Foundation Primitive Recognition Calculus Physical One Act Calibration One Act I

The one-act instrument

A one-act instrument is a formal object in the Recognition Science framework: a positive real number called the unit, a real number called the readout, and two proofs. The first proof says the readout equals the one-act curvature of the unit, a measure of how much the unit deviates from perfect self-consistency. The second proof says the readout equals 1. The framework proves that any such instrument forces its unit to be exactly 1, and that a consistent instrument exists at that canonical unit.

The structure is defined in the machine-checked library of formal theorems as a record with four fields: unit, positive, readout, reads_curvature, and locked_to_one. The positive field is a proof that the unit is greater than 0. The reads_curvature field is a proof that readout equals oneActCurvature unit. The locked_to_one field is a proof that readout equals 1. Together these force unit = 1.

The framework's theorem instrument_forces_canonical_unit states: for any one-act instrument I, I.unit = 1. The proof works by converting the instrument into a normalized interface and then applying the framework's earlier result that a normalized interface forces the canonical cost unit. The headline theorem physical_one_act_calibration_headline bundles three facts: every instrument has unit 1, some instrument exists with unit 1, and the interface conversion preserves the unit.

The canonical instrument is a consistency witness, not a construction of lab hardware. It sets unit := 1, readout := 1, and proves both required identities by direct computation. The framework is explicit that this is not a blueprint for a physical device; it is a formal guarantee that the abstract normalization is coherent.

In Recognition Science, this declaration establishes the bridge between the abstract one-act normalization and a physical calibration datum. The framework models a one-act instrument as exactly the datum needed to produce the normalized interface, and the interface forces the canonical unit. The consequence is that the unit of recognition cost is not free: any instrument that reads out 1 must have unit 1.

/-- The physical one-act instrument forces the canonical cost unit. -/
theorem instrument_forces_canonical_unit (I : OneActInstrument) :
    I.unit = 1 :=
  normalized_interface_forces_J I.toInterface

/-- The canonical instrument exists at the canonical unit. This is a consistency
witness, not a construction of lab hardware. -/
def canonicalInstrument : OneActInstrument where
  unit := 1
  positive := by norm_num
  readout := 1
  reads_curvature := by
    rw [oneActCurvature_eq]
    norm_num
  locked_to_one := rfl

/-- The canonical instrument exists at the canonical unit. This is a consistency
witness, not a construction of lab hardware. -/
def canonicalInstrument : OneActInstrument where
  unit := 1
  positive := by norm_num
  readout := 1
  reads_curvature := by
    rw [oneActCurvature_eq]
    norm_num
  locked_to_one := rfl

What this page does not claim

No physical hardware is constructed or specified. No claim that a real laboratory instrument exists. No claim about the value of any measured physical constant.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Foundation/PrimitiveRecognitionCalculus/PhysicalOneActCalibration.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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