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Papers 82 and 83 ran the Closure Identity on one pair of tables. This paper proves it for any two algebraic relations that share one scale: when a joint closure test exists, what it must look like, and why its printed offsets are slopes in costume — the lever-arm law, proved, then checked digit for digit against the sealed SPARC record (all nine registered verification checks pass, including the lever arm 2.103017). P1 stands in derived form; P2 is narrowed; P3–P5 and P6a/P6b stand. On SPARC the centering passes for every form; the slope doesn't. Why the slope fails stays an open question, printed at full size.
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William Alexander Aldred (2026) studied this question.
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