{"artifact_id":"L1-914","layer":"L1","title":"Black-Hole Information — Page Curve & Unitarity","domain":"Quantum Gravity","sub_domain":"Black-Hole Information","physics_fingerprint":{"intro":"Hawking's calculation implies black holes destroy information, contradicting quantum unitarity. The island / replica-wormhole prescription recovers a unitary 'Page curve' for radiation entropy. Reproducing it tests whether information survives.","title":"Black-Hole Information — Page Curve & Unitarity","domain":"Quantum Gravity","chapter":"Ch.11 Physics & Cosmology","why_hard":"It requires fine-grained entanglement entropy with quantum-extremal-surface (island) contributions; analytic only in toy models; deviations diagnose where semiclassical gravity fails.","agent_idea":"An agent that, given an evaporation model, computes the entropy curve and locates the Page time and islands.","approaches":["Quantum-extremal-surface / island solvers for radiation entropy","Replica-wormhole emulators","Learning the Page transition in toy evaporating models"],"sub_domain":"Black-Hole Information","forward_model":"Fine-grained entropy of Hawking radiation S_rad(t) with the island/QES prescription; unitarity ⇒ Page curve that rises then falls.","benchmark_goal":"Recover the unitary Page curve for an evaporating model with low deviation, using the island formula.","challenge_blurb":"Show that black holes preserve information — recover the unitary Page curve of Hawking radiation via the island formula.","challenge_group":"physics","challenge_short":"Black-Hole Information","grand_challenge":true,"governing_equation":"S_rad = min ext_I [ Area(∂I)/4G_N + S_bulk(R∪I) ]  (island formula)"},"observable_profile":{"unit":"deviation from unitary Page curve (lower better)","floor":0.1,"metric":"page_dev","sota_reference":"Islands / replica-wormhole Page-curve derivations"},"size_tiers":{"modes":[16,64,256],"time_steps":[50,200,1000]},"hardness_fn":{"type":"grand_challenge","metric":"page_dev","baseline":"Semiclassical Hawking (no islands)","delta_tier":50},"initiator_dataset":[{"name":"Replica-wormhole entropy benchmark set","weight":0.6,"ipfs_cid":null,"license_hash":null},{"name":"Evaporating-model entanglement series","weight":0.4,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":5000.0,"chain_hash":null,"chain_tx_hash":null,"chain_block":null,"wp":{},"plain_intro":"Black-Hole Information — Page Curve & Unitarity is a problem in Quantum Gravity. The forward model maps the hidden the unknown quantity to a measurement. The inverse goal is to recover the the unknown quantity from the observed data."}