Representation implementation record

Page status: research and software record; implementation coverage is evidence about the current repository, not a claim that the architecture is complete.

The mathematical architecture is defined normatively in Formal representation frameworks. This page records the engineering status of the small executable facade and its fixture coverage so that package maturity is not confused with representation theory.

Public transformation API boundary

The reusable facade in experiments/src/GraphModelsForPowerNetworks.jl currently exports a small, dependency-light surface: identified multigraph primitives, incidence and cycle-space queries, simple projection, typed linear Kron operations, coordinate and recovery maps, unit conversion, boundary projections, and structural certificate validation. Solver-backed AC cases, generated figures, literature adapters, and BMOPFTools integration remain experimental evidence, not package-stability promises.

The generated experiments/generated/public-api-manifest.json is the checked record of that boundary. Promotion to a standalone package should wait until the state-space and unit types, conversion contracts, and recovery semantics are versioned. Otherwise a representation change could silently alter the meaning of a reduction while leaving the Julia method names unchanged.

Fixture coverage and evidence status

experiments/generated/fixture-coverage-matrix.json keeps coverage separate from API existence. It distinguishes direct fixture evidence, related evidence, and explicit $not_yet_tested$ rows for the running network, five-bus cycle-space example, and multiwinding transformer. A certificate on a synthetic fixture is therefore not silently promoted to validation of a canonical network fixture.

The multiwinding fixture records two cycle views: its native factor–port incidence is a star with cycle rank zero, while a derived clique compilation has cycle rank one. The latter is a view choice, not a new electrical loop. Likewise, active radiality for the isolated transformer contract remains $not_yet_tested$ because no switching or energized-state domain is declared.

The matrix distinguishes typed map families as well. The running-network state-space/unit witness is direct evidence for its declaration and conversion contract; the multiwinding entry is related evidence because it is not a separate state-space instantiation. Winding-terminal normalization is direct for the serialized $x1$ transformer contract but only related to the running network as a whole. Parameterized transformer control is tracked separately from fixed transformer compilation and has direct evidence in the retained-tap AC certificate.

Current research boundary

These records establish a reproducible implementation inventory. They do not establish categorical composition, universal factor evaluation, complete schema coverage, or package API stability. Those remain research tasks and are kept separate from the normative definitions and the generated transformation certificates.