This paper presents Necto, a low-carbon CNC-knitted tensile membrane made from natural flax fibers and installed in the Corderie of the Arsenale at the 19th International Architecture Exhibition of the Venice Biennale. Suspended between four existing historic masonry columns and anchored to the floor at four additional points, the membrane forms a lightweight, form-active system within a protected heritage environment. Its functionally graded knit architecture aligns flax fiber inlays and density variations with the two principal stress directions, yielding a material-efficient and biodegradable structure. The structural design combines physics-based form-finding refined through the Force Density Method, nonlinear Finite Element Analysis for prestress calibration and boundary cable sizing under Eurocode-based load combinations, and detailed verification of all structural interfaces—including anchored ground supports, non-invasive clamped column supports with pressure-distributing layers, and a ring support that distributes the membrane stresses at the funnel over eight suspension cables. By treating form-finding, analysis, detailing, fabrication, and assembly as mutually informing constraints, Necto demonstrates how a multi-fidelity structural design process can deliver a full-scale CNC-knitted membrane within a protected heritage context. ... Read more