Atomic Common-Day Invoice Clearing under Causal Daily Scheduling: Path-Enabled and Bounded-Cycle Policies

Abstract

Late payment propagates working-capital pressure through supply networks because firms are simultaneously creditors and debtors. We develop an atomic-record temporal invoice-graph method for path-enabled clearing and compares it with complete-candidate bounded-cycle netting under a causal daily greedy schedule. Each invoice remains a residual record with its issue date, due date, amount, and identifier. A candidate is executable through source capacity active on every supporting edge on one common day. A non-bilateral two-edge path reduces two invoice legs, creates a direct settlement instruction between the endpoints, and preserves net positions for all participants on the combined invoice-plus-instruction state; payable-mass reduction is distinguished from invoice compression. The empirical sequence contains 749,952 invoices issued from 2012 through 2023, totalling EUR99.7 billion, and maintains one rolling state across annual boundaries so bridge invoices are introduced once and residual balances continue. Path clearing reduces 48.2% of issue-cohort mass, compared with 43.3% for length-eight cycle netting, an advantage of EUR4.841 billion and 4.855 percentage points. It leads materially in ten cohorts, is practically tied in 2013, and trails in 2012. The result survives alternative ordering, mixed path-cycle policies, cycle-length sensitivity, component resampling, acceleration constraints, and fragment replay. In reciprocal 2022, where almost all local paths lie in the cyclic core, path clearing still leads. Tractable full-information linear programs show path advantage and path-cycle complementarity. The findings establish a policy-level benefit, not global optimality or welfare dominance,and motivate future asynchronous agent-to-agent clearing built around deterministic common-day verification,private mandates,reservations, explicit consent,and atomic commit.