ckEdges

Phase 59 of the Recognition Science cosmology stack studies whether integer-rung descent preserves the unit-step invariant: every edge changes the integer rung field $k:V\to\mathbb{Z}$ by at most one. That invariant is the hypothesis of the Phase-56 graded recognition-cost law, so the cost meter is only theorem-backed if descent keeps unit-step.

The module works with a concrete three-site chain whose rungs are $0,1,2$. The present definition supplies the ordered adjacency of that chain (two directed pairs as the engine stores edges). Sibling material defines the matching level assignment and the shift-down operator that lowers selected vertices by one rung.

Module context: Phase 58 showed that a blind global claim for the real-valued mean move fails; Phase 59 gives the positive half for integer top-rung descent, and needs a fixed small graph on which non-top descent demonstrably breaks unit-step.

Pure definition: the Finset literal with the two ordered pairs $(0,1)$ and $(1,2)$ on $\mathrm{Fin},3$. No lemmas, tactics, or computation beyond constructing that set.

Without a fixed adjacency, the necessity half of Phase 59 cannot be stated. Downstream, ckLevels_unitStep shows the chain with levels $0,1,2$ is unit-step on these edges; ckLevels_descend_min_breaks shows that descending the bottom cell alone produces a gap of $2$ on the edge to the middle vertex, so unit-step fails. The Phase-59 headline bundles top-rung preservation with that counterexample: top descent is safe and necessary, not cosmetic.

In the forcing picture this supports the claim that the live engine's forced one-rung top descent (T-3 style) keeps the graded-rung hypothesis of the cost law cycle to cycle, while arbitrary single-cell descent does not. It is scaffolding data for the honest positive/negative pair that closes the unit-step preservation item for integer rungs.