LSMT2: Finite Labeling of Two-Segment Relation-State Streams Derived from Non-Periodic Series

Preprint. This paper defines LSMT2, a finite labeling layer for relation-state streams derived from two role-bearing segments with ordered endpoints. In the implementation pattern considered here, an upstream generator produces two derived objects from a non-periodic source stream by different procedures, supplies the corresponding ordered segment pair, and lets LSMT2 compare the pair in one frame. LSMT2 normalizes the segment pair, induces two triangles, and maps crossing, contact, non-crossing separation, angle alignment, thin four-endpoint states, and near-overlap to finite labels. Crossing pairs induce opposed triangles around the intersection; non-crossing pairs induce two triangles by a fixed split preserving role order. As an illustrative implementation instance, BTCUSD 15-minute OHLC bars are converted into two ordered segments in a common comparison frame. The emitted per-bar labels include LSMT2 cases and nested alignment stages. On 2772 effective rows, ordinary crossings are separated as X opposing, angle-aligned thin non-crossing states as P thin-quad, and adjacent-row persistence is 91.95% for case and 95.67% for stage. The contribution is an interface for downstream finite-state use, rather than a forecasting-performance result.