## 1 Introduction
The gap between the targeted circular systems is grounded in quite a robust theoretical framework, and the concrete application in the real market is still underexplored, with studies more focused on product and component production processes rather than the whole construction stream, not yet sufficiently supporting a systemic perspective on the transition progress [20; 21; 22; 23]. Some Member States, such as Italy, have therefore invested a part of the exceptional measures of the EU Recovery Fund comprehensively addressed to support the achievement of sustainable development goals, for funding specific actions aimed to introduce mandatory metrics and impact assessment tools in regulations regarding the construction sector. Within this context, the Italian Ministry for University and Research supported, under the umbrella of the competitive national PRIN 2022 programme, the project \"BETTER POLICY Building Environmental Tools to Empower Responsive Policies Outreaching LifeCYcle. Guidelines and protocols to enable Public Administration-driven processes in the Italian construction sector\", with the overall aim of facilitating the introduction of life cycle assessment tools in public projects. A specific task force has been dedicated to life cycle-oriented circular economy practices and tools within the project. The investigation was originated by the very slow implementation rate of circular-oriented processes in public-driven construction initiatives, which are instead supposed to be the pilot of a massive adoption at the national level [24]. Despite the national obligations introduced to comply with the EU vision, the actual adoption of CAM (Minimum Environmental Criteria)--which are supposed to set the conditions to meet adequate design and construction solutions and enable low-impact and circular-based systems--is largely fulfilled more as an administrative step rather than a real mindset shift opportunity. Accordingly, the core research question is to identify and understand which barriers and gaps still need to be addressed, and what good practices and drivers could stimulate the change, considering tools and policies at the same time. The study examines the gap between the progress in the theoretical framework and the limitations in the real market application, where sustainability assessment tools seem to represent the main (voluntary) way to monitor both the quality and performance resulting in the building process. Therefore, the scope of the research project is to understand why circularity of resources in the construction sector has failed to be systematically implemented so far, with particular reference to the Italian national context. A methodology to correlate the two ends of the topic is developed. On the one hand, the scientific literature about CE policies is reviewed; on the other, a systematic analysis of the most diffused building sustainability assessment tools is carried out. Thereafter, a critical discussion of the outcomes is performed to search matches and uneven topics (Sections 2 and 3). This cross-search method aims at identifying the mutual connections between measures and targets established by the policies and the performances assessed by the tools, so mapping potential integrations to build consistent decision sequences among the two investigated fields. This should couple the advancing knowledge and practice in the field of circular construction, overcoming the lack of complementarity that is argued to exist between the two domains. Findings are systematized to discuss challenges at the policy level to better support the adoption of circular economy principles, practices, and measures in buildings (Section 4).