Assembly Geometry for Proof Construction: DOF-Ranked MATE Planning on Simplicial Complexes and Moment-Based Intent Gates

Technical report of the LNFdex(TM) engine transplanting CAD assembly mathematics to epistemic construction: GF(2) boundary operators derive the work front of a plan; missing faces become MATE lists ordered by degrees-of-freedom reduction (DOF = slots - rank, exact over Q); gluing carries orientation gates; every state change must declare its delta ex ante and is convicted on mismatch by exact integer moment algebra (named verdict R_ABSICHT_LUEGE). Everything lands in a typed proof hypergraph with four edge types (part_of, supports, enables, inhibits; measured census 3,902 nodes / 5,536 hyperedges) with hash-pinned datasets — operationalizing EU AI Act Art. 12/13 traceability as a byproduct of normal operation. Measured live on Raspberry Pi 5 against the frozen artifact PLANWERK_v0_1_24_PI5.