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def definition def or abbrev high

status

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The status definition supplies a static summary string of the Recognition Science native unit conventions. Constant derivations and falsification structures reference it to confirm base assumptions before further work. The body is a direct string literal that concatenates the listed invariants without computation or lemma calls.

claimThe RS-native unit status asserts base units satisfy $τ_0 = ℓ_0 = 1$, speed of light equals 1 in voxel per tick, coherence quantum equals $φ^{-5}$, action quantum equals $ħ = φ^{-5}$, quantities scale as $φ^n$ on the ladder, octave period equals 8 ticks, recovery parameter satisfies $λ_{kin} = π/(4 ln φ)$, and all dimensionless physics is fixed by $φ$ alone.

background

The module establishes a Recognition-Science-native measurement system whose base units are the ledger primitives tick ($τ_0$, one discrete posting interval) and voxel ($ℓ_0$, one causal spatial step). Derived quanta are the coherence quantum $coh = φ^{-5}$ and action quantum $act = ħ = E_{coh} · τ_0$. Key conventions include $c = 1$ in voxel/tick, the $φ$-ladder for scaling masses and energies as $φ^n$, and the eight-tick octave period. Upstream definitions fix tick as the constant 1 and $K$ as $φ^{1/2}$, while the ExternalCalibration structure supplies optional SI mapping factors.

proof idea

The definition is a direct string literal formed by concatenating the status messages for each listed invariant. No tactics or upstream lemmas are applied; the body simply assembles the fixed text.

why it matters in Recognition Science

This declaration functions as an internal checkpoint inside the Constants.RSNativeUnits module and is referenced by downstream results such as c_in_si and the InflationFalsifier structure. It codifies the T7 eight-tick octave and the $φ$-ladder scaling that follow from the forcing chain T0-T8. The summary also anchors the Recognition Composition Law applications by fixing the unit conventions used throughout the framework.

scope and limits

formal statement (Lean)

 338def status : String :=

proof body

Definition body.

 339  "✓ Base units: tick, voxel (τ₀ = ℓ₀ = 1)\n" ++
 340  "✓ Speed of light: c = 1 voxel/tick\n" ++
 341  "✓ Coherence quantum: coh = φ⁻⁵\n" ++
 342  "✓ Action quantum: act = ħ = φ⁻⁵ (in RS-native)\n" ++
 343  "✓ φ-ladder: phiRung n = φⁿ\n" ++
 344  "✓ 8-tick cycle: octavePeriod = 8 ticks\n" ++
 345  "✓ K-gate: tau_rec = lambda_kin = π/(4 ln φ)\n" ++
 346  "✓ External calibration: ExternalCalibration structure\n" ++
 347  "✓ All dimensionless physics fixed by φ"
 348
 349#eval status
 350
 351end RSNativeUnits
 352end Constants
 353end IndisputableMonolith

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depends on (24)

Lean names referenced from this declaration's body.