ENDURANCE OR DENSITY: Formalizing the Entropy-Resistant Institution Index, Why the Same Data Produce Opposite Rankings, and What Would Have to Be True to Trust Either One

The Structural Residue (Huynh 2026) defines the Entropy-Resistant Institution (ERI) as a threshold classifier: an institution either has survived two or more qualifying disruptions with constitutive function intact, or it has not. This paper converts that classifier into a quantitative index, applies it to the same three case studies — the Jiankang Empire (220–589 CE), the Japanese Imperial House (c. 500–2026 CE), and the Holy See (c. 33–2026 CE) — and reports the finding that matters most: two independently defensible weighting schemes, built from the same coded data, produce opposite rankings. An endurance-weighted composite (ERI_A = 0.35·Y_norm + 0.25·A_norm + 0.25·T + 0.15·D_sev_norm) ranks Holy See (0.90) above Japan (0.50) above Jiankang (0.15). A density-weighted composite (ERI_B = 0.40·δ_norm + 0.25·A_norm + 0.20·D_sev_norm + 0.15·T), where δ is disruptions survived per century, ranks Jiankang (0.60) above Holy See (0.49) above Japan (0.15). No historical fact changes between the two calculations. Only the weighting changes. This is not a defect to be patched with a better formula. It is a discovery about the construct: “entropy resistance,” as currently specified, bundles at least two properties that do not co-vary — raw longevity and disruption-density — and the base paper does not yet say which one, or what blend, is relevant to the F2 governance-design question its Section VII raises. The index borrows one design principle from each of three established institutional-measurement tools rather than inventing a scoring system from first principles: Polity5’s DURABLE variable (Marshall & Gurr 2020), which defines regime change by a pre-registered operational trigger — a three-point shift in the coded POLITY score within three years or less — rather than a post-hoc judgment call, supplying the principle that a qualifying disruption needs a trigger specified in advance; the Fragile States Index (Fund for Peace, annual), which builds a composite from twelve independently scored, triangulated sub-indicators rather than one holistic judgment, supplying the principle of decomposition before aggregation; and V-Dem (Coppedge et al.), which uses multiple independent coders per item and publishes inter-coder reliability statistics, supplying the standard this paper’s own coding does not yet meet — every score below is produced by a single reader from a single document, a limitation stated in Section VI rather than concealed. The paper states five specific limitations, each of which would change the reported numbers if corrected, two of which cannot be corrected without new data collection: the six structural attributes were induced from the same three cases they are then used to score, which is close to circular; the current design has zero failure comparators, meaning it selects entirely on the dependent variable and cannot yet show the attributes discriminate survival from mere age; single-coder scoring has no reliability check, and a second coder working from the same source material could reasonably move any attribute score by ±2 on a 0–12 scale; the base paper’s own prose includes at least one cited disruption that fails its own three-part definition when checked against it; and the Holy See’s maximum possible attribute score (12/12) cannot currently be distinguished from an artifact of the scale having been shaped by the Holy See’s own case. The paper converts these limitations into four dated, actionable falsification conditions in the Popperian-Holmesian format this corpus uses elsewhere (Huynh 2026n, 2026x), proposes four specific comparator cases — Byzantine terminal collapse (1453),