LHC results do not confirm conventional natural solutions to the Higgs mass hierarchy problem, motivating alternative interpretations where a hierarchically small weak scale is generated from a dimension-less quantum dynamics. We propose weakly and strongly-coupled models where the field that breaks classical scale invariance giving mass to itself and to the Higgs is identified with a possible new resonance within the LHC reach. As an example, we identify such resonance with the 750 GeV

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... excess recently reported by ATLAS and CMS. Such models can be extrapolated up to the Planck scale, provide Dark Matter candidates and eliminate the SM vacuum instability.