Hawk04, Hawk04-A-v1, 2026, pp. 1-22
Hawk04-A Unitary Information Preservation and Radiation Recovery: A Complete-Complement Formulation of the Black-Hole Information Problem
Ngo Cheung
2026
Abstract
We prove the precise conditional statement that quantum information cannot be destroyed by unitary evolution of a complete closed system. For a finite logical code, a fixed pure ancillary preparation, and a unitary evolution, the complete output channel has a CPTP left inverse, including every external reference. Every logical matrix unit and every input-state trace distance are preserved. This global statement does not imply recovery from radiation alone. For a complete isometry V:C→ R⊗ B, we prove that one decoder recovers the entire code from R exactly if and only if the complete complementary channel to B is constant. A Schmidt-space construction provides the decoder and the exact no-hiding normal form. We distinguish this result from partial decoherence, restricted input ensembles, and mixed-output descriptions with omitted preparation purifiers. For the regulated quartic SYK–scalar architecture of Hawk02-E, we reconstruct the self-adjoint dynamics and a reference-preserving finite approximation. A finite complementary Choi certificate e, input dimension d, and complete-channel regulator allowance b yield δ_(full)≤ d e+b. A finite decoder can be lifted to the continuum with recovery error at most √(2de)+b, or certified directly using its decoded Choi operator. We also give an exact four-Majorana realization with nonzero coupling for which the optimal radiation recovery error is (3-z(t))/4≥1/2, although global recovery is exact. This is a dynamical negative control, not a scrambling argument. Finally, we prove endpoint continuity with access-preserving output identifications and state the separate gravitational obligations. The results establish unitary preservation and operational recovery criteria. They do not establish unitarity of quantum gravity, a generic interacting evaporation-recovery window, or a gravitational endpoint.
Bibliographic record
- Title
- Hawk04-A Unitary Information Preservation and Radiation Recovery: A Complete-Complement Formulation of the Black-Hole Information Problem
- Author
- Cheung, Ngo
- Publication date
- 2026
- Institution
- Hawk04
- Report number
- Hawk04-A-v1
- Publisher
- Cheung Ngo Medical Limited
- First page
- 1
- Last page
- 22
- Language
- en