The Guarino Infrastructure Dependency Metric: Buffered Edges as a Complete Dimensionless Basis for Interdependent Infrastructure

Paper I of the Guarino Infrastructure Dependency Metric (GIDM). First revision, 20 September 2026. DOI 10.5281/zenodo.22864280. Infrastructure fails in chains. The February 2021 freeze in Texas began at frozen wellheads, ran through load-shed gas processing plants, took 61,800 MW of generation offline, and ended in boil-water notices for almost 18 million people. Existing resilience frameworks describe such cascades qualitatively. This paper derives them. Treating a node's service unit U as a base dimension alongside time T and, following the author's value programme, economic value V, the Buckingham pi theorem applied to the minimal variable set of any single infrastructure node yields exactly three dimensionless groups, and one complete basis is the availability, performance, and quality triple already known from manufacturing as OEE. An infrastructure node is therefore a machine in the sense of the Guarino Manufacturing Effectiveness Metric, and inherits its theorem. The new result concerns the edges. Each dependency between two nodes purchases exactly one further group, the ratio of the downstream node's autonomy time to the upstream outage's duration, PiB = Ta / Tx, and the downstream node's availability during that outage is shown to equal min(1, PiB) by direct construction rather than by definition. The composite chain score is the node's OEE gated by the binding buffer group on each upstream edge, with a log-additive loss ledger that names which edge broke. Cycles in the dependency graph, such as the gas-to-electric loop that governed the Texas event, are handled by the same group and reveal that some buffers are set by policy rather than hardware: a critical-load designation form fixes an edge's exposure time at zero. Applied to the Texas chain, the metric finds six edges whose buffer group fell below unity, two whose group held above it, and two the record leaves unmeasured; on the grid-to-water edge, the statutory 24-hour buffer Texas adopted after the storm gives PiB = 0.34 against the 70.5-hour load shed. The paper closes with a structural observation: a single planner sizing every buffer from one outage model adds a hidden edge to the graph, the model itself, with no buffer on it. What is in the deposit. The manuscript of record (GIDM_Paper_I.pdf, two-column, 8 pages) and its LaTeX source; the abstract; Figure 1 (the Texas chain, wellhead to tap) as PDF, PNG and standalone TikZ source; Tables 1 to 3 and the nomenclature register as CSV; the rank and independence check (code/rank_check.py) with its output, which verifies that the node set of five variables in {U, T} has rank two and yields three groups, that the extended set of eight variables in {U, T, V} has rank three and yields five groups, and that the five reported groups are dimensionless and independent; MANIFEST.md; SHA256SUMS.txt; and METADATA.pdf. Relation to the author's other work. The node basis inherits the completeness theorem of the Guarino Manufacturing Effectiveness Metric (doi:10.5281/zenodo.21882580). The value dimension V and its decay rate are taken from Value as a Conventional Base Dimension (doi:10.5281/zenodo.22016164) and the Value Dimension Programme research deposit (doi:10.5281/zenodo.22016414). A second paper will extend the chain upstream through refining and mining and compute plant-level buffer groups for the Texas edges from EIA and NERC data. Declaration on the use of artificial intelligence. The research questions, the dimensional framework, the choice of base dimensions and governing variables, the decision to model each dependency edge as a buffer group, the selection of the worked example and of which edges to include, and the interpretation of every result are the author's. An artificial-intelligence assistant was used substantially as a tool, under the author's direction, for drafting prose, writing and running the rank and independence code, locating and reading the public sources cited, and preparing the figure and the typeset document. Every computation reported is deposited with its code and can be re-run by a third party, and every empirical figure is taken from a cited public document. The author takes full responsibility for the content.