software verification teams

Abstract: Vectors addition systems with states (VASS), a model equivalent to Petri nets, are finite-state machines with finitely many counters ranging over the natural numbers. The decidable reachability problem for VASS has many applications in logic, automata, and verification. In this paper we study the reachability problem for BVASS, a branching generalization of VASS. We show that BVASS reachability sets are very similar to VASS reachability sets, namely that they are sections of VASS. Our proof relies on a new well-quasi-order (wqo) on BVASS runs that generalizes the well-known wqo on VASS runs. By leveraging an amalgamation property, we prove that every BVASS run can be transformed into an equivalent one of bounded branching complexity. This allows us to derive several results on the geometry of BVASS reachability sets. As an application we obtain that reachability sets of 5-dimensional BVAS are effectively semilinear, as is the case for 5-dimensional VAS.

Abstract: Multi-step LLM reasoning lacks a machine-recheckable ledger: discarded reasoning paths leave no auditable record. We propose the Deposon scattering layer, which binds each node of an LLM-generated concept-decomposition graph to a two-parameter Deposon state; paths undergo three-channel scattering -- transmission, reflection, irreversible dissipation -- obeying T+R+A=1 for arbitrary parameters, with a maximum per-path energy-audit deviation of 2.2E-16 (machine epsilon). We report all three evidence tiers honestly. On synthetic trap benchmarks the path-filtering gain is closed (pre-registered): unified reaches 100% versus a decoy-capture baseline at 7%/10%. On real benchmarks the layer is indistinguishable from a trivial six-keyword rule filter (GSM8K 0.87 >= 0.85, McNemar p=0.5; StrategyQA 0.899 = 0.899); no difference is detected here, so we sharpen the claim to "the differential value lies solely in machine verifiability." Fusion yields a second negative result: convex combinations with a semantic prior never improve (physics 0.484 -> 0.452), and the apparent lambda=2 gain is an anti-field artifact; any fusion gain must be nonlinear. Modeling the reverse dynamics as a potential game on the graph, we evidence an auditable scalar's monotonicity and near-gradientness and quantify the empirical coordination ratio (ECR). The three formalized dynamical-equivalence propositions (P1a/P1b/T-P1c) are falsified under the pre-registered kill protocol, and the potential-game claim is downgraded to approximate (cyclic-graph median residual 0.669): only consistency-level evidence survives at the dynamical level. Code: github.com/zeroandcat/Deposon.