`tau0`

definition

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module: IndisputableMonolith.Constants
domain: Constants
line: 271 · github
papers citing: none yet

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IndisputableMonolith.Constants on GitHub at line 271.

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formal source

 268and `IndisputableMonolith.Constants.RSNativeUnits`). -/
 269
 270/-- The fundamental time unit τ₀ (duration of one tick) in RS-native units. -/
 271@[simp] noncomputable def tau0 : ℝ := tick
 272
 273lemma tau0_pos : 0 < tau0 := by
 274  simp [tau0, tick]
 275
 276/-! ## C-004: Planck's Constant ħ Derivation
 277
 278### The RS Derivation of ħ
 279
 280In Recognition Science, the reduced Planck constant ℏ is not a free parameter
 281but is derived from the fundamental ledger structure:
 282
 2831. **Coherence Energy** (E_coh): The minimal energy quantum for recognition events
 284   E_coh = φ⁻⁵ (from self-similar reciprocal closure on the discrete ledger)
 285
 2862. **Fundamental Time** (τ₀): The duration of one recognition tick
 287   τ₀ = 1 tick (the atomic unit of time in RS)
 288
 2893. **Planck's Identity**: ℏ = E_coh · τ₀ = φ⁻⁵ · 1 = φ⁻⁵
 290
 291This derivation has **zero free parameters** — both E_coh and τ₀ are forced
 292by the RS forcing chain (T0-T8).
 293
 294**Physical Interpretation**: ℏ represents the minimal "action" (energy × time)
 295required for a single recognition event in the ledger. The smallness of ℏ
 296(≈ 0.09 in RS-native units, or ~10⁻³⁴ J·s in SI) reflects the fine-grained
 297nature of the recognition substrate.
 298
 299**SI Conversion**: When mapping to SI units, ℏ acquires its familiar value
 300through the calibration length λ_rec:
 301   ℏ_SI = E_coh_SI · τ₀_SI = (φ⁻⁵ · ℏ_base) · (λ_rec/c)

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