The Closure Ledger: A Procedure for Any Quantity Reached by More Than One Path

Many quantities in the exact sciences are not measured once but reached by several independent routes — direct determinations, differences around a cycle, combinations through intermediates — and are then quoted as a single number, the route suppressed. When the routes disagree, the disagreement is real information about the quantity's foundations, and the single number hides it. This paper defines a bookkeeping instrument, the closure ledger, and states its procedure: every multi-path quantity is entered with its paths and its representations; a closure residual is computed for each pair of paths within each representation separately; the worst residual is printed as the quantity's closure price; and no quantity is quoted downstream without its ledger entry. The procedure is exhibited end-to-end on a worked corpus already computed in this program — the electronegativity cycles of census attack CC-146, where six halogen pairs are run around their cycles under two representations: no cycle closes under either; the largest residual is 0.354149 of the scale's own unit (Cl–I, arithmetic form) and even the sign of that pair's debt flips under the geometric form (+0.066266); two atoms whose direct difference the definition returns as exactly 0.000000 are separated by 0.243234 on the anchored path; and the scale's founding anchor, read back through its own network, returns 3.871278 against its assigned 4.000000. The ledger prices path-dependence; it repairs nothing and pins nothing. Grade: procedure, exhibited on a complete worked corpus. Program headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.