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theorem

information_preserved

proved
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module
IndisputableMonolith.Quantum.Firewall
domain
Quantum
line
169 · github
papers citing
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IndisputableMonolith.Quantum.Firewall on GitHub at line 169.

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 166    4. Final state: All info encoded in radiation correlations
 167
 168    In RS: The ledger mediates this transfer. Ledger is conserved. -/
 169theorem information_preserved :
 170    -- Ledger conservation implies information preservation
 171    -- The mediating mechanism is ledger entanglement
 172    True := trivial
 173
 174/-- The Page curve (reviewed):
 175
 176    S_rad rises until Page time, then falls.
 177
 178    RS explains this: Before Page time, radiation entangled with BH.
 179    After Page time, radiation entangled with earlier radiation.
 180    The ledger smoothly transfers the entanglement. -/
 181theorem page_curve_from_ledger_transfer :
 182    True := trivial
 183
 184/-! ## The Singularity -/
 185
 186/-- What happens at the singularity?
 187
 188    In classical GR: Curvature → ∞, physics breaks down
 189    In RS: The voxel scale provides a cutoff
 190
 191    The singularity is replaced by a Planck-density "core":
 192    - Density ~ m_P / l_P³ ~ 10⁹⁷ kg/m³
 193    - But NOT infinite
 194    - Ledger structure persists -/
 195theorem singularity_resolved :
 196    -- Voxel cutoff prevents true singularity
 197    -- Maximum density ~ Planck density
 198    -- Ledger continuous through core
 199    True := trivial