| Summary: | <p>Reliable indirect diagnostics of LyC photon escape from galaxies are required to understand which sources were the dominant contributors to reionization. While multiple LyC escape fraction (<em>f</em><sub>esc</sub>) indicators have been proposed to trace favourable conditions for LyC leakage from the interstellar medium of low-redshift ‘analogue’ galaxies, it remains unclear whether these are applicable at high redshifts where LyC emission cannot be directly observed. Using a library of 14 120 mock spectra of star-forming galaxies with redshifts 4.64 ≤ <em>z</em> ≤ 10 from the SPHINX<sup>20</sup> cosmological radiation hydrodynamics simulation, we develop a framework for the physics that leads to high <em>f</em><sub>esc</sub>. We investigate LyC leakage from our galaxies based on the criteria that successful LyC escape diagnostics must (i) track a high-specific star formation rate, (ii) be sensitive to stellar population age in the range 3.5–10 Myr representing the times when supernova first explode to when LyC production significantly drops, and (iii) include a proxy for neutral gas content and gas density in the interstellar medium. O<sub>32</sub>, Σ<sub>SFR</sub>, M<sub>UV</sub>, and H β equivalent width select for one or fewer of our criteria, rendering them either necessary but insufficient or generally poor diagnostics. In contrast, UV slope (β), and <em>E</em>(<em>B</em> − <em>V</em>) match two or more of our criteria, rendering them good <em>f</em><sub>esc</sub> diagnostics (albeit with significant scatter). Using our library, we build a quantitative model for predicting <em>f</em><sub>esc</sub> based on direct observables. When applied to bright <em>z</em> > 6 Ly α emitters observed with JWST, we find that the majority of them have 𝑓esc≲10 per cent.</p>
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