the preference vector while retaining every supplied raw candidate value. The capacity proposal becomes the leading entry because its represented impact receives much greater emphasis. This is an explicit mandate reversal. It does not require the analyst to claim that capacity suddenly became cheaper, more ready or less risky. The experiment shows why a committee must authorise the tradeoff appropriate to its decision. Performance evidence alone cannot choose between these mandates.

The impact-led result remains compensatory and bounded by the same missing feasibility representation. It does not resolve permission, financing or delivery capacity. A real strategy envelope might legitimately give impact priority while still requiring gates and a credible implementation plan. The study should therefore lead to a discussion about decision scope and authority, followed by the appropriate appraisal work. It should not be used to erase the lower readiness and higher risk positions that remain in the raw record.

The initial-capital study gives cost a stronger preference while preserving the same raw candidates. The commercial-learning proposal becomes preferred. This demonstrates the consequence of a cost-oriented vector and the tradeoff it expresses. It does not impose a spending limit, model recurring obligations or compare complete cashflow profiles. A committee interested in preserving capital should identify whether its concern is an authorised preference, an affordability constraint or a timing problem. Those concerns require different representations.

The preferred low-cost proposal may also serve a different commitment stage from the capacity intervention. The charter must explain why those alternatives are legitimately compared in one envelope. If the committee is allocating learning effort rather than implementing a service, the raw impact and readiness definitions may need revision. The study is a controlled mathematical experiment; its names do not validate an actual programme design. The interpretation should remain conditional on the decision envelope that makes the vector meaningful.

The range-artifact case adds a deliberately unattractive reference proposal while retaining the original values and weights. Its raw profile expands the observed ranges. The original alternatives receive higher scores even though none of their performances improves. The baseline leader stays first. This non-reversal is part of the evidence: the fixture demonstrates scale movement, not every possible rank-reversal phenomenon. A reviewer should not infer a stronger result than the authored experiment actually produces.

The methodological consequence is that scores belong to a frozen comparison set. A higher total after candidate admission is not automatically a higher absolute value. The committee should apply its inclusion rule and recompute a coherent set whenever the universe changes. If an externally anchored scale is appropriate, it should be designed and reviewed as a separate model rather than assumed to be present. The current app intentionally exposes current-set normalisation and its limitation.

The close contest supplies opposing profiles under equal relative weights. The service and operating-readiness proposals share the leading total, while their contributions differ. The engine displays the tied names deterministically. Selected individual shifts move the preferred entry between those profiles and can move the original display entry below the balanced candidate. The table and diagnostic identify this conditionality. They do not estimate the probability that either option is best or interpolate an analytical reversal boundary.

This study is useful for testing presentation behaviour as well as arithmetic. A briefing must not turn the literal text display into a unique substantive recommendation. The committee can acknowledge indifference, apply an authorised secondary rule or deliberate about the represented swings. The full output retains the ranking in each selected test so a reserve or staged choice can be examined. A leader-retention percentage alone would hide the tie convention and much of that decision content.

The ignored-dominance case gives preference only to impact, which is equal for both candidates. The weighted totals therefore tie. The cheaper proven system is nevertheless the sole raw Pareto entry because it is no worse on impact and better on the other represented attributes. The engine reports both results correctly under its separate rules. The apparent disagreement tests whether the committee's indifference to the ignored concerns is intended or whether those concerns should be restored to preference or handled as gates.

This is not a defect repaired by secretly adding a tie-break weight. The transparency principle requires the declared vector to govern the weighted result. A real committee might decide that cost and risk cannot be ignored, but that is a new authorised preference or eligibility decision. The original fixture should remain available as the reason for reopening it. The example also demonstrates the equal-range midpoint convention and why raw dominance can carry information that a zero-weight criterion does not contribute to the sum.

The less favourable evidence case assigns the logistics proposal low readiness and higher execution risk while retaining its supplied cost and impact. The metering proposal leads and the inspection service is the runner-up. The labels describe the direction of authored assumptions, not their empirical probability. An actual analyst would need credible evidence supporting the bounds and a proposition that the next investigation could resolve. The fixture tests the model under those inputs without validating the logistics concept.

Its use is to identify which decision could depend on the disputed interpretation. If the present action is investigation of the leader, the logistics uncertainty does not automatically require delaying that action. If the committee needs a reserve or another compatible intervention, runner-up preference may matter. The actual action defines relevance. The fixture alone cannot infer package compatibility or the value of learning, and the report should not add those conclusions to the numerical result.

The more favourable evidence case improves only the logistics readiness and risk interpretations. The metering proposal remains first, while logistics moves ahead of the inspection service. The inspection raw values are unchanged, but its transformed positions move because the shared ranges change. The appendix preserves that distinction. A revised score is not necessarily revised performance, and a changed runner-up is not a changed leading choice. Both statements matter to honest interpretation.

The pair does not supply a confidence interval or an expected-value calculation. There are no probabilities attached to the interpretations. The correct conclusion is a bounded conditional one: the selected evidence changes affect the ordering below the leader and the normalised scores, while retaining the leading entry. Further evidence should be requested if that consequence matters to the intended action or if credible values lie outside the supplied bounds. The paper does not promise that better evidence will necessarily overturn the recommendation.

The complete input files are the definitive fixture records. The appendix prints the consequential parameters and result interpretations, while earlier exhibits show raw candidate tables and selected sensitivity rows. The files retain every required field and can be opened through the replication workflow. A reader should compare candidate identities rather than assuming that array position stays constant across rankings. Scalar pointers in the claims ledger identify the field selected for each printed value and prevent an author from substituting a similar-looking result from another study.

Replication should distinguish successful recomputation from acceptance of the decision. Matching an archived output verifies that the same inputs and model semantics produce the same result. It does not verify rating evidence, legitimise a mandate or establish that the proposals are feasible. After reproducing the study, the reviewer should challenge the experiment's held-constant statement and interpretation. That sequence separates an implementation discrepancy from a methodological objection and gives each a concrete route to repair.

The studies support the conditional thesis through different challenges. They demonstrate that explicit changes to tradeoffs can reverse preference, that a zero-weight architecture can tie a raw dominator with its dominated comparator, that universe changes can move scores and that bounded evidence changes need not alter the leader. The paper's original contribution is the decision reading connecting those mechanisms to eligibility, authority, learning and funding. The frozen outputs support those particular mechanisms, while the broader process architecture remains an original proposal subject to independent review.

A supported positive preference weight should remain in the stated redistribution rule even when it is small. The positive-weight-tail diagnostic sets cost weight to 1000, impact to 1e-09 and the other two criteria to zero. Alternatives A, B and C use capital costs 0, 0.25 and 2 USDm. Only B has impact 100; only C has readiness 100 and execution risk zero. Under the original normalised weights A leads, but applying a cost-weight shift of -20 percentage points releases weight to the sole other positive criterion, impact. The preferred alternative becomes B, at a rounded score 90.00. This illustrates the supplied preference rule, not stakeholder approval of that rule.

The revised engine normalises canonical decimal inputs, computes criterion contributions and ranks alternatives using rational arithmetic. Sensitivity distributes the remainder in proportion to the other supplied weights. It uses the documented equal-thirds fallback only when all those other supplied weights are exactly zero. Thus a positive tail is not discarded through a numeric threshold or subtraction cancellation. Exported fractions allow the case to be reproduced beyond its rounded chart values. The arithmetic does not settle whether that tiny weight is intentional, whether the criteria are measured comparably, or whether a compensatory decision is permitted. Those remain committee questions, and the diagnostic should prompt correction if the supplied preference record is wrong.