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lemma

two_mul_alphaLock

proved
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module
IndisputableMonolith.Constants
domain
Constants
line
224 · github
papers citing
1 paper (below)

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IndisputableMonolith.Constants on GitHub at line 224.

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formal source

 221/-- Useful bridge identity: the “acceleration-parameterized” exponent is `2·alphaLock`.
 222
 223This is purely algebraic (no physics): it just clears the `/2` in the definition. -/
 224lemma two_mul_alphaLock : 2 * alphaLock = 1 - 1 / phi := by
 225  unfold alphaLock
 226  ring_nf
 227
 228lemma alphaLock_pos : 0 < alphaLock := by
 229  have hphi := one_lt_phi
 230  unfold alphaLock
 231  have : 1 / phi < 1 := (div_lt_one phi_pos).mpr hphi
 232  linarith
 233
 234lemma alphaLock_lt_one : alphaLock < 1 := by
 235  have hpos : 0 < phi := phi_pos
 236  unfold alphaLock
 237  have : 1 / phi > 0 := one_div_pos.mpr hpos
 238  linarith
 239
 240/-- Canonical locked C_lag constant: C_lock = φ^{−5}. -/
 241@[simp] noncomputable def cLagLock : ℝ := phi ^ (-(5 : ℝ))
 242
 243lemma cLagLock_pos : 0 < cLagLock := by
 244  have hphi : 0 < phi := phi_pos
 245  unfold cLagLock
 246  exact Real.rpow_pos_of_pos hphi (-(5 : ℝ))
 247
 248/-- The elementary ledger bit cost J_bit = ln φ. -/
 249noncomputable def J_bit : ℝ := Real.log phi
 250
 251/-- Coherence energy in RS units (dimensionless).
 252    By Phase 2 derivation, E_coh = C_lock = φ⁻⁵. -/
 253noncomputable def E_coh : ℝ := cLagLock
 254

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