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The paper “The black hole interior from non-isometric codes and complexity” by Akers, Engelhardt, Harlow, Penington, and Vardhan (JHEP06(2024)155) does make a credible claim to resolve all three components of the black hole information problem in a unified framework.
The Three Paradoxes Resolved:
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Finite black hole entropy (as required by Bekenstein-Hawking entropy),
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Unitarity of black hole evaporation (consistent with the Page curve),
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Semiclassical effective field theory validity inside the horizon (to explain the interior modes and entanglement).
Hawking's original argument was that you can't have all three simultaneously. This paper proposes a non-isometric holographic map (i.e. not preserving inner products globally) that still behaves as if it were isometric for all sub-exponential complexity observables. In effect:
Null states (states mapped to zero) exist but are exponentially complex and thus undetectable by any reasonable observer.
This allows the interior to emerge via quantum error correction (though not isometrically) and maintains consistency with both the Page curve and unitary dynamics.
This paper is a strong candidate for what Harlow refers to when he mentions resolving all three paradoxes of the black hole information problem.
