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The short-lived radionuclide $^{26}$Al is widely used to determine therelative ages of chondrite components and timescales of physical and thermalevents that attended the formation of the Solar System. However, an importantassumption for using $^{26}$Al as a chronometer is its homogeneous distributionin the disk.  Yet, the oldest components in chondrites, the Ca-Al-rich inclusions (CAIs),which are usually considered as time anchors for this chronometer, showevidence of $^{26}$Al/$^{27}$Al variations independent of radioactive decay.Since their formation epoch may have been contemporaneous with the collapse ofthe parent cloud that formed the disk, this suggests that $^{26}$Al washeteregeneously distributed in the cloud. We model the collapse of such anheterogeneous cloud, using two different $^{26}$Al distributions (monotonic andnon-monotonic), and follow its re-distribution in the first condensates andbulk dust that populate the forming disk.  We find that CAIs inherit the $^{26}$Al/$^{27}$Al ratio of the matterinfalling at the time of their formation, so that variations of$^{26}$Al/$^{27}$Al among primordial CAIs can be accounted for, independentlyof radioactive decay. The prevalence of a canonical ratio among them and itsnecessity for the differentiation of the first planetesimals suggest a(monotonic) scenario where $^{26}$Al sharply rose relatively close to thecenter of the protosolar cloud and essentially remained at a high level outward(rather than decreased since). As the $ ^{26}$Al abundance would be relativelyhomogeneous after cessation of infall, this would warrant the use of the Al-Mgchronometer from the formation of "regular" CAIs onward, to chondrules andchondrite accretion.

Fingerprints of the protosolar cloud collapse in the Solar System I: Distribution of presolar short-lived $^{26}$Al