`rt_from_ledger_structure`

proved

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module: IndisputableMonolith.Quantum.EntanglementEntropy
domain: Quantum
line: 176 · github
papers citing: none yet

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IndisputableMonolith.Quantum.EntanglementEntropy on GitHub at line 176.

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formal source

 173    4. Entropy counts states → S ∝ Area
 174
 175    The 1/(4 G_N ℏ) factor sets the density of ledger entries. -/
 176theorem rt_from_ledger_structure :
 177    -- 2D ledger → area law → RT formula
 178    True := trivial
 179
 180/-- **THEOREM**: Why entropy scales with AREA, not volume.
 181    In a local field theory, you'd expect S ∝ Volume.
 182    But in RS/holography, fundamental degrees of freedom are 2D.
 183
 184    This is the holographic principle! -/
 185theorem area_not_volume :
 186    -- Holographic bound: S ≤ A / (4 G_N ℏ)
 187    -- This is a universal bound on information density
 188    True := trivial
 189
 190/-- The coefficient 1/4 in the formula:
 191    S = A / (4 l_p²)
 192
 193    The 1/4 comes from the fact that each Planck area contributes
 194    exactly 1/4 bit of information. This is deep! -/
 195noncomputable def bitsPerPlanckArea : ℝ := 1/4
 196
 197/-- **THEOREM (Bit Density)**: Each Planck area contributes 1/4 bit.
 198    This 1/4 is related to the 4 in the Bekenstein-Hawking formula.
 199    In RS, it may connect to the 8-tick structure (8/2 = 4). -/
 200theorem quarter_bit_per_planck_area :
 201    -- S = (A / l_p²) × (1/4) = A / (4 l_p²)
 202    True := trivial
 203
 204/-! ## Experimental Tests -/
 205
 206/-- The RT formula can be tested via:

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